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php、javascript使用rsa进行加密/解密

时间:2018-10-25 19:23:49      阅读:342      评论:0      收藏:0      [点我收藏+]

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  • 生成密钥:
    a. 生成原始文件:
    openssl  genrsa  -out  rsa_private_key.pem  1024

    b. 转换格式:

    openssl  pkcs8  -topk8  -inform  PEM  -in rsa_private_key.pem  -outform  PEM -nocrypt  -out  private_key.pem

    c. 生成公钥:

    openssl  rsa  -in  rsa_private_key.pem  -pubout  -out  rsa_public_key.pem
  • php:
    a. 代码:
    <?php
    namespace dollarphp;
    /**
    * @desc:php rsa加密解密类
    * @author [Lee] <[<complet@163.com>]>
    */
    class rsa{
    private static $private_key = <<<HH
    -----BEGIN RSA PRIVATE KEY-----
    MIICXQIBAAKBgQDjcuqtaq1rq6XVPqAS9oYh16CAi/woORCyq8FKlpthj/9azU+v
    cXmra7VIlSjwckRoxpK/j0FjeVNf1BAj5XXctqnh5X8BZYiZxYQdfr6U20zu8bjK
    zHLPF4ZbzpAhXd9pYrFSawt5U3RtIw8nq5MDJIlOLupxTx9gWLRCC9gHYwIDAQAB
    AoGAJVi0Mf9nNFu94hLjY9m40ou+Xf0eTVh5Zm0PUvkB0HY9fqJhqDQgv0XzQVTE
    oR6SHwYkCHI0UWoVh5GhiNNfk6vIqlNwwI7gxi5kIhMQbF7x2ghvwGPvfxzUxY4x
    3zq7QnTChpmrFudJrCliosY+FTdoAWxtRDSTm8//74k6eSkCQQD/JZjc6/r42H0j
    JUsy9YFVwnOrZXPYUCRDo34ottFrowUdNdmIjdf7kHkNW6bd05XiyX74MYdnFUVz
    Xfju2uEPAkEA5DWcRVTEiUBYy1Qg/MSwSVL7HPv9AziBSIFwKzogO9ROw+B/hHUx
    845S7r0WKGO7D56IJNcELIKpW3t0vU6MbQJAMeAcmJr8jWZsV9FzeLurE6OWTtvf
    IFrSK/Kqt7S9DUhpuIMNSfdIUCG2uBjBbr1soE95JXUxHcJ3uAyXm8FnmwJBANFl
    N5yOKT/e4RrAePw15aOCFpQDy6Z25HmI+0lOrmD3b8ZfaeI6PrlCMGqK6Zfp2qx8
    RGO5P0UwJwGgB//j4QkCQQDe8Ogu3JJ256Z4NDy/GC3VSZqKxnApTJICScYFt3hQ
    M5/d8kDpkvcugI0ADjjBYs0FpnSiYsyq85GCAFQZsym4
    -----END RSA PRIVATE KEY-----
    HH;
    private static $public_key = <<<HH
    -----BEGIN PUBLIC KEY-----
    MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQDjcuqtaq1rq6XVPqAS9oYh16CA
    i/woORCyq8FKlpthj/9azU+vcXmra7VIlSjwckRoxpK/j0FjeVNf1BAj5XXctqnh
    5X8BZYiZxYQdfr6U20zu8bjKzHLPF4ZbzpAhXd9pYrFSawt5U3RtIw8nq5MDJIlO
    LupxTx9gWLRCC9gHYwIDAQAB
    -----END PUBLIC KEY-----
    HH;
    /**
     * 获取私钥
     * @return bool|resource
     */
    private static function getPrivateKey(){
        $privKey = self::$private_key; 
        return openssl_pkey_get_private($privKey);    }
    /**
     * 获取公钥
     * @return bool|resource
     */
    private static function getPublicKey(){
        $publicKey = self::$public_key;
        return openssl_pkey_get_public($publicKey);
    }
    /**
     * 私钥加密
     * @param string $data
     * @return null|string
     */
    public static function privEncrypt($data = ‘‘){
        if (!is_string($data)) {
            return null;
        }
        return openssl_private_encrypt($data,$encrypted,self::getPrivateKey()) ? base64_encode($encrypted) : null;
    }
    /**
     * 公钥加密
     * @param string $data
     * @return null|string
     */
    public static function publicEncrypt($data = ‘‘){
        if (!is_string($data)) {
            return null;
        }
        return openssl_public_encrypt($data,$encrypted,self::getPublicKey()) ? base64_encode($encrypted) : null;
    }
    /**     
     * 私钥解密
     * @param string $encrypted
     * @return null
     */
    public static function privDecrypt($encrypted = ‘‘){
        if (!is_string($encrypted)) {
            return null;
        }
        return (openssl_private_decrypt(base64_decode($encrypted), $decrypted, self::getPrivateKey())) ? $decrypted : null;
    }
    /**
     * 公钥解密
     * @param string $encrypted
     * @return null
     */
    public static function publicDecrypt($encrypted = ‘‘){
        if (!is_string($encrypted)) {
            return null;
        }
    return (openssl_public_decrypt(base64_decode($encrypted), $decrypted, self::getPublicKey())) ? $decrypted : null;
    }
    }

    b. 测试:

    $rsa = new rsa();
    $str = ‘hello world‘;
    // 私钥加密
    $privEncrypt = $rsa->privEncrypt($str);
    echo $privEncrypt.PHP_EOL.PHP_EOL;
    // 公钥解密
    $publicDecrypt = $rsa->publicDecrypt($privEncrypt);
    echo $publicDecrypt.PHP_EOL.PHP_EOL;
    // 公钥加密
    $publicEncrypt = $rsa->publicEncrypt($str);
    echo $publicEncrypt.PHP_EOL.PHP_EOL;
    // 私钥解密
    $privDecrypt = $rsa->privDecrypt($publicEncrypt);
    echo $privDecrypt.PHP_EOL.PHP_EOL;

    c. 输出:

    wGk8Cyb0eDwjiqRGqoBkVlpNWFAeD8zxqDTrOjpBSyIdqKL3ZyoluiNOzzWmOnqWtHwtGfpKQuUuoeI1ANqsuKct/w1O9/IyiDwrDIkfXijGTz8ofj4eZHBnIlIY1gT9AaDXzR61rRQu0+K3aG4PA+Z2zxhf5mAuN7LbHQlQU5A=
    hello world
    kBYs+bPMLaDbyLultt5UoBhcbJh37exGFvoyr42MfU7/428XFYfOdCeFJDqt16iCByrL+YOe2GgOVuCkxmMD2thOKYjWAkfZI+gnfVu8w2nQoXAFSfejwFvhnIMBd/IFTJoQs7jJG5ELEwCYVjDI10nzXOtYPlDa+szzambMuMs=
    hello world
    [Finished in 0.7s]

    技术分享图片

  • javascript:
    a. 代码:
    rsa.js
    /*
    @desc:rsa加密/解密类
    @author lee <complet@163.com>
    */
    function rsa() {
    var obj = {}
    ‘use strict‘;
    var BI_RM = "0123456789abcdefghijklmnopqrstuvwxyz";
    function int2char(n) {
        return BI_RM.charAt(n);
    }
    //#region BIT_OPERATIONS
    // (public) this & a
    function op_and(x, y) {
        return x & y;
    }
    // (public) this | a
    function op_or(x, y) {
        return x | y;
    }
    // (public) this ^ a
    function op_xor(x, y) {
        return x ^ y;
    }
    // (public) this & ~a
    function op_andnot(x, y) {
        return x & ~y;
    }
    // return index of lowest 1-bit in x, x < 2^31
    function lbit(x) {
        if (x == 0) {
            return -1;
        }
        var r = 0;
        if ((x & 0xffff) == 0) {
            x >>= 16;
            r += 16;
        }
        if ((x & 0xff) == 0) {
            x >>= 8;
            r += 8;
        }
        if ((x & 0xf) == 0) {
            x >>= 4;
            r += 4;
        }
        if ((x & 3) == 0) {
            x >>= 2;
            r += 2;
        }
        if ((x & 1) == 0) {
            ++r;
        }
        return r;
    }
    // return number of 1 bits in x
    function cbit(x) {
        var r = 0;
        while (x != 0) {
            x &= x - 1;
            ++r;
        }
        return r;
    }
    //#endregion BIT_OPERATIONS
    var b64map = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
    var b64pad = "=";
    function hex2b64(h) {
        var i;
        var c;
        var ret = "";
        for (i = 0; i + 3 <= h.length; i += 3) {
            c = parseInt(h.substring(i, i + 3), 16);
            ret += b64map.charAt(c >> 6) + b64map.charAt(c & 63);
        }
        if (i + 1 == h.length) {
            c = parseInt(h.substring(i, i + 1), 16);
            ret += b64map.charAt(c << 2);
        }
        else if (i + 2 == h.length) {
            c = parseInt(h.substring(i, i + 2), 16);
            ret += b64map.charAt(c >> 2) + b64map.charAt((c & 3) << 4);
        }
        while ((ret.length & 3) > 0) {
            ret += b64pad;
        }
        return ret;
    }
    // convert a base64 string to hex
    function b64tohex(s) {
        var ret = "";
        var i;
        var k = 0; // b64 state, 0-3
        var slop = 0;
        for (i = 0; i < s.length; ++i) {
            if (s.charAt(i) == b64pad) {
                break;
            }
            var v = b64map.indexOf(s.charAt(i));
            if (v < 0) {
                continue;
            }
            if (k == 0) {
                ret += int2char(v >> 2);
                slop = v & 3;
                k = 1;
            }
            else if (k == 1) {
                ret += int2char((slop << 2) | (v >> 4));
                slop = v & 0xf;
                k = 2;
            }
            else if (k == 2) {
                ret += int2char(slop);
                ret += int2char(v >> 2);
                slop = v & 3;
                k = 3;
            }
            else {
                ret += int2char((slop << 2) | (v >> 4));
                ret += int2char(v & 0xf);
                k = 0;
            }
        }
        if (k == 1) {
            ret += int2char(slop << 2);
        }
        return ret;
    }
    /*! *****************************************************************************
    Copyright (c) Microsoft Corporation. All rights reserved.
    Licensed under the Apache License, Version 2.0 (the "License"); you may not use
    this file except in compliance with the License. You may obtain a copy of the
    License at http://www.apache.org/licenses/LICENSE-2.0
    THIS CODE IS PROVIDED ON AN *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
    KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
    WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
    MERCHANTABLITY OR NON-INFRINGEMENT.
    See the Apache Version 2.0 License for specific language governing permissions
    and limitations under the License.
    ***************************************************************************** */
    /* global Reflect, Promise */
    var extendStatics = function(d, b) {
        extendStatics = Object.setPrototypeOf ||
            ({ __proto__: [] } instanceof Array && function (d, b) { d.__proto__ = b; }) ||
            function (d, b) { for (var p in b) if (b.hasOwnProperty(p)) d[p] = b[p]; };
        return extendStatics(d, b);
    };
    function __extends(d, b) {
        extendStatics(d, b);
        function __() { this.constructor = d; }
        d.prototype = b === null ? Object.create(b) : (__.prototype = b.prototype, new __());
    }
    // Hex JavaScript decoder
    // Copyright (c) 2008-2013 Lapo Luchini <lapo@lapo.it>
    // Permission to use, copy, modify, and/or distribute this software for any
    // purpose with or without fee is hereby granted, provided that the above
    // copyright notice and this permission notice appear in all copies.
    //
    // THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
    // WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    // MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
    // ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    // WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
    // ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
    // OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
    /*jshint browser: true, strict: true, immed: true, latedef: true, undef: true, regexdash: false */
    var decoder;
    var Hex = {
        decode: function (a) {
            var i;
            if (decoder === undefined) {
                var hex = "0123456789ABCDEF";
                var ignore = " \f\n\r\t\u00A0\u2028\u2029";
                decoder = {};
                for (i = 0; i < 16; ++i) {
                    decoder[hex.charAt(i)] = i;
                }
                hex = hex.toLowerCase();
                for (i = 10; i < 16; ++i) {
                    decoder[hex.charAt(i)] = i;
                }
                for (i = 0; i < ignore.length; ++i) {
                    decoder[ignore.charAt(i)] = -1;
                }
            }
            var out = [];
            var bits = 0;
            var char_count = 0;
            for (i = 0; i < a.length; ++i) {
                var c = a.charAt(i);
                if (c == "=") {
                    break;
                }
                c = decoder[c];
                if (c == -1) {
                    continue;
                }
                if (c === undefined) {
                    throw new Error("Illegal character at offset " + i);
                }
                bits |= c;
                if (++char_count >= 2) {
                    out[out.length] = bits;
                    bits = 0;
                    char_count = 0;
                }
                else {
                    bits <<= 4;
                }
            }
            if (char_count) {
                throw new Error("Hex encoding incomplete: 4 bits missing");
            }
            return out;
        }
    };
    // Base64 JavaScript decoder
    // Copyright (c) 2008-2013 Lapo Luchini <lapo@lapo.it>
    // Permission to use, copy, modify, and/or distribute this software for any
    // purpose with or without fee is hereby granted, provided that the above
    // copyright notice and this permission notice appear in all copies.
    //
    // THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
    // WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    // MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
    // ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    // WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
    // ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
    // OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
    /*jshint browser: true, strict: true, immed: true, latedef: true, undef: true, regexdash: false */
    var decoder$1;
    var Base64 = {
        decode: function (a) {
            var i;
            if (decoder$1 === undefined) {
                var b64 = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
                var ignore = "= \f\n\r\t\u00A0\u2028\u2029";
                decoder$1 = Object.create(null);
                for (i = 0; i < 64; ++i) {
                    decoder$1[b64.charAt(i)] = i;
                }
                for (i = 0; i < ignore.length; ++i) {
                    decoder$1[ignore.charAt(i)] = -1;
                }
            }
            var out = [];
            var bits = 0;
            var char_count = 0;
            for (i = 0; i < a.length; ++i) {
                var c = a.charAt(i);
                if (c == "=") {
                    break;
                }
                c = decoder$1[c];
                if (c == -1) {
                    continue;
                }
                if (c === undefined) {
                    throw new Error("Illegal character at offset " + i);
                }
                bits |= c;
                if (++char_count >= 4) {
                    out[out.length] = (bits >> 16);
                    out[out.length] = (bits >> 8) & 0xFF;
                    out[out.length] = bits & 0xFF;
                    bits = 0;
                    char_count = 0;
                }
                else {
                    bits <<= 6;
                }
            }
            switch (char_count) {
                case 1:
                    throw new Error("Base64 encoding incomplete: at least 2 bits missing");
                case 2:
                    out[out.length] = (bits >> 10);
                    break;
                case 3:
                    out[out.length] = (bits >> 16);
                    out[out.length] = (bits >> 8) & 0xFF;
                    break;
            }
            return out;
        },
        re: /-----BEGIN [^-]+-----([A-Za-z0-9+\/=\s]+)-----END [^-]+-----|begin-base64[^\n]+\n([A-Za-z0-9+\/=\s]+)====/,
        unarmor: function (a) {
            var m = Base64.re.exec(a);
            if (m) {
                if (m[1]) {
                    a = m[1];
                }
                else if (m[2]) {
                    a = m[2];
                }
                else {
                    throw new Error("RegExp out of sync");
                }
            }
            return Base64.decode(a);
        }
    };
    // Big integer base-10 printing library
    // Copyright (c) 2014 Lapo Luchini <lapo@lapo.it>
    // Permission to use, copy, modify, and/or distribute this software for any
    // purpose with or without fee is hereby granted, provided that the above
    // copyright notice and this permission notice appear in all copies.
    //
    // THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
    // WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    // MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
    // ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    // WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
    // ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
    // OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
    /*jshint browser: true, strict: true, immed: true, latedef: true, undef: true, regexdash: false */
    var max = 10000000000000; // biggest integer that can still fit 2^53 when multiplied by 256
    var Int10 = /** @class */ (function () {
        function Int10(value) {
            this.buf = [+value || 0];
        }
        Int10.prototype.mulAdd = function (m, c) {
            // assert(m <= 256)
            var b = this.buf;
            var l = b.length;
            var i;
            var t;
            for (i = 0; i < l; ++i) {
                t = b[i] * m + c;
                if (t < max) {
                    c = 0;
                }
                else {
                    c = 0 | (t / max);
                    t -= c * max;
                }
                b[i] = t;
            }
            if (c > 0) {
                b[i] = c;
            }
        };
        Int10.prototype.sub = function (c) {
            // assert(m <= 256)
            var b = this.buf;
            var l = b.length;
            var i;
            var t;
            for (i = 0; i < l; ++i) {
                t = b[i] - c;
                if (t < 0) {
                    t += max;
                    c = 1;
                }
                else {
                    c = 0;
                }
                b[i] = t;
            }
            while (b[b.length - 1] === 0) {
                b.pop();
            }
        };
        Int10.prototype.toString = function (base) {
            if ((base || 10) != 10) {
                throw new Error("only base 10 is supported");
            }
            var b = this.buf;
            var s = b[b.length - 1].toString();
            for (var i = b.length - 2; i >= 0; --i) {
                s += (max + b[i]).toString().substring(1);
            }
            return s;
        };
        Int10.prototype.valueOf = function () {
            var b = this.buf;
            var v = 0;
            for (var i = b.length - 1; i >= 0; --i) {
                v = v * max + b[i];
            }
            return v;
        };
        Int10.prototype.simplify = function () {
            var b = this.buf;
            return (b.length == 1) ? b[0] : this;
        };
        return Int10;
    }());
    // ASN.1 JavaScript decoder
    var ellipsis = "\u2026";
    var reTimeS = /^(\d\d)(0[1-9]|1[0-2])(0[1-9]|[12]\d|3[01])([01]\d|2[0-3])(?:([0-5]\d)(?:([0-5]\d)(?:[.,](\d{1,3}))?)?)?(Z|[-+](?:[0]\d|1[0-2])([0-5]\d)?)?$/;
    var reTimeL = /^(\d\d\d\d)(0[1-9]|1[0-2])(0[1-9]|[12]\d|3[01])([01]\d|2[0-3])(?:([0-5]\d)(?:([0-5]\d)(?:[.,](\d{1,3}))?)?)?(Z|[-+](?:[0]\d|1[0-2])([0-5]\d)?)?$/;
    function stringCut(str, len) {
        if (str.length > len) {
            str = str.substring(0, len) + ellipsis;
        }
        return str;
    }
    var Stream = /** @class */ (function () {
        function Stream(enc, pos) {
            this.hexDigits = "0123456789ABCDEF";
            if (enc instanceof Stream) {
                this.enc = enc.enc;
                this.pos = enc.pos;
            }
            else {
                // enc should be an array or a binary string
                this.enc = enc;
                this.pos = pos;
            }
        }
        Stream.prototype.get = function (pos) {
            if (pos === undefined) {
                pos = this.pos++;
            }
            if (pos >= this.enc.length) {
                throw new Error("Requesting byte offset " + pos + " on a stream of length " + this.enc.length);
            }
            return ("string" === typeof this.enc) ? this.enc.charCodeAt(pos) : this.enc[pos];
        };
        Stream.prototype.hexByte = function (b) {
            return this.hexDigits.charAt((b >> 4) & 0xF) + this.hexDigits.charAt(b & 0xF);
        };
        Stream.prototype.hexDump = function (start, end, raw) {
            var s = "";
            for (var i = start; i < end; ++i) {
                s += this.hexByte(this.get(i));
                if (raw !== true) {
                    switch (i & 0xF) {
                        case 0x7:
                            s += "  ";
                            break;
                        case 0xF:
                            s += "\n";
                            break;
                        default:
                            s += " ";
                    }
                }
            }
            return s;
        };
        Stream.prototype.isASCII = function (start, end) {
            for (var i = start; i < end; ++i) {
                var c = this.get(i);
                if (c < 32 || c > 176) {
                    return false;
                }
            }
            return true;
        };
        Stream.prototype.parseStringISO = function (start, end) {
            var s = "";
            for (var i = start; i < end; ++i) {
                s += String.fromCharCode(this.get(i));
            }
            return s;
        };
        Stream.prototype.parseStringUTF = function (start, end) {
            var s = "";
            for (var i = start; i < end;) {
                var c = this.get(i++);
                if (c < 128) {
                    s += String.fromCharCode(c);
                }
                else if ((c > 191) && (c < 224)) {
                    s += String.fromCharCode(((c & 0x1F) << 6) | (this.get(i++) & 0x3F));
                }
                else {
                    s += String.fromCharCode(((c & 0x0F) << 12) | ((this.get(i++) & 0x3F) << 6) | (this.get(i++) & 0x3F));
                }
            }
            return s;
        };
        Stream.prototype.parseStringBMP = function (start, end) {
            var str = "";
            var hi;
            var lo;
            for (var i = start; i < end;) {
                hi = this.get(i++);
                lo = this.get(i++);
                str += String.fromCharCode((hi << 8) | lo);
            }
            return str;
        };
        Stream.prototype.parseTime = function (start, end, shortYear) {
            var s = this.parseStringISO(start, end);
            var m = (shortYear ? reTimeS : reTimeL).exec(s);
            if (!m) {
                return "Unrecognized time: " + s;
            }
            if (shortYear) {
                // to avoid querying the timer, use the fixed range [1970, 2069]
                // it will conform with ITU X.400 [-10, +40] sliding window until 2030
                m[1] = +m[1];
                m[1] += (+m[1] < 70) ? 2000 : 1900;
            }
            s = m[1] + "-" + m[2] + "-" + m[3] + " " + m[4];
            if (m[5]) {
                s += ":" + m[5];
                if (m[6]) {
                    s += ":" + m[6];
                    if (m[7]) {
                        s += "." + m[7];
                    }
                }
            }
            if (m[8]) {
                s += " UTC";
                if (m[8] != "Z") {
                    s += m[8];
                    if (m[9]) {
                        s += ":" + m[9];
                    }
                }
            }
            return s;
        };
        Stream.prototype.parseInteger = function (start, end) {
            var v = this.get(start);
            var neg = (v > 127);
            var pad = neg ? 255 : 0;
            var len;
            var s = "";
            // skip unuseful bits (not allowed in DER)
            while (v == pad && ++start < end) {
                v = this.get(start);
            }
            len = end - start;
            if (len === 0) {
                return neg ? -1 : 0;
            }
            // show bit length of huge integers
            if (len > 4) {
                s = v;
                len <<= 3;
                while (((+s ^ pad) & 0x80) == 0) {
                    s = +s << 1;
                    --len;
                }
                s = "(" + len + " bit)\n";
            }
            // decode the integer
            if (neg) {
                v = v - 256;
            }
            var n = new Int10(v);
            for (var i = start + 1; i < end; ++i) {
                n.mulAdd(256, this.get(i));
            }
            return s + n.toString();
        };
        Stream.prototype.parseBitString = function (start, end, maxLength) {
            var unusedBit = this.get(start);
            var lenBit = ((end - start - 1) << 3) - unusedBit;
            var intro = "(" + lenBit + " bit)\n";
            var s = "";
            for (var i = start + 1; i < end; ++i) {
                var b = this.get(i);
                var skip = (i == end - 1) ? unusedBit : 0;
                for (var j = 7; j >= skip; --j) {
                    s += (b >> j) & 1 ? "1" : "0";
                }
                if (s.length > maxLength) {
                    return intro + stringCut(s, maxLength);
                }
            }
            return intro + s;
        };
        Stream.prototype.parseOctetString = function (start, end, maxLength) {
            if (this.isASCII(start, end)) {
                return stringCut(this.parseStringISO(start, end), maxLength);
            }
            var len = end - start;
            var s = "(" + len + " byte)\n";
            maxLength /= 2; // we work in bytes
            if (len > maxLength) {
                end = start + maxLength;
            }
            for (var i = start; i < end; ++i) {
                s += this.hexByte(this.get(i));
            }
            if (len > maxLength) {
                s += ellipsis;
            }
            return s;
        };
        Stream.prototype.parseOID = function (start, end, maxLength) {
            var s = "";
            var n = new Int10();
            var bits = 0;
            for (var i = start; i < end; ++i) {
                var v = this.get(i);
                n.mulAdd(128, v & 0x7F);
                bits += 7;
                if (!(v & 0x80)) { // finished
                    if (s === "") {
                        n = n.simplify();
                        if (n instanceof Int10) {
                            n.sub(80);
                            s = "2." + n.toString();
                        }
                        else {
                            var m = n < 80 ? n < 40 ? 0 : 1 : 2;
                            s = m + "." + (n - m * 40);
                        }
                    }
                    else {
                        s += "." + n.toString();
                    }
                    if (s.length > maxLength) {
                        return stringCut(s, maxLength);
                    }
                    n = new Int10();
                    bits = 0;
                }
            }
            if (bits > 0) {
                s += ".incomplete";
            }
            return s;
        };
        return Stream;
    }());
    var ASN1 = /** @class */ (function () {
        function ASN1(stream, header, length, tag, sub) {
            if (!(tag instanceof ASN1Tag)) {
                throw new Error("Invalid tag value.");
            }
            this.stream = stream;
            this.header = header;
            this.length = length;
            this.tag = tag;
            this.sub = sub;
        }
        ASN1.prototype.typeName = function () {
            switch (this.tag.tagClass) {
                case 0: // universal
                    switch (this.tag.tagNumber) {
                        case 0x00:
                            return "EOC";
                        case 0x01:
                            return "BOOLEAN";
                        case 0x02:
                            return "INTEGER";
                        case 0x03:
                            return "BIT_STRING";
                        case 0x04:
                            return "OCTET_STRING";
                        case 0x05:
                            return "NULL";
                        case 0x06:
                            return "OBJECT_IDENTIFIER";
                        case 0x07:
                            return "ObjectDescriptor";
                        case 0x08:
                            return "EXTERNAL";
                        case 0x09:
                            return "REAL";
                        case 0x0A:
                            return "ENUMERATED";
                        case 0x0B:
                            return "EMBEDDED_PDV";
                        case 0x0C:
                            return "UTF8String";
                        case 0x10:
                            return "SEQUENCE";
                        case 0x11:
                            return "SET";
                        case 0x12:
                            return "NumericString";
                        case 0x13:
                            return "PrintableString"; // ASCII subset
                        case 0x14:
                            return "TeletexString"; // aka T61String
                        case 0x15:
                            return "VideotexString";
                        case 0x16:
                            return "IA5String"; // ASCII
                        case 0x17:
                            return "UTCTime";
                        case 0x18:
                            return "GeneralizedTime";
                        case 0x19:
                            return "GraphicString";
                        case 0x1A:
                            return "VisibleString"; // ASCII subset
                        case 0x1B:
                            return "GeneralString";
                        case 0x1C:
                            return "UniversalString";
                        case 0x1E:
                            return "BMPString";
                    }
                    return "Universal_" + this.tag.tagNumber.toString();
                case 1:
                    return "Application_" + this.tag.tagNumber.toString();
                case 2:
                    return "[" + this.tag.tagNumber.toString() + "]"; // Context
                case 3:
                    return "Private_" + this.tag.tagNumber.toString();
            }
        };
        ASN1.prototype.content = function (maxLength) {
            if (this.tag === undefined) {
                return null;
            }
            if (maxLength === undefined) {
                maxLength = Infinity;
            }
            var content = this.posContent();
            var len = Math.abs(this.length);
            if (!this.tag.isUniversal()) {
                if (this.sub !== null) {
                    return "(" + this.sub.length + " elem)";
                }
                return this.stream.parseOctetString(content, content + len, maxLength);
            }
            switch (this.tag.tagNumber) {
                case 0x01: // BOOLEAN
                    return (this.stream.get(content) === 0) ? "false" : "true";
                case 0x02: // INTEGER
                    return this.stream.parseInteger(content, content + len);
                case 0x03: // BIT_STRING
                    return this.sub ? "(" + this.sub.length + " elem)" :
                        this.stream.parseBitString(content, content + len, maxLength);
                case 0x04: // OCTET_STRING
                    return this.sub ? "(" + this.sub.length + " elem)" :
                        this.stream.parseOctetString(content, content + len, maxLength);
                // case 0x05: // NULL
                case 0x06: // OBJECT_IDENTIFIER
                    return this.stream.parseOID(content, content + len, maxLength);
                // case 0x07: // ObjectDescriptor
                // case 0x08: // EXTERNAL
                // case 0x09: // REAL
                // case 0x0A: // ENUMERATED
                // case 0x0B: // EMBEDDED_PDV
                case 0x10: // SEQUENCE
                case 0x11: // SET
                    if (this.sub !== null) {
                        return "(" + this.sub.length + " elem)";
                    }
                    else {
                        return "(no elem)";
                    }
                case 0x0C: // UTF8String
                    return stringCut(this.stream.parseStringUTF(content, content + len), maxLength);
                case 0x12: // NumericString
                case 0x13: // PrintableString
                case 0x14: // TeletexString
                case 0x15: // VideotexString
                case 0x16: // IA5String
                // case 0x19: // GraphicString
                case 0x1A: // VisibleString
                    // case 0x1B: // GeneralString
                    // case 0x1C: // UniversalString
                    return stringCut(this.stream.parseStringISO(content, content + len), maxLength);
                case 0x1E: // BMPString
                    return stringCut(this.stream.parseStringBMP(content, content + len), maxLength);
                case 0x17: // UTCTime
                case 0x18: // GeneralizedTime
                    return this.stream.parseTime(content, content + len, (this.tag.tagNumber == 0x17));
            }
            return null;
        };
        ASN1.prototype.toString = function () {
            return this.typeName() + "@" + this.stream.pos + "[header:" + this.header + ",length:" + this.length + ",sub:" + ((this.sub === null) ? "null" : this.sub.length) + "]";
        };
        ASN1.prototype.toPrettyString = function (indent) {
            if (indent === undefined) {
                indent = "";
            }
            var s = indent + this.typeName() + " @" + this.stream.pos;
            if (this.length >= 0) {
                s += "+";
            }
            s += this.length;
            if (this.tag.tagConstructed) {
                s += " (constructed)";
            }
            else if ((this.tag.isUniversal() && ((this.tag.tagNumber == 0x03) || (this.tag.tagNumber == 0x04))) && (this.sub !== null)) {
                s += " (encapsulates)";
            }
            s += "\n";
            if (this.sub !== null) {
                indent += "  ";
                for (var i = 0, max = this.sub.length; i < max; ++i) {
                    s += this.sub[i].toPrettyString(indent);
                }
            }
            return s;
        };
        ASN1.prototype.posStart = function () {
            return this.stream.pos;
        };
        ASN1.prototype.posContent = function () {
            return this.stream.pos + this.header;
        };
        ASN1.prototype.posEnd = function () {
            return this.stream.pos + this.header + Math.abs(this.length);
        };
        ASN1.prototype.toHexString = function () {
            return this.stream.hexDump(this.posStart(), this.posEnd(), true);
        };
        ASN1.decodeLength = function (stream) {
            var buf = stream.get();
            var len = buf & 0x7F;
            if (len == buf) {
                return len;
            }
            // no reason to use Int10, as it would be a huge buffer anyways
            if (len > 6) {
                throw new Error("Length over 48 bits not supported at position " + (stream.pos - 1));
            }
            if (len === 0) {
                return null;
            } // undefined
            buf = 0;
            for (var i = 0; i < len; ++i) {
                buf = (buf * 256) + stream.get();
            }
            return buf;
        };
        /**
         * Retrieve the hexadecimal value (as a string) of the current ASN.1 element
         * @returns {string}
         * @public
         */
        ASN1.prototype.getHexStringValue = function () {
            var hexString = this.toHexString();
            var offset = this.header * 2;
            var length = this.length * 2;
            return hexString.substr(offset, length);
        };
        ASN1.decode = function (str) {
            var stream;
            if (!(str instanceof Stream)) {
                stream = new Stream(str, 0);
            }
            else {
                stream = str;
            }
            var streamStart = new Stream(stream);
            var tag = new ASN1Tag(stream);
            var len = ASN1.decodeLength(stream);
            var start = stream.pos;
            var header = start - streamStart.pos;
            var sub = null;
            var getSub = function () {
                var ret = [];
                if (len !== null) {
                    // definite length
                    var end = start + len;
                    while (stream.pos < end) {
                        ret[ret.length] = ASN1.decode(stream);
                    }
                    if (stream.pos != end) {
                        throw new Error("Content size is not correct for container starting at offset " + start);
                    }
                }
                else {
                    // undefined length
                    try {
                        for (;;) {
                            var s = ASN1.decode(stream);
                            if (s.tag.isEOC()) {
                                break;
                            }
                            ret[ret.length] = s;
                        }
                        len = start - stream.pos; // undefined lengths are represented as negative values
                    }
                    catch (e) {
                        throw new Error("Exception while decoding undefined length content: " + e);
                    }
                }
                return ret;
            };
            if (tag.tagConstructed) {
                // must have valid content
                sub = getSub();
            }
            else if (tag.isUniversal() && ((tag.tagNumber == 0x03) || (tag.tagNumber == 0x04))) {
                // sometimes BitString and OctetString are used to encapsulate ASN.1
                try {
                    if (tag.tagNumber == 0x03) {
                        if (stream.get() != 0) {
                            throw new Error("BIT STRINGs with unused bits cannot encapsulate.");
                        }
                    }
                    sub = getSub();
                    for (var i = 0; i < sub.length; ++i) {
                        if (sub[i].tag.isEOC()) {
                            throw new Error("EOC is not supposed to be actual content.");
                        }
                    }
                }
                catch (e) {
                    // but silently ignore when they don‘t
                    sub = null;
                }
            }
            if (sub === null) {
                if (len === null) {
                    throw new Error("We can‘t skip over an invalid tag with undefined length at offset " + start);
                }
                stream.pos = start + Math.abs(len);
            }
            return new ASN1(streamStart, header, len, tag, sub);
        };
        return ASN1;
    }());
    var ASN1Tag = /** @class */ (function () {
        function ASN1Tag(stream) {
            var buf = stream.get();
            this.tagClass = buf >> 6;
            this.tagConstructed = ((buf & 0x20) !== 0);
            this.tagNumber = buf & 0x1F;
            if (this.tagNumber == 0x1F) { // long tag
                var n = new Int10();
                do {
                    buf = stream.get();
                    n.mulAdd(128, buf & 0x7F);
                } while (buf & 0x80);
                this.tagNumber = n.simplify();
            }
        }
        ASN1Tag.prototype.isUniversal = function () {
            return this.tagClass === 0x00;
        };
        ASN1Tag.prototype.isEOC = function () {
            return this.tagClass === 0x00 && this.tagNumber === 0x00;
        };
        return ASN1Tag;
    }());
    // Copyright (c) 2005  Tom Wu
    // Bits per digit
    var dbits;
    // JavaScript engine analysis
    var canary = 0xdeadbeefcafe;
    var j_lm = ((canary & 0xffffff) == 0xefcafe);
    //#region
    var lowprimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997];
    var lplim = (1 << 26) / lowprimes[lowprimes.length - 1];
    //#endregion
    // (public) Constructor
    var BigInteger = /** @class */ (function () {
        function BigInteger(a, b, c) {
            if (a != null) {
                if ("number" == typeof a) {
                    this.fromNumber(a, b, c);
                }
                else if (b == null && "string" != typeof a) {
                    this.fromString(a, 256);
                }
                else {
                    this.fromString(a, b);
                }
            }
        }
        //#region PUBLIC
        // BigInteger.prototype.toString = bnToString;
        // (public) return string representation in given radix
        BigInteger.prototype.toString = function (b) {
            if (this.s < 0) {
                return "-" + this.negate().toString(b);
            }
            var k;
            if (b == 16) {
                k = 4;
            }
            else if (b == 8) {
                k = 3;
            }
            else if (b == 2) {
                k = 1;
            }
            else if (b == 32) {
                k = 5;
            }
            else if (b == 4) {
                k = 2;
            }
            else {
                return this.toRadix(b);
            }
            var km = (1 << k) - 1;
            var d;
            var m = false;
            var r = "";
            var i = this.t;
            var p = this.DB - (i * this.DB) % k;
            if (i-- > 0) {
                if (p < this.DB && (d = this[i] >> p) > 0) {
                    m = true;
                    r = int2char(d);
                }
                while (i >= 0) {
                    if (p < k) {
                        d = (this[i] & ((1 << p) - 1)) << (k - p);
                        d |= this[--i] >> (p += this.DB - k);
                    }
                    else {
                        d = (this[i] >> (p -= k)) & km;
                        if (p <= 0) {
                            p += this.DB;
                            --i;
                        }
                    }
                    if (d > 0) {
                        m = true;
                    }
                    if (m) {
                        r += int2char(d);
                    }
                }
            }
            return m ? r : "0";
        };
        // BigInteger.prototype.negate = bnNegate;
        // (public) -this
        BigInteger.prototype.negate = function () {
            var r = nbi();
            BigInteger.ZERO.subTo(this, r);
            return r;
        };
        // BigInteger.prototype.abs = bnAbs;
        // (public) |this|
        BigInteger.prototype.abs = function () {
            return (this.s < 0) ? this.negate() : this;
        };
        // BigInteger.prototype.compareTo = bnCompareTo;
        // (public) return + if this > a, - if this < a, 0 if equal
        BigInteger.prototype.compareTo = function (a) {
            var r = this.s - a.s;
            if (r != 0) {
                return r;
            }
            var i = this.t;
            r = i - a.t;
            if (r != 0) {
                return (this.s < 0) ? -r : r;
            }
            while (--i >= 0) {
                if ((r = this[i] - a[i]) != 0) {
                    return r;
                }
            }
            return 0;
        };
        // BigInteger.prototype.bitLength = bnBitLength;
        // (public) return the number of bits in "this"
        BigInteger.prototype.bitLength = function () {
            if (this.t <= 0) {
                return 0;
            }
            return this.DB * (this.t - 1) + nbits(this[this.t - 1] ^ (this.s & this.DM));
        };
        // BigInteger.prototype.mod = bnMod;
        // (public) this mod a
        BigInteger.prototype.mod = function (a) {
            var r = nbi();
            this.abs().divRemTo(a, null, r);
            if (this.s < 0 && r.compareTo(BigInteger.ZERO) > 0) {
                a.subTo(r, r);
            }
            return r;
        };
        // BigInteger.prototype.modPowInt = bnModPowInt;
        // (public) this^e % m, 0 <= e < 2^32
        BigInteger.prototype.modPowInt = function (e, m) {
            var z;
            if (e < 256 || m.isEven()) {
                z = new Classic(m);
            }
            else {
                z = new Montgomery(m);
            }
            return this.exp(e, z);
        };
        // BigInteger.prototype.clone = bnClone;
        // (public)
        BigInteger.prototype.clone = function () {
            var r = nbi();
            this.copyTo(r);
            return r;
        };
        // BigInteger.prototype.intValue = bnIntValue;
        // (public) return value as integer
        BigInteger.prototype.intValue = function () {
            if (this.s < 0) {
                if (this.t == 1) {
                    return this[0] - this.DV;
                }
                else if (this.t == 0) {
                    return -1;
                }
            }
            else if (this.t == 1) {
                return this[0];
            }
            else if (this.t == 0) {
                return 0;
            }
            // assumes 16 < DB < 32
            return ((this[1] & ((1 << (32 - this.DB)) - 1)) << this.DB) | this[0];
        };
        // BigInteger.prototype.byteValue = bnByteValue;
        // (public) return value as byte
        BigInteger.prototype.byteValue = function () {
            return (this.t == 0) ? this.s : (this[0] << 24) >> 24;
        };
        // BigInteger.prototype.shortValue = bnShortValue;
        // (public) return value as short (assumes DB>=16)
        BigInteger.prototype.shortValue = function () {
            return (this.t == 0) ? this.s : (this[0] << 16) >> 16;
        };
        // BigInteger.prototype.signum = bnSigNum;
        // (public) 0 if this == 0, 1 if this > 0
        BigInteger.prototype.signum = function () {
            if (this.s < 0) {
                return -1;
            }
            else if (this.t <= 0 || (this.t == 1 && this[0] <= 0)) {
                return 0;
            }
            else {
                return 1;
            }
        };
        // BigInteger.prototype.toByteArray = bnToByteArray;
        // (public) convert to bigendian byte array
        BigInteger.prototype.toByteArray = function () {
            var i = this.t;
            var r = [];
            r[0] = this.s;
            var p = this.DB - (i * this.DB) % 8;
            var d;
            var k = 0;
            if (i-- > 0) {
                if (p < this.DB && (d = this[i] >> p) != (this.s & this.DM) >> p) {
                    r[k++] = d | (this.s << (this.DB - p));
                }
                while (i >= 0) {
                    if (p < 8) {
                        d = (this[i] & ((1 << p) - 1)) << (8 - p);
                        d |= this[--i] >> (p += this.DB - 8);
                    }
                    else {
                        d = (this[i] >> (p -= 8)) & 0xff;
                        if (p <= 0) {
                            p += this.DB;
                            --i;
                        }
                    }
                    if ((d & 0x80) != 0) {
                        d |= -256;
                    }
                    if (k == 0 && (this.s & 0x80) != (d & 0x80)) {
                        ++k;
                    }
                    if (k > 0 || d != this.s) {
                        r[k++] = d;
                    }
                }
            }
            return r;
        };
        // BigInteger.prototype.equals = bnEquals;
        BigInteger.prototype.equals = function (a) {
            return (this.compareTo(a) == 0);
        };
        // BigInteger.prototype.min = bnMin;
        BigInteger.prototype.min = function (a) {
            return (this.compareTo(a) < 0) ? this : a;
        };
        // BigInteger.prototype.max = bnMax;
        BigInteger.prototype.max = function (a) {
            return (this.compareTo(a) > 0) ? this : a;
        };
        // BigInteger.prototype.and = bnAnd;
        BigInteger.prototype.and = function (a) {
            var r = nbi();
            this.bitwiseTo(a, op_and, r);
            return r;
        };
        // BigInteger.prototype.or = bnOr;
        BigInteger.prototype.or = function (a) {
            var r = nbi();
            this.bitwiseTo(a, op_or, r);
            return r;
        };
        // BigInteger.prototype.xor = bnXor;
        BigInteger.prototype.xor = function (a) {
            var r = nbi();
            this.bitwiseTo(a, op_xor, r);
            return r;
        };
        // BigInteger.prototype.andNot = bnAndNot;
        BigInteger.prototype.andNot = function (a) {
            var r = nbi();
            this.bitwiseTo(a, op_andnot, r);
            return r;
        };
        // BigInteger.prototype.not = bnNot;
        // (public) ~this
        BigInteger.prototype.not = function () {
            var r = nbi();
            for (var i = 0; i < this.t; ++i) {
                r[i] = this.DM & ~this[i];
            }
            r.t = this.t;
            r.s = ~this.s;
            return r;
        };
        // BigInteger.prototype.shiftLeft = bnShiftLeft;
        // (public) this << n
        BigInteger.prototype.shiftLeft = function (n) {
            var r = nbi();
            if (n < 0) {
                this.rShiftTo(-n, r);
            }
            else {
                this.lShiftTo(n, r);
            }
            return r;
        };
        // BigInteger.prototype.shiftRight = bnShiftRight;
        // (public) this >> n
        BigInteger.prototype.shiftRight = function (n) {
            var r = nbi();
            if (n < 0) {
                this.lShiftTo(-n, r);
            }
            else {
                this.rShiftTo(n, r);
            }
            return r;
        };
        // BigInteger.prototype.getLowestSetBit = bnGetLowestSetBit;
        // (public) returns index of lowest 1-bit (or -1 if none)
        BigInteger.prototype.getLowestSetBit = function () {
            for (var i = 0; i < this.t; ++i) {
                if (this[i] != 0) {
                    return i * this.DB + lbit(this[i]);
                }
            }
            if (this.s < 0) {
                return this.t * this.DB;
            }
            return -1;
        };
        // BigInteger.prototype.bitCount = bnBitCount;
        // (public) return number of set bits
        BigInteger.prototype.bitCount = function () {
            var r = 0;
            var x = this.s & this.DM;
            for (var i = 0; i < this.t; ++i) {
                r += cbit(this[i] ^ x);
            }
            return r;
        };
        // BigInteger.prototype.testBit = bnTestBit;
        // (public) true iff nth bit is set
        BigInteger.prototype.testBit = function (n) {
            var j = Math.floor(n / this.DB);
            if (j >= this.t) {
                return (this.s != 0);
            }
            return ((this[j] & (1 << (n % this.DB))) != 0);
        };
        // BigInteger.prototype.setBit = bnSetBit;
        // (public) this | (1<<n)
        BigInteger.prototype.setBit = function (n) {
            return this.changeBit(n, op_or);
        };
        // BigInteger.prototype.clearBit = bnClearBit;
        // (public) this & ~(1<<n)
        BigInteger.prototype.clearBit = function (n) {
            return this.changeBit(n, op_andnot);
        };
        // BigInteger.prototype.flipBit = bnFlipBit;
        // (public) this ^ (1<<n)
        BigInteger.prototype.flipBit = function (n) {
            return this.changeBit(n, op_xor);
        };
        // BigInteger.prototype.add = bnAdd;
        // (public) this + a
        BigInteger.prototype.add = function (a) {
            var r = nbi();
            this.addTo(a, r);
            return r;
        };
        // BigInteger.prototype.subtract = bnSubtract;
        // (public) this - a
        BigInteger.prototype.subtract = function (a) {
            var r = nbi();
            this.subTo(a, r);
            return r;
        };
        // BigInteger.prototype.multiply = bnMultiply;
        // (public) this * a
        BigInteger.prototype.multiply = function (a) {
            var r = nbi();
            this.multiplyTo(a, r);
            return r;
        };
        // BigInteger.prototype.divide = bnDivide;
        // (public) this / a
        BigInteger.prototype.divide = function (a) {
            var r = nbi();
            this.divRemTo(a, r, null);
            return r;
        };
        // BigInteger.prototype.remainder = bnRemainder;
        // (public) this % a
        BigInteger.prototype.remainder = function (a) {
            var r = nbi();
            this.divRemTo(a, null, r);
            return r;
        };
        // BigInteger.prototype.divideAndRemainder = bnDivideAndRemainder;
        // (public) [this/a,this%a]
        BigInteger.prototype.divideAndRemainder = function (a) {
            var q = nbi();
            var r = nbi();
            this.divRemTo(a, q, r);
            return [q, r];
        };
        // BigInteger.prototype.modPow = bnModPow;
        // (public) this^e % m (HAC 14.85)
        BigInteger.prototype.modPow = function (e, m) {
            var i = e.bitLength();
            var k;
            var r = nbv(1);
            var z;
            if (i <= 0) {
                return r;
            }
            else if (i < 18) {
                k = 1;
            }
            else if (i < 48) {
                k = 3;
            }
            else if (i < 144) {
                k = 4;
            }
            else if (i < 768) {
                k = 5;
            }
            else {
                k = 6;
            }
            if (i < 8) {
                z = new Classic(m);
            }
            else if (m.isEven()) {
                z = new Barrett(m);
            }
            else {
                z = new Montgomery(m);
            }
            // precomputation
            var g = [];
            var n = 3;
            var k1 = k - 1;
            var km = (1 << k) - 1;
            g[1] = z.convert(this);
            if (k > 1) {
                var g2 = nbi();
                z.sqrTo(g[1], g2);
                while (n <= km) {
                    g[n] = nbi();
                    z.mulTo(g2, g[n - 2], g[n]);
                    n += 2;
                }
            }
            var j = e.t - 1;
            var w;
            var is1 = true;
            var r2 = nbi();
            var t;
            i = nbits(e[j]) - 1;
            while (j >= 0) {
                if (i >= k1) {
                    w = (e[j] >> (i - k1)) & km;
                }
                else {
                    w = (e[j] & ((1 << (i + 1)) - 1)) << (k1 - i);
                    if (j > 0) {
                        w |= e[j - 1] >> (this.DB + i - k1);
                    }
                }
                n = k;
                while ((w & 1) == 0) {
                    w >>= 1;
                    --n;
                }
                if ((i -= n) < 0) {
                    i += this.DB;
                    --j;
                }
                if (is1) { // ret == 1, don‘t bother squaring or multiplying it
                    g[w].copyTo(r);
                    is1 = false;
                }
                else {
                    while (n > 1) {
                        z.sqrTo(r, r2);
                        z.sqrTo(r2, r);
                        n -= 2;
                    }
                    if (n > 0) {
                        z.sqrTo(r, r2);
                    }
                    else {
                        t = r;
                        r = r2;
                        r2 = t;
                    }
                    z.mulTo(r2, g[w], r);
                }
                while (j >= 0 && (e[j] & (1 << i)) == 0) {
                    z.sqrTo(r, r2);
                    t = r;
                    r = r2;
                    r2 = t;
                    if (--i < 0) {
                        i = this.DB - 1;
                        --j;
                    }
                }
            }
            return z.revert(r);
        };
        // BigInteger.prototype.modInverse = bnModInverse;
        // (public) 1/this % m (HAC 14.61)
        BigInteger.prototype.modInverse = function (m) {
            var ac = m.isEven();
            if ((this.isEven() && ac) || m.signum() == 0) {
                return BigInteger.ZERO;
            }
            var u = m.clone();
            var v = this.clone();
            var a = nbv(1);
            var b = nbv(0);
            var c = nbv(0);
            var d = nbv(1);
            while (u.signum() != 0) {
                while (u.isEven()) {
                    u.rShiftTo(1, u);
                    if (ac) {
                        if (!a.isEven() || !b.isEven()) {
                            a.addTo(this, a);
                            b.subTo(m, b);
                        }
                        a.rShiftTo(1, a);
                    }
                    else if (!b.isEven()) {
                        b.subTo(m, b);
                    }
                    b.rShiftTo(1, b);
                }
                while (v.isEven()) {
                    v.rShiftTo(1, v);
                    if (ac) {
                        if (!c.isEven() || !d.isEven()) {
                            c.addTo(this, c);
                            d.subTo(m, d);
                        }
                        c.rShiftTo(1, c);
                    }
                    else if (!d.isEven()) {
                        d.subTo(m, d);
                    }
                    d.rShiftTo(1, d);
                }
                if (u.compareTo(v) >= 0) {
                    u.subTo(v, u);
                    if (ac) {
                        a.subTo(c, a);
                    }
                    b.subTo(d, b);
                }
                else {
                    v.subTo(u, v);
                    if (ac) {
                        c.subTo(a, c);
                    }
                    d.subTo(b, d);
                }
            }
            if (v.compareTo(BigInteger.ONE) != 0) {
                return BigInteger.ZERO;
            }
            if (d.compareTo(m) >= 0) {
                return d.subtract(m);
            }
            if (d.signum() < 0) {
                d.addTo(m, d);
            }
            else {
                return d;
            }
            if (d.signum() < 0) {
                return d.add(m);
            }
            else {
                return d;
            }
        };
        // BigInteger.prototype.pow = bnPow;
        // (public) this^e
        BigInteger.prototype.pow = function (e) {
            return this.exp(e, new NullExp());
        };
        // BigInteger.prototype.gcd = bnGCD;
        // (public) gcd(this,a) (HAC 14.54)
        BigInteger.prototype.gcd = function (a) {
            var x = (this.s < 0) ? this.negate() : this.clone();
            var y = (a.s < 0) ? a.negate() : a.clone();
            if (x.compareTo(y) < 0) {
                var t = x;
                x = y;
                y = t;
            }
            var i = x.getLowestSetBit();
            var g = y.getLowestSetBit();
            if (g < 0) {
                return x;
            }
            if (i < g) {
                g = i;
            }
            if (g > 0) {
                x.rShiftTo(g, x);
                y.rShiftTo(g, y);
            }
            while (x.signum() > 0) {
                if ((i = x.getLowestSetBit()) > 0) {
                    x.rShiftTo(i, x);
                }
                if ((i = y.getLowestSetBit()) > 0) {
                    y.rShiftTo(i, y);
                }
                if (x.compareTo(y) >= 0) {
                    x.subTo(y, x);
                    x.rShiftTo(1, x);
                }
                else {
                    y.subTo(x, y);
                    y.rShiftTo(1, y);
                }
            }
            if (g > 0) {
                y.lShiftTo(g, y);
            }
            return y;
        };
        // BigInteger.prototype.isProbablePrime = bnIsProbablePrime;
        // (public) test primality with certainty >= 1-.5^t
        BigInteger.prototype.isProbablePrime = function (t) {
            var i;
            var x = this.abs();
            if (x.t == 1 && x[0] <= lowprimes[lowprimes.length - 1]) {
                for (i = 0; i < lowprimes.length; ++i) {
                    if (x[0] == lowprimes[i]) {
                        return true;
                    }
                }
                return false;
            }
            if (x.isEven()) {
                return false;
            }
            i = 1;
            while (i < lowprimes.length) {
                var m = lowprimes[i];
                var j = i + 1;
                while (j < lowprimes.length && m < lplim) {
                    m *= lowprimes[j++];
                }
                m = x.modInt(m);
                while (i < j) {
                    if (m % lowprimes[i++] == 0) {
                        return false;
                    }
                }
            }
            return x.millerRabin(t);
        };
        //#endregion PUBLIC
        //#region PROTECTED
        // BigInteger.prototype.copyTo = bnpCopyTo;
        // (protected) copy this to r
        BigInteger.prototype.copyTo = function (r) {
            for (var i = this.t - 1; i >= 0; --i) {
                r[i] = this[i];
            }
            r.t = this.t;
            r.s = this.s;
        };
        // BigInteger.prototype.fromInt = bnpFromInt;
        // (protected) set from integer value x, -DV <= x < DV
        BigInteger.prototype.fromInt = function (x) {
            this.t = 1;
            this.s = (x < 0) ? -1 : 0;
            if (x > 0) {
                this[0] = x;
            }
            else if (x < -1) {
                this[0] = x + this.DV;
            }
            else {
                this.t = 0;
            }
        };
        // BigInteger.prototype.fromString = bnpFromString;
        // (protected) set from string and radix
        BigInteger.prototype.fromString = function (s, b) {
            var k;
            if (b == 16) {
                k = 4;
            }
            else if (b == 8) {
                k = 3;
            }
            else if (b == 256) {
                k = 8;
                /* byte array */
            }
            else if (b == 2) {
                k = 1;
            }
            else if (b == 32) {
                k = 5;
            }
            else if (b == 4) {
                k = 2;
            }
            else {
                this.fromRadix(s, b);
                return;
            }
            this.t = 0;
            this.s = 0;
            var i = s.length;
            var mi = false;
            var sh = 0;
            while (--i >= 0) {
                var x = (k == 8) ? (+s[i]) & 0xff : intAt(s, i);
                if (x < 0) {
                    if (s.charAt(i) == "-") {
                        mi = true;
                    }
                    continue;
                }
                mi = false;
                if (sh == 0) {
                    this[this.t++] = x;
                }
                else if (sh + k > this.DB) {
                    this[this.t - 1] |= (x & ((1 << (this.DB - sh)) - 1)) << sh;
                    this[this.t++] = (x >> (this.DB - sh));
                }
                else {
                    this[this.t - 1] |= x << sh;
                }
                sh += k;
                if (sh >= this.DB) {
                    sh -= this.DB;
                }
            }
            if (k == 8 && ((+s[0]) & 0x80) != 0) {
                this.s = -1;
                if (sh > 0) {
                    this[this.t - 1] |= ((1 << (this.DB - sh)) - 1) << sh;
                }
            }
            this.clamp();
            if (mi) {
                BigInteger.ZERO.subTo(this, this);
            }
        };
        // BigInteger.prototype.clamp = bnpClamp;
        // (protected) clamp off excess high words
        BigInteger.prototype.clamp = function () {
            var c = this.s & this.DM;
            while (this.t > 0 && this[this.t - 1] == c) {
                --this.t;
            }
        };
        // BigInteger.prototype.dlShiftTo = bnpDLShiftTo;
        // (protected) r = this << n*DB
        BigInteger.prototype.dlShiftTo = function (n, r) {
            var i;
            for (i = this.t - 1; i >= 0; --i) {
                r[i + n] = this[i];
            }
            for (i = n - 1; i >= 0; --i) {
                r[i] = 0;
            }
            r.t = this.t + n;
            r.s = this.s;
        };
        // BigInteger.prototype.drShiftTo = bnpDRShiftTo;
        // (protected) r = this >> n*DB
        BigInteger.prototype.drShiftTo = function (n, r) {
            for (var i = n; i < this.t; ++i) {
                r[i - n] = this[i];
            }
            r.t = Math.max(this.t - n, 0);
            r.s = this.s;
        };
        // BigInteger.prototype.lShiftTo = bnpLShiftTo;
        // (protected) r = this << n
        BigInteger.prototype.lShiftTo = function (n, r) {
            var bs = n % this.DB;
            var cbs = this.DB - bs;
            var bm = (1 << cbs) - 1;
            var ds = Math.floor(n / this.DB);
            var c = (this.s << bs) & this.DM;
            for (var i = this.t - 1; i >= 0; --i) {
                r[i + ds + 1] = (this[i] >> cbs) | c;
                c = (this[i] & bm) << bs;
            }
            for (var i = ds - 1; i >= 0; --i) {
                r[i] = 0;
            }
            r[ds] = c;
            r.t = this.t + ds + 1;
            r.s = this.s;
            r.clamp();
        };
        // BigInteger.prototype.rShiftTo = bnpRShiftTo;
        // (protected) r = this >> n
        BigInteger.prototype.rShiftTo = function (n, r) {
            r.s = this.s;
            var ds = Math.floor(n / this.DB);
            if (ds >= this.t) {
                r.t = 0;
                return;
            }
            var bs = n % this.DB;
            var cbs = this.DB - bs;
            var bm = (1 << bs) - 1;
            r[0] = this[ds] >> bs;
            for (var i = ds + 1; i < this.t; ++i) {
                r[i - ds - 1] |= (this[i] & bm) << cbs;
                r[i - ds] = this[i] >> bs;
            }
            if (bs > 0) {
                r[this.t - ds - 1] |= (this.s & bm) << cbs;
            }
            r.t = this.t - ds;
            r.clamp();
        };
        // BigInteger.prototype.subTo = bnpSubTo;
        // (protected) r = this - a
        BigInteger.prototype.subTo = function (a, r) {
            var i = 0;
            var c = 0;
            var m = Math.min(a.t, this.t);
            while (i < m) {
                c += this[i] - a[i];
                r[i++] = c & this.DM;
                c >>= this.DB;
            }
            if (a.t < this.t) {
                c -= a.s;
                while (i < this.t) {
                    c += this[i];
                    r[i++] = c & this.DM;
                    c >>= this.DB;
                }
                c += this.s;
            }
            else {
                c += this.s;
                while (i < a.t) {
                    c -= a[i];
                    r[i++] = c & this.DM;
                    c >>= this.DB;
                }
                c -= a.s;
            }
            r.s = (c < 0) ? -1 : 0;
            if (c < -1) {
                r[i++] = this.DV + c;
            }
            else if (c > 0) {
                r[i++] = c;
            }
            r.t = i;
            r.clamp();
        };
        // BigInteger.prototype.multiplyTo = bnpMultiplyTo;
        // (protected) r = this * a, r != this,a (HAC 14.12)
        // "this" should be the larger one if appropriate.
        BigInteger.prototype.multiplyTo = function (a, r) {
            var x = this.abs();
            var y = a.abs();
            var i = x.t;
            r.t = i + y.t;
            while (--i >= 0) {
                r[i] = 0;
            }
            for (i = 0; i < y.t; ++i) {
                r[i + x.t] = x.am(0, y[i], r, i, 0, x.t);
            }
            r.s = 0;
            r.clamp();
            if (this.s != a.s) {
                BigInteger.ZERO.subTo(r, r);
            }
        };
        // BigInteger.prototype.squareTo = bnpSquareTo;
        // (protected) r = this^2, r != this (HAC 14.16)
        BigInteger.prototype.squareTo = function (r) {
            var x = this.abs();
            var i = r.t = 2 * x.t;
            while (--i >= 0) {
                r[i] = 0;
            }
            for (i = 0; i < x.t - 1; ++i) {
                var c = x.am(i, x[i], r, 2 * i, 0, 1);
                if ((r[i + x.t] += x.am(i + 1, 2 * x[i], r, 2 * i + 1, c, x.t - i - 1)) >= x.DV) {
                    r[i + x.t] -= x.DV;
                    r[i + x.t + 1] = 1;
                }
            }
            if (r.t > 0) {
                r[r.t - 1] += x.am(i, x[i], r, 2 * i, 0, 1);
            }
            r.s = 0;
            r.clamp();
        };
        // BigInteger.prototype.divRemTo = bnpDivRemTo;
        // (protected) divide this by m, quotient and remainder to q, r (HAC 14.20)
        // r != q, this != m.  q or r may be null.
        BigInteger.prototype.divRemTo = function (m, q, r) {
            var pm = m.abs();
            if (pm.t <= 0) {
                return;
            }
            var pt = this.abs();
            if (pt.t < pm.t) {
                if (q != null) {
                    q.fromInt(0);
                }
                if (r != null) {
                    this.copyTo(r);
                }
                return;
            }
            if (r == null) {
                r = nbi();
            }
            var y = nbi();
            var ts = this.s;
            var ms = m.s;
            var nsh = this.DB - nbits(pm[pm.t - 1]); // normalize modulus
            if (nsh > 0) {
                pm.lShiftTo(nsh, y);
                pt.lShiftTo(nsh, r);
            }
            else {
                pm.copyTo(y);
                pt.copyTo(r);
            }
            var ys = y.t;
            var y0 = y[ys - 1];
            if (y0 == 0) {
                return;
            }
            var yt = y0 * (1 << this.F1) + ((ys > 1) ? y[ys - 2] >> this.F2 : 0);
            var d1 = this.FV / yt;
            var d2 = (1 << this.F1) / yt;
            var e = 1 << this.F2;
            var i = r.t;
            var j = i - ys;
            var t = (q == null) ? nbi() : q;
            y.dlShiftTo(j, t);
            if (r.compareTo(t) >= 0) {
                r[r.t++] = 1;
                r.subTo(t, r);
            }
            BigInteger.ONE.dlShiftTo(ys, t);
            t.subTo(y, y); // "negative" y so we can replace sub with am later
            while (y.t < ys) {
                y[y.t++] = 0;
            }
            while (--j >= 0) {
                // Estimate quotient digit
                var qd = (r[--i] == y0) ? this.DM : Math.floor(r[i] * d1 + (r[i - 1] + e) * d2);
                if ((r[i] += y.am(0, qd, r, j, 0, ys)) < qd) { // Try it out
                    y.dlShiftTo(j, t);
                    r.subTo(t, r);
                    while (r[i] < --qd) {
                        r.subTo(t, r);
                    }
                }
            }
            if (q != null) {
                r.drShiftTo(ys, q);
                if (ts != ms) {
                    BigInteger.ZERO.subTo(q, q);
                }
            }
            r.t = ys;
            r.clamp();
            if (nsh > 0) {
                r.rShiftTo(nsh, r);
            } // Denormalize remainder
            if (ts < 0) {
                BigInteger.ZERO.subTo(r, r);
            }
        };
        // BigInteger.prototype.invDigit = bnpInvDigit;
        // (protected) return "-1/this % 2^DB"; useful for Mont. reduction
        // justification:
        //         xy == 1 (mod m)
        //         xy =  1+km
        //   xy(2-xy) = (1+km)(1-km)
        // x[y(2-xy)] = 1-k^2m^2
        // x[y(2-xy)] == 1 (mod m^2)
        // if y is 1/x mod m, then y(2-xy) is 1/x mod m^2
        // should reduce x and y(2-xy) by m^2 at each step to keep size bounded.
        // JS multiply "overflows" differently from C/C++, so care is needed here.
        BigInteger.prototype.invDigit = function () {
            if (this.t < 1) {
                return 0;
            }
            var x = this[0];
            if ((x & 1) == 0) {
                return 0;
            }
            var y = x & 3; // y == 1/x mod 2^2
            y = (y * (2 - (x & 0xf) * y)) & 0xf; // y == 1/x mod 2^4
            y = (y * (2 - (x & 0xff) * y)) & 0xff; // y == 1/x mod 2^8
            y = (y * (2 - (((x & 0xffff) * y) & 0xffff))) & 0xffff; // y == 1/x mod 2^16
            // last step - calculate inverse mod DV directly;
            // assumes 16 < DB <= 32 and assumes ability to handle 48-bit ints
            y = (y * (2 - x * y % this.DV)) % this.DV; // y == 1/x mod 2^dbits
            // we really want the negative inverse, and -DV < y < DV
            return (y > 0) ? this.DV - y : -y;
        };
        // BigInteger.prototype.isEven = bnpIsEven;
        // (protected) true iff this is even
        BigInteger.prototype.isEven = function () {
            return ((this.t > 0) ? (this[0] & 1) : this.s) == 0;
        };
        // BigInteger.prototype.exp = bnpExp;
        // (protected) this^e, e < 2^32, doing sqr and mul with "r" (HAC 14.79)
        BigInteger.prototype.exp = function (e, z) {
            if (e > 0xffffffff || e < 1) {
                return BigInteger.ONE;
            }
            var r = nbi();
            var r2 = nbi();
            var g = z.convert(this);
            var i = nbits(e) - 1;
            g.copyTo(r);
            while (--i >= 0) {
                z.sqrTo(r, r2);
                if ((e & (1 << i)) > 0) {
                    z.mulTo(r2, g, r);
                }
                else {
                    var t = r;
                    r = r2;
                    r2 = t;
                }
            }
            return z.revert(r);
        };
        // BigInteger.prototype.chunkSize = bnpChunkSize;
        // (protected) return x s.t. r^x < DV
        BigInteger.prototype.chunkSize = function (r) {
            return Math.floor(Math.LN2 * this.DB / Math.log(r));
        };
        // BigInteger.prototype.toRadix = bnpToRadix;
        // (protected) convert to radix string
        BigInteger.prototype.toRadix = function (b) {
            if (b == null) {
                b = 10;
            }
            if (this.signum() == 0 || b < 2 || b > 36) {
                return "0";
            }
            var cs = this.chunkSize(b);
            var a = Math.pow(b, cs);
            var d = nbv(a);
            var y = nbi();
            var z = nbi();
            var r = "";
            this.divRemTo(d, y, z);
            while (y.signum() > 0) {
                r = (a + z.intValue()).toString(b).substr(1) + r;
                y.divRemTo(d, y, z);
            }
            return z.intValue().toString(b) + r;
        };
        // BigInteger.prototype.fromRadix = bnpFromRadix;
        // (protected) convert from radix string
        BigInteger.prototype.fromRadix = function (s, b) {
            this.fromInt(0);
            if (b == null) {
                b = 10;
            }
            var cs = this.chunkSize(b);
            var d = Math.pow(b, cs);
            var mi = false;
            var j = 0;
            var w = 0;
            for (var i = 0; i < s.length; ++i) {
                var x = intAt(s, i);
                if (x < 0) {
                    if (s.charAt(i) == "-" && this.signum() == 0) {
                        mi = true;
                    }
                    continue;
                }
                w = b * w + x;
                if (++j >= cs) {
                    this.dMultiply(d);
                    this.dAddOffset(w, 0);
                    j = 0;
                    w = 0;
                }
            }
            if (j > 0) {
                this.dMultiply(Math.pow(b, j));
                this.dAddOffset(w, 0);
            }
            if (mi) {
                BigInteger.ZERO.subTo(this, this);
            }
        };
        // BigInteger.prototype.fromNumber = bnpFromNumber;
        // (protected) alternate constructor
        BigInteger.prototype.fromNumber = function (a, b, c) {
            if ("number" == typeof b) {
                // new BigInteger(int,int,RNG)
                if (a < 2) {
                    this.fromInt(1);
                }
                else {
                    this.fromNumber(a, c);
                    if (!this.testBit(a - 1)) {
                        // force MSB set
                        this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this);
                    }
                    if (this.isEven()) {
                        this.dAddOffset(1, 0);
                    } // force odd
                    while (!this.isProbablePrime(b)) {
                        this.dAddOffset(2, 0);
                        if (this.bitLength() > a) {
                            this.subTo(BigInteger.ONE.shiftLeft(a - 1), this);
                        }
                    }
                }
            }
            else {
                // new BigInteger(int,RNG)
                var x = [];
                var t = a & 7;
                x.length = (a >> 3) + 1;
                b.nextBytes(x);
                if (t > 0) {
                    x[0] &= ((1 << t) - 1);
                }
                else {
                    x[0] = 0;
                }
                this.fromString(x, 256);
            }
        };
        // BigInteger.prototype.bitwiseTo = bnpBitwiseTo;
        // (protected) r = this op a (bitwise)
        BigInteger.prototype.bitwiseTo = function (a, op, r) {
            var i;
            var f;
            var m = Math.min(a.t, this.t);
            for (i = 0; i < m; ++i) {
                r[i] = op(this[i], a[i]);
            }
            if (a.t < this.t) {
                f = a.s & this.DM;
                for (i = m; i < this.t; ++i) {
                    r[i] = op(this[i], f);
                }
                r.t = this.t;
            }
            else {
                f = this.s & this.DM;
                for (i = m; i < a.t; ++i) {
                    r[i] = op(f, a[i]);
                }
                r.t = a.t;
            }
            r.s = op(this.s, a.s);
            r.clamp();
        };
        // BigInteger.prototype.changeBit = bnpChangeBit;
        // (protected) this op (1<<n)
        BigInteger.prototype.changeBit = function (n, op) {
            var r = BigInteger.ONE.shiftLeft(n);
            this.bitwiseTo(r, op, r);
            return r;
        };
        // BigInteger.prototype.addTo = bnpAddTo;
        // (protected) r = this + a
        BigInteger.prototype.addTo = function (a, r) {
            var i = 0;
            var c = 0;
            var m = Math.min(a.t, this.t);
            while (i < m) {
                c += this[i] + a[i];
                r[i++] = c & this.DM;
                c >>= this.DB;
            }
            if (a.t < this.t) {
                c += a.s;
                while (i < this.t) {
                    c += this[i];
                    r[i++] = c & this.DM;
                    c >>= this.DB;
                }
                c += this.s;
            }
            else {
                c += this.s;
                while (i < a.t) {
                    c += a[i];
                    r[i++] = c & this.DM;
                    c >>= this.DB;
                }
                c += a.s;
            }
            r.s = (c < 0) ? -1 : 0;
            if (c > 0) {
                r[i++] = c;
            }
            else if (c < -1) {
                r[i++] = this.DV + c;
            }
            r.t = i;
            r.clamp();
        };
        // BigInteger.prototype.dMultiply = bnpDMultiply;
        // (protected) this *= n, this >= 0, 1 < n < DV
        BigInteger.prototype.dMultiply = function (n) {
            this[this.t] = this.am(0, n - 1, this, 0, 0, this.t);
            ++this.t;
            this.clamp();
        };
        // BigInteger.prototype.dAddOffset = bnpDAddOffset;
        // (protected) this += n << w words, this >= 0
        BigInteger.prototype.dAddOffset = function (n, w) {
            if (n == 0) {
                return;
            }
            while (this.t <= w) {
                this[this.t++] = 0;
            }
            this[w] += n;
            while (this[w] >= this.DV) {
                this[w] -= this.DV;
                if (++w >= this.t) {
                    this[this.t++] = 0;
                }
                ++this[w];
            }
        };
        // BigInteger.prototype.multiplyLowerTo = bnpMultiplyLowerTo;
        // (protected) r = lower n words of "this * a", a.t <= n
        // "this" should be the larger one if appropriate.
        BigInteger.prototype.multiplyLowerTo = function (a, n, r) {
            var i = Math.min(this.t + a.t, n);
            r.s = 0; // assumes a,this >= 0
            r.t = i;
            while (i > 0) {
                r[--i] = 0;
            }
            for (var j = r.t - this.t; i < j; ++i) {
                r[i + this.t] = this.am(0, a[i], r, i, 0, this.t);
            }
            for (var j = Math.min(a.t, n); i < j; ++i) {
                this.am(0, a[i], r, i, 0, n - i);
            }
            r.clamp();
        };
        // BigInteger.prototype.multiplyUpperTo = bnpMultiplyUpperTo;
        // (protected) r = "this * a" without lower n words, n > 0
        // "this" should be the larger one if appropriate.
        BigInteger.prototype.multiplyUpperTo = function (a, n, r) {
            --n;
            var i = r.t = this.t + a.t - n;
            r.s = 0; // assumes a,this >= 0
            while (--i >= 0) {
                r[i] = 0;
            }
            for (i = Math.max(n - this.t, 0); i < a.t; ++i) {
                r[this.t + i - n] = this.am(n - i, a[i], r, 0, 0, this.t + i - n);
            }
            r.clamp();
            r.drShiftTo(1, r);
        };
        // BigInteger.prototype.modInt = bnpModInt;
        // (protected) this % n, n < 2^26
        BigInteger.prototype.modInt = function (n) {
            if (n <= 0) {
                return 0;
            }
            var d = this.DV % n;
            var r = (this.s < 0) ? n - 1 : 0;
            if (this.t > 0) {
                if (d == 0) {
                    r = this[0] % n;
                }
                else {
                    for (var i = this.t - 1; i >= 0; --i) {
                        r = (d * r + this[i]) % n;
                    }
                }
            }
            return r;
        };
        // BigInteger.prototype.millerRabin = bnpMillerRabin;
        // (protected) true if probably prime (HAC 4.24, Miller-Rabin)
        BigInteger.prototype.millerRabin = function (t) {
            var n1 = this.subtract(BigInteger.ONE);
            var k = n1.getLowestSetBit();
            if (k <= 0) {
                return false;
            }
            var r = n1.shiftRight(k);
            t = (t + 1) >> 1;
            if (t > lowprimes.length) {
                t = lowprimes.length;
            }
            var a = nbi();
            for (var i = 0; i < t; ++i) {
                // Pick bases at random, instead of starting at 2
                a.fromInt(lowprimes[Math.floor(Math.random() * lowprimes.length)]);
                var y = a.modPow(r, this);
                if (y.compareTo(BigInteger.ONE) != 0 && y.compareTo(n1) != 0) {
                    var j = 1;
                    while (j++ < k && y.compareTo(n1) != 0) {
                        y = y.modPowInt(2, this);
                        if (y.compareTo(BigInteger.ONE) == 0) {
                            return false;
                        }
                    }
                    if (y.compareTo(n1) != 0) {
                        return false;
                    }
                }
            }
            return true;
        };
        // BigInteger.prototype.square = bnSquare;
        // (public) this^2
        BigInteger.prototype.square = function () {
            var r = nbi();
            this.squareTo(r);
            return r;
        };
        //#region ASYNC
        // Public API method
        BigInteger.prototype.gcda = function (a, callback) {
            var x = (this.s < 0) ? this.negate() : this.clone();
            var y = (a.s < 0) ? a.negate() : a.clone();
            if (x.compareTo(y) < 0) {
                var t = x;
                x = y;
                y = t;
            }
            var i = x.getLowestSetBit();
            var g = y.getLowestSetBit();
            if (g < 0) {
                callback(x);
                return;
            }
            if (i < g) {
                g = i;
            }
            if (g > 0) {
                x.rShiftTo(g, x);
                y.rShiftTo(g, y);
            }
            // Workhorse of the algorithm, gets called 200 - 800 times per 512 bit keygen.
            var gcda1 = function () {
                if ((i = x.getLowestSetBit()) > 0) {
                    x.rShiftTo(i, x);
                }
                if ((i = y.getLowestSetBit()) > 0) {
                    y.rShiftTo(i, y);
                }
                if (x.compareTo(y) >= 0) {
                    x.subTo(y, x);
                    x.rShiftTo(1, x);
                }
                else {
                    y.subTo(x, y);
                    y.rShiftTo(1, y);
                }
                if (!(x.signum() > 0)) {
                    if (g > 0) {
                        y.lShiftTo(g, y);
                    }
                    setTimeout(function () { callback(y); }, 0); // escape
                }
                else {
                    setTimeout(gcda1, 0);
                }
            };
            setTimeout(gcda1, 10);
        };
        // (protected) alternate constructor
        BigInteger.prototype.fromNumberAsync = function (a, b, c, callback) {
            if ("number" == typeof b) {
                if (a < 2) {
                    this.fromInt(1);
                }
                else {
                    this.fromNumber(a, c);
                    if (!this.testBit(a - 1)) {
                        this.bitwiseTo(BigInteger.ONE.shiftLeft(a - 1), op_or, this);
                    }
                    if (this.isEven()) {
                        this.dAddOffset(1, 0);
                    }
                    var bnp_1 = this;
                    var bnpfn1_1 = function () {
                        bnp_1.dAddOffset(2, 0);
                        if (bnp_1.bitLength() > a) {
                            bnp_1.subTo(BigInteger.ONE.shiftLeft(a - 1), bnp_1);
                        }
                        if (bnp_1.isProbablePrime(b)) {
                            setTimeout(function () { callback(); }, 0); // escape
                        }
                        else {
                            setTimeout(bnpfn1_1, 0);
                        }
                    };
                    setTimeout(bnpfn1_1, 0);
                }
            }
            else {
                var x = [];
                var t = a & 7;
                x.length = (a >> 3) + 1;
                b.nextBytes(x);
                if (t > 0) {
                    x[0] &= ((1 << t) - 1);
                }
                else {
                    x[0] = 0;
                }
                this.fromString(x, 256);
            }
        };
        return BigInteger;
    }());
    //#region REDUCERS
    //#region NullExp
    var NullExp = /** @class */ (function () {
        function NullExp() {
        }
        // NullExp.prototype.convert = nNop;
        NullExp.prototype.convert = function (x) {
            return x;
        };
        // NullExp.prototype.revert = nNop;
        NullExp.prototype.revert = function (x) {
            return x;
        };
        // NullExp.prototype.mulTo = nMulTo;
        NullExp.prototype.mulTo = function (x, y, r) {
            x.multiplyTo(y, r);
        };
        // NullExp.prototype.sqrTo = nSqrTo;
        NullExp.prototype.sqrTo = function (x, r) {
            x.squareTo(r);
        };
        return NullExp;
    }());
    // Modular reduction using "classic" algorithm
    var Classic = /** @class */ (function () {
        function Classic(m) {
            this.m = m;
        }
        // Classic.prototype.convert = cConvert;
        Classic.prototype.convert = function (x) {
            if (x.s < 0 || x.compareTo(this.m) >= 0) {
                return x.mod(this.m);
            }
            else {
                return x;
            }
        };
        // Classic.prototype.revert = cRevert;
        Classic.prototype.revert = function (x) {
            return x;
        };
        // Classic.prototype.reduce = cReduce;
        Classic.prototype.reduce = function (x) {
            x.divRemTo(this.m, null, x);
        };
        // Classic.prototype.mulTo = cMulTo;
        Classic.prototype.mulTo = function (x, y, r) {
            x.multiplyTo(y, r);
            this.reduce(r);
        };
        // Classic.prototype.sqrTo = cSqrTo;
        Classic.prototype.sqrTo = function (x, r) {
            x.squareTo(r);
            this.reduce(r);
        };
        return Classic;
    }());
    //#endregion
    //#region Montgomery
    // Montgomery reduction
    var Montgomery = /** @class */ (function () {
        function Montgomery(m) {
            this.m = m;
            this.mp = m.invDigit();
            this.mpl = this.mp & 0x7fff;
            this.mph = this.mp >> 15;
            this.um = (1 << (m.DB - 15)) - 1;
            this.mt2 = 2 * m.t;
        }
        // Montgomery.prototype.convert = montConvert;
        // xR mod m
        Montgomery.prototype.convert = function (x) {
            var r = nbi();
            x.abs().dlShiftTo(this.m.t, r);
            r.divRemTo(this.m, null, r);
            if (x.s < 0 && r.compareTo(BigInteger.ZERO) > 0) {
                this.m.subTo(r, r);
            }
            return r;
        };
        // Montgomery.prototype.revert = montRevert;
        // x/R mod m
        Montgomery.prototype.revert = function (x) {
            var r = nbi();
            x.copyTo(r);
            this.reduce(r);
            return r;
        };
        // Montgomery.prototype.reduce = montReduce;
        // x = x/R mod m (HAC 14.32)
        Montgomery.prototype.reduce = function (x) {
            while (x.t <= this.mt2) {
                // pad x so am has enough room later
                x[x.t++] = 0;
            }
            for (var i = 0; i < this.m.t; ++i) {
                // faster way of calculating u0 = x[i]*mp mod DV
                var j = x[i] & 0x7fff;
                var u0 = (j * this.mpl + (((j * this.mph + (x[i] >> 15) * this.mpl) & this.um) << 15)) & x.DM;
                // use am to combine the multiply-shift-add into one call
                j = i + this.m.t;
                x[j] += this.m.am(0, u0, x, i, 0, this.m.t);
                // propagate carry
                while (x[j] >= x.DV) {
                    x[j] -= x.DV;
                    x[++j]++;
                }
            }
            x.clamp();
            x.drShiftTo(this.m.t, x);
            if (x.compareTo(this.m) >= 0) {
                x.subTo(this.m, x);
            }
        };
        // Montgomery.prototype.mulTo = montMulTo;
        // r = "xy/R mod m"; x,y != r
        Montgomery.prototype.mulTo = function (x, y, r) {
            x.multiplyTo(y, r);
            this.reduce(r);
        };
        // Montgomery.prototype.sqrTo = montSqrTo;
        // r = "x^2/R mod m"; x != r
        Montgomery.prototype.sqrTo = function (x, r) {
            x.squareTo(r);
            this.reduce(r);
        };
        return Montgomery;
    }());
    //#endregion Montgomery
    //#region Barrett
    // Barrett modular reduction
    var Barrett = /** @class */ (function () {
        function Barrett(m) {
            this.m = m;
            // setup Barrett
            this.r2 = nbi();
            this.q3 = nbi();
            BigInteger.ONE.dlShiftTo(2 * m.t, this.r2);
            this.mu = this.r2.divide(m);
        }
        // Barrett.prototype.convert = barrettConvert;
        Barrett.prototype.convert = function (x) {
            if (x.s < 0 || x.t > 2 * this.m.t) {
                return x.mod(this.m);
            }
            else if (x.compareTo(this.m) < 0) {
                return x;
            }
            else {
                var r = nbi();
                x.copyTo(r);
                this.reduce(r);
                return r;
            }
        };
        // Barrett.prototype.revert = barrettRevert;
        Barrett.prototype.revert = function (x) {
            return x;
        };
        // Barrett.prototype.reduce = barrettReduce;
        // x = x mod m (HAC 14.42)
        Barrett.prototype.reduce = function (x) {
            x.drShiftTo(this.m.t - 1, this.r2);
            if (x.t > this.m.t + 1) {
                x.t = this.m.t + 1;
                x.clamp();
            }
            this.mu.multiplyUpperTo(this.r2, this.m.t + 1, this.q3);
            this.m.multiplyLowerTo(this.q3, this.m.t + 1, this.r2);
            while (x.compareTo(this.r2) < 0) {
                x.dAddOffset(1, this.m.t + 1);
            }
            x.subTo(this.r2, x);
            while (x.compareTo(this.m) >= 0) {
                x.subTo(this.m, x);
            }
        };
        // Barrett.prototype.mulTo = barrettMulTo;
        // r = x*y mod m; x,y != r
        Barrett.prototype.mulTo = function (x, y, r) {
            x.multiplyTo(y, r);
            this.reduce(r);
        };
        // Barrett.prototype.sqrTo = barrettSqrTo;
        // r = x^2 mod m; x != r
        Barrett.prototype.sqrTo = function (x, r) {
            x.squareTo(r);
            this.reduce(r);
        };
        return Barrett;
    }());
    //#endregion
    //#endregion REDUCERS
    // return new, unset BigInteger
    function nbi() { return new BigInteger(null); }
    function parseBigInt(str, r) {
        return new BigInteger(str, r);
    }
    // am: Compute w_j += (x*this_i), propagate carries,
    // c is initial carry, returns final carry.
    // c < 3*dvalue, x < 2*dvalue, this_i < dvalue
    // We need to select the fastest one that works in this environment.
    // am1: use a single mult and divide to get the high bits,
    // max digit bits should be 26 because
    // max internal value = 2*dvalue^2-2*dvalue (< 2^53)
    function am1(i, x, w, j, c, n) {
        while (--n >= 0) {
            var v = x * this[i++] + w[j] + c;
            c = Math.floor(v / 0x4000000);
            w[j++] = v & 0x3ffffff;
        }
        return c;
    }
    // am2 avoids a big mult-and-extract completely.
    // Max digit bits should be <= 30 because we do bitwise ops
    // on values up to 2*hdvalue^2-hdvalue-1 (< 2^31)
    function am2(i, x, w, j, c, n) {
        var xl = x & 0x7fff;
        var xh = x >> 15;
        while (--n >= 0) {
            var l = this[i] & 0x7fff;
            var h = this[i++] >> 15;
            var m = xh * l + h * xl;
            l = xl * l + ((m & 0x7fff) << 15) + w[j] + (c & 0x3fffffff);
            c = (l >>> 30) + (m >>> 15) + xh * h + (c >>> 30);
            w[j++] = l & 0x3fffffff;
        }
        return c;
    }
    // Alternately, set max digit bits to 28 since some
    // browsers slow down when dealing with 32-bit numbers.
    function am3(i, x, w, j, c, n) {
        var xl = x & 0x3fff;
        var xh = x >> 14;
        while (--n >= 0) {
            var l = this[i] & 0x3fff;
            var h = this[i++] >> 14;
            var m = xh * l + h * xl;
            l = xl * l + ((m & 0x3fff) << 14) + w[j] + c;
            c = (l >> 28) + (m >> 14) + xh * h;
            w[j++] = l & 0xfffffff;
        }
        return c;
    }
    if (j_lm && (navigator.appName == "Microsoft Internet Explorer")) {
        BigInteger.prototype.am = am2;
        dbits = 30;
    }
    else if (j_lm && (navigator.appName != "Netscape")) {
        BigInteger.prototype.am = am1;
        dbits = 26;
    }
    else { // Mozilla/Netscape seems to prefer am3
        BigInteger.prototype.am = am3;
        dbits = 28;
    }
    BigInteger.prototype.DB = dbits;
    BigInteger.prototype.DM = ((1 << dbits) - 1);
    BigInteger.prototype.DV = (1 << dbits);
    var BI_FP = 52;
    BigInteger.prototype.FV = Math.pow(2, BI_FP);
    BigInteger.prototype.F1 = BI_FP - dbits;
    BigInteger.prototype.F2 = 2 * dbits - BI_FP;
    // Digit conversions
    var BI_RC = [];
    var rr;
    var vv;
    rr = "0".charCodeAt(0);
    for (vv = 0; vv <= 9; ++vv) {
        BI_RC[rr++] = vv;
    }
    rr = "a".charCodeAt(0);
    for (vv = 10; vv < 36; ++vv) {
        BI_RC[rr++] = vv;
    }
    rr = "A".charCodeAt(0);
    for (vv = 10; vv < 36; ++vv) {
        BI_RC[rr++] = vv;
    }
    function intAt(s, i) {
        var c = BI_RC[s.charCodeAt(i)];
        return (c == null) ? -1 : c;
    }
    // return bigint initialized to value
    function nbv(i) {
        var r = nbi();
        r.fromInt(i);
        return r;
    }
    // returns bit length of the integer x
    function nbits(x) {
        var r = 1;
        var t;
        if ((t = x >>> 16) != 0) {
            x = t;
            r += 16;
        }
        if ((t = x >> 8) != 0) {
            x = t;
            r += 8;
        }
        if ((t = x >> 4) != 0) {
            x = t;
            r += 4;
        }
        if ((t = x >> 2) != 0) {
            x = t;
            r += 2;
        }
        if ((t = x >> 1) != 0) {
            x = t;
            r += 1;
        }
        return r;
    }
    // "constants"
    BigInteger.ZERO = nbv(0);
    BigInteger.ONE = nbv(1);
    // prng4.js - uses Arcfour as a PRNG
    var Arcfour = /** @class */ (function () {
        function Arcfour() {
            this.i = 0;
            this.j = 0;
            this.S = [];
        }
        // Arcfour.prototype.init = ARC4init;
        // Initialize arcfour context from key, an array of ints, each from [0..255]
        Arcfour.prototype.init = function (key) {
            var i;
            var j;
            var t;
            for (i = 0; i < 256; ++i) {
                this.S[i] = i;
            }
            j = 0;
            for (i = 0; i < 256; ++i) {
                j = (j + this.S[i] + key[i % key.length]) & 255;
                t = this.S[i];
                this.S[i] = this.S[j];
                this.S[j] = t;
            }
            this.i = 0;
            this.j = 0;
        };
        // Arcfour.prototype.next = ARC4next;
        Arcfour.prototype.next = function () {
            var t;
            this.i = (this.i + 1) & 255;
            this.j = (this.j + this.S[this.i]) & 255;
            t = this.S[this.i];
            this.S[this.i] = this.S[this.j];
            this.S[this.j] = t;
            return this.S[(t + this.S[this.i]) & 255];
        };
        return Arcfour;
    }());
    // Plug in your RNG constructor here
    function prng_newstate() {
        return new Arcfour();
    }
    // Pool size must be a multiple of 4 and greater than 32.
    // An array of bytes the size of the pool will be passed to init()
    var rng_psize = 256;
    // Random number generator - requires a PRNG backend, e.g. prng4.js
    var rng_state;
    var rng_pool = null;
    var rng_pptr;
    // Initialize the pool with junk if needed.
    if (rng_pool == null) {
        rng_pool = [];
        rng_pptr = 0;
        var t = void 0;
        if (window.crypto && window.crypto.getRandomValues) {
            // Extract entropy (2048 bits) from RNG if available
            var z = new Uint32Array(256);
            window.crypto.getRandomValues(z);
            for (t = 0; t < z.length; ++t) {
                rng_pool[rng_pptr++] = z[t] & 255;
            }
        }
        // Use mouse events for entropy, if we do not have enough entropy by the time
        // we need it, entropy will be generated by Math.random.
        var onMouseMoveListener_1 = function (ev) {
            this.count = this.count || 0;
            if (this.count >= 256 || rng_pptr >= rng_psize) {
                if (window.removeEventListener) {
                    window.removeEventListener("mousemove", onMouseMoveListener_1, false);
                }
                else if (window.detachEvent) {
                    window.detachEvent("onmousemove", onMouseMoveListener_1);
                }
                return;
            }
            try {
                var mouseCoordinates = ev.x + ev.y;
                rng_pool[rng_pptr++] = mouseCoordinates & 255;
                this.count += 1;
            }
            catch (e) {
                // Sometimes Firefox will deny permission to access event properties for some reason. Ignore.
            }
        };
        if (window.addEventListener) {
            window.addEventListener("mousemove", onMouseMoveListener_1, false);
        }
        else if (window.attachEvent) {
            window.attachEvent("onmousemove", onMouseMoveListener_1);
        }
    }
    function rng_get_byte() {
        if (rng_state == null) {
            rng_state = prng_newstate();
            // At this point, we may not have collected enough entropy.  If not, fall back to Math.random
            while (rng_pptr < rng_psize) {
                var random = Math.floor(65536 * Math.random());
                rng_pool[rng_pptr++] = random & 255;
            }
            rng_state.init(rng_pool);
            for (rng_pptr = 0; rng_pptr < rng_pool.length; ++rng_pptr) {
                rng_pool[rng_pptr] = 0;
            }
            rng_pptr = 0;
        }
        // TODO: allow reseeding after first request
        return rng_state.next();
    }
    var SecureRandom = /** @class */ (function () {
        function SecureRandom() {
        }
        SecureRandom.prototype.nextBytes = function (ba) {
            for (var i = 0; i < ba.length; ++i) {
                ba[i] = rng_get_byte();
            }
        };
        return SecureRandom;
    }());
    // Depends on jsbn.js and rng.js
    // function linebrk(s,n) {
    //   var ret = "";
    //   var i = 0;
    //   while(i + n < s.length) {
    //     ret += s.substring(i,i+n) + "\n";
    //     i += n;
    //   }
    //   return ret + s.substring(i,s.length);
    // }
    // function byte2Hex(b) {
    //   if(b < 0x10)
    //     return "0" + b.toString(16);
    //   else
    //     return b.toString(16);
    // }
    function pkcs1pad1(s, n) {
        if (n < s.length + 22) {
            console.error("Message too long for RSA");
            return null;
        }
        var len = n - s.length - 6;
        var filler = "";
        for (var f = 0; f < len; f += 2) {
            filler += "ff";
        }
        var m = "0001" + filler + "00" + s;
        return parseBigInt(m, 16);
    }
    // PKCS#1 (type 2, random) pad input string s to n bytes, and return a bigint
    function pkcs1pad2(s, n) {
        if (n < s.length + 11) { // TODO: fix for utf-8
            console.error("Message too long for RSA");
            return null;
        }
        var ba = [];
        var i = s.length - 1;
        while (i >= 0 && n > 0) {
            var c = s.charCodeAt(i--);
            if (c < 128) { // encode using utf-8
                ba[--n] = c;
            }
            else if ((c > 127) && (c < 2048)) {
                ba[--n] = (c & 63) | 128;
                ba[--n] = (c >> 6) | 192;
            }
            else {
                ba[--n] = (c & 63) | 128;
                ba[--n] = ((c >> 6) & 63) | 128;
                ba[--n] = (c >> 12) | 224;
            }
        }
        ba[--n] = 0;
        var rng = new SecureRandom();
        var x = [];
        while (n > 2) { // random non-zero pad
            x[0] = 0;
            while (x[0] == 0) {
                rng.nextBytes(x);
            }
            ba[--n] = x[0];
        }
        ba[--n] = 2;
        ba[--n] = 0;
        return new BigInteger(ba);
    }
    // "empty" RSA key constructor
    var RSAKey = /** @class */ (function () {
        function RSAKey() {
            this.n = null;
            this.e = 0;
            this.d = null;
            this.p = null;
            this.q = null;
            this.dmp1 = null;
            this.dmq1 = null;
            this.coeff = null;
        }
        //#region PROTECTED
        // protected
        // RSAKey.prototype.doPublic = RSADoPublic;
        // Perform raw public operation on "x": return x^e (mod n)
        RSAKey.prototype.doPublic = function (x) {
            return x.modPowInt(this.e, this.n);
        };
        // RSAKey.prototype.doPrivate = RSADoPrivate;
        // Perform raw private operation on "x": return x^d (mod n)
        RSAKey.prototype.doPrivate = function (x) {
            if (this.p == null || this.q == null) {
                return x.modPow(this.d, this.n);
            }
            // TODO: re-calculate any missing CRT params
            var xp = x.mod(this.p).modPow(this.dmp1, this.p);
            var xq = x.mod(this.q).modPow(this.dmq1, this.q);
            while (xp.compareTo(xq) < 0) {
                xp = xp.add(this.p);
            }
            return xp.subtract(xq).multiply(this.coeff).mod(this.p).multiply(this.q).add(xq);
        };
        //#endregion PROTECTED
        //#region PUBLIC
        // RSAKey.prototype.setPublic = RSASetPublic;
        // Set the public key fields N and e from hex strings
        RSAKey.prototype.setPublic = function (N, E) {
            if (N != null && E != null && N.length > 0 && E.length > 0) {
                this.n = parseBigInt(N, 16);
                this.e = parseInt(E, 16);
            }
            else {
                console.error("Invalid RSA public key");
            }
        };
        // RSAKey.prototype.encrypt = RSAEncrypt;
        // Return the PKCS#1 RSA encryption of "text" as an even-length hex string
        RSAKey.prototype.encrypt = function (text) {
            var m = pkcs1pad2(text, (this.n.bitLength() + 7) >> 3);
            if (m == null) {
                return null;
            }
            var c = this.doPublic(m);
            if (c == null) {
                return null;
            }
            var h = c.toString(16);
            if ((h.length & 1) == 0) {
                return h;
            }
            else {
                return "0" + h;
            }
        };
        // RSAKey.prototype.setPrivate = RSASetPrivate;
        // Set the private key fields N, e, and d from hex strings
        RSAKey.prototype.setPrivate = function (N, E, D) {
            if (N != null && E != null && N.length > 0 && E.length > 0) {
                this.n = parseBigInt(N, 16);
                this.e = parseInt(E, 16);
                this.d = parseBigInt(D, 16);
            }
            else {
                console.error("Invalid RSA private key");
            }
        };
        // RSAKey.prototype.setPrivateEx = RSASetPrivateEx;
        // Set the private key fields N, e, d and CRT params from hex strings
        RSAKey.prototype.setPrivateEx = function (N, E, D, P, Q, DP, DQ, C) {
            if (N != null && E != null && N.length > 0 && E.length > 0) {
                this.n = parseBigInt(N, 16);
                this.e = parseInt(E, 16);
                this.d = parseBigInt(D, 16);
                this.p = parseBigInt(P, 16);
                this.q = parseBigInt(Q, 16);
                this.dmp1 = parseBigInt(DP, 16);
                this.dmq1 = parseBigInt(DQ, 16);
                this.coeff = parseBigInt(C, 16);
            }
            else {
                console.error("Invalid RSA private key");
            }
        };
        // RSAKey.prototype.generate = RSAGenerate;
        // Generate a new random private key B bits long, using public expt E
        RSAKey.prototype.generate = function (B, E) {
            var rng = new SecureRandom();
            var qs = B >> 1;
            this.e = parseInt(E, 16);
            var ee = new BigInteger(E, 16);
            for (;;) {
                for (;;) {
                    this.p = new BigInteger(B - qs, 1, rng);
                    if (this.p.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.p.isProbablePrime(10)) {
                        break;
                    }
                }
                for (;;) {
                    this.q = new BigInteger(qs, 1, rng);
                    if (this.q.subtract(BigInteger.ONE).gcd(ee).compareTo(BigInteger.ONE) == 0 && this.q.isProbablePrime(10)) {
                        break;
                    }
                }
                if (this.p.compareTo(this.q) <= 0) {
                    var t = this.p;
                    this.p = this.q;
                    this.q = t;
                }
                var p1 = this.p.subtract(BigInteger.ONE);
                var q1 = this.q.subtract(BigInteger.ONE);
                var phi = p1.multiply(q1);
                if (phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
                    this.n = this.p.multiply(this.q);
                    this.d = ee.modInverse(phi);
                    this.dmp1 = this.d.mod(p1);
                    this.dmq1 = this.d.mod(q1);
                    this.coeff = this.q.modInverse(this.p);
                    break;
                }
            }
        };
        // RSAKey.prototype.decrypt = RSADecrypt;
        // Return the PKCS#1 RSA decryption of "ctext".
        // "ctext" is an even-length hex string and the output is a plain string.
        RSAKey.prototype.decrypt = function (ctext) {
            var c = parseBigInt(ctext, 16);
            var m = this.doPrivate(c);
            if (m == null) {
                return null;
            }
            return pkcs1unpad2(m, (this.n.bitLength() + 7) >> 3);
        };
        // Generate a new random private key B bits long, using public expt E
        RSAKey.prototype.generateAsync = function (B, E, callback) {
            var rng = new SecureRandom();
            var qs = B >> 1;
            this.e = parseInt(E, 16);
            var ee = new BigInteger(E, 16);
            var rsa = this;
            // These functions have non-descript names because they were originally for(;;) loops.
            // I don‘t know about cryptography to give them better names than loop1-4.
            var loop1 = function () {
                var loop4 = function () {
                    if (rsa.p.compareTo(rsa.q) <= 0) {
                        var t = rsa.p;
                        rsa.p = rsa.q;
                        rsa.q = t;
                    }
                    var p1 = rsa.p.subtract(BigInteger.ONE);
                    var q1 = rsa.q.subtract(BigInteger.ONE);
                    var phi = p1.multiply(q1);
                    if (phi.gcd(ee).compareTo(BigInteger.ONE) == 0) {
                        rsa.n = rsa.p.multiply(rsa.q);
                        rsa.d = ee.modInverse(phi);
                        rsa.dmp1 = rsa.d.mod(p1);
                        rsa.dmq1 = rsa.d.mod(q1);
                        rsa.coeff = rsa.q.modInverse(rsa.p);
                        setTimeout(function () { callback(); }, 0); // escape
                    }
                    else {
                        setTimeout(loop1, 0);
                    }
                };
                var loop3 = function () {
                    rsa.q = nbi();
                    rsa.q.fromNumberAsync(qs, 1, rng, function () {
                        rsa.q.subtract(BigInteger.ONE).gcda(ee, function (r) {
                            if (r.compareTo(BigInteger.ONE) == 0 && rsa.q.isProbablePrime(10)) {
                                setTimeout(loop4, 0);
                            }
                            else {
                                setTimeout(loop3, 0);
                            }
                        });
                    });
                };
                var loop2 = function () {
                    rsa.p = nbi();
                    rsa.p.fromNumberAsync(B - qs, 1, rng, function () {
                        rsa.p.subtract(BigInteger.ONE).gcda(ee, function (r) {
                            if (r.compareTo(BigInteger.ONE) == 0 && rsa.p.isProbablePrime(10)) {
                                setTimeout(loop3, 0);
                            }
                            else {
                                setTimeout(loop2, 0);
                            }
                        });
                    });
                };
                setTimeout(loop2, 0);
            };
            setTimeout(loop1, 0);
        };
        RSAKey.prototype.sign = function (text, digestMethod, digestName) {
            var header = getDigestHeader(digestName);
            var digest = header + digestMethod(text).toString();
            var m = pkcs1pad1(digest, this.n.bitLength() / 4);
            if (m == null) {
                return null;
            }
            var c = this.doPrivate(m);
            if (c == null) {
                return null;
            }
            var h = c.toString(16);
            if ((h.length & 1) == 0) {
                return h;
            }
            else {
                return "0" + h;
            }
        };
        RSAKey.prototype.verify = function (text, signature, digestMethod) {
            var c = parseBigInt(signature, 16);
            var m = this.doPublic(c);
            if (m == null) {
                return null;
            }
            var unpadded = m.toString(16).replace(/^1f+00/, "");
            var digest = removeDigestHeader(unpadded);
            return digest == digestMethod(text).toString();
        };
        return RSAKey;
    }());
    // Undo PKCS#1 (type 2, random) padding and, if valid, return the plaintext
    function pkcs1unpad2(d, n) {
        var b = d.toByteArray();
        var i = 0;
        while (i < b.length && b[i] == 0) {
            ++i;
        }
        if (b.length - i != n - 1 || b[i] != 2) {
            return null;
        }
        ++i;
        while (b[i] != 0) {
            if (++i >= b.length) {
                return null;
            }
        }
        var ret = "";
        while (++i < b.length) {
            var c = b[i] & 255;
            if (c < 128) { // utf-8 decode
                ret += String.fromCharCode(c);
            }
            else if ((c > 191) && (c < 224)) {
                ret += String.fromCharCode(((c & 31) << 6) | (b[i + 1] & 63));
                ++i;
            }
            else {
                ret += String.fromCharCode(((c & 15) << 12) | ((b[i + 1] & 63) << 6) | (b[i + 2] & 63));
                i += 2;
            }
        }
        return ret;
    }
    // https://tools.ietf.org/html/rfc3447#page-43
    var DIGEST_HEADERS = {
        md2: "3020300c06082a864886f70d020205000410",
        md5: "3020300c06082a864886f70d020505000410",
        sha1: "3021300906052b0e03021a05000414",
        sha224: "302d300d06096086480165030402040500041c",
        sha256: "3031300d060960864801650304020105000420",
        sha384: "3041300d060960864801650304020205000430",
        sha512: "3051300d060960864801650304020305000440",
        ripemd160: "3021300906052b2403020105000414",
    };
    function getDigestHeader(name) {
        return DIGEST_HEADERS[name] || "";
    }
    function removeDigestHeader(str) {
        for (var name_1 in DIGEST_HEADERS) {
            if (DIGEST_HEADERS.hasOwnProperty(name_1)) {
                var header = DIGEST_HEADERS[name_1];
                var len = header.length;
                if (str.substr(0, len) == header) {
                    return str.substr(len);
                }
            }
        }
        return str;
    }
    // Return the PKCS#1 RSA encryption of "text" as a Base64-encoded string
    // function RSAEncryptB64(text) {
    //  var h = this.encrypt(text);
    //  if(h) return hex2b64(h); else return null;
    // }
    // public
    // RSAKey.prototype.encrypt_b64 = RSAEncryptB64;
    /*!
    Copyright (c) 2011, Yahoo! Inc. All rights reserved.
    Code licensed under the BSD License:
    http://developer.yahoo.com/yui/license.html
    version: 2.9.0
    */
    var YAHOO = {};
    YAHOO.lang = {
        /**
         * Utility to set up the prototype, constructor and superclass properties to
         * support an inheritance strategy that can chain constructors and methods.
         * Static members will not be inherited.
         *
         * @method extend
         * @static
         * @param {Function} subc   the object to modify
         * @param {Function} superc the object to inherit
         * @param {Object} overrides  additional properties/methods to add to the
         *                              subclass prototype.  These will override the
         *                              matching items obtained from the superclass
         *                              if present.
         */
        extend: function(subc, superc, overrides) {
            if (! superc || ! subc) {
                throw new Error("YAHOO.lang.extend failed, please check that " +
                    "all dependencies are included.");
            }
            var F = function() {};
            F.prototype = superc.prototype;
            subc.prototype = new F();
            subc.prototype.constructor = subc;
            subc.superclass = superc.prototype;
            if (superc.prototype.constructor == Object.prototype.constructor) {
                superc.prototype.constructor = superc;
            }
            if (overrides) {
                var i;
                for (i in overrides) {
                    subc.prototype[i] = overrides[i];
                }
                /*
                 * IE will not enumerate native functions in a derived object even if the
                 * function was overridden.  This is a workaround for specific functions
                 * we care about on the Object prototype.
                 * @property _IEEnumFix
                 * @param {Function} r  the object to receive the augmentation
                 * @param {Function} s  the object that supplies the properties to augment
                 * @static
                 * @private
                 */
                var _IEEnumFix = function() {},
                    ADD = ["toString", "valueOf"];
                try {
                    if (/MSIE/.test(navigator.userAgent)) {
                        _IEEnumFix = function(r, s) {
                            for (i = 0; i < ADD.length; i = i + 1) {
                                var fname = ADD[i], f = s[fname];
                                if (typeof f === ‘function‘ && f != Object.prototype[fname]) {
                                    r[fname] = f;
                                }
                            }
                        };
                    }
                } catch (ex) {}            _IEEnumFix(subc.prototype, overrides);
            }
        }
    };
    /* asn1-1.0.13.js (c) 2013-2017 Kenji Urushima | kjur.github.com/jsrsasign/license
     */
    /**
     * @fileOverview
     * @name asn1-1.0.js
     * @author Kenji Urushima kenji.urushima@gmail.com
     * @version asn1 1.0.13 (2017-Jun-02)
     * @since jsrsasign 2.1
     * @license <a href="https://kjur.github.io/jsrsasign/license/">MIT License</a>
     */
    /**
     * kjur‘s class library name space
     * <p>
     * This name space provides following name spaces:
     * <ul>
     * <li>{@link KJUR.asn1} - ASN.1 primitive hexadecimal encoder</li>
     * <li>{@link KJUR.asn1.x509} - ASN.1 structure for X.509 certificate and CRL</li>
     * <li>{@link KJUR.crypto} - Java Cryptographic Extension(JCE) style MessageDigest/Signature
     * class and utilities</li>
     * </ul>
     * </p>
     * NOTE: Please ignore method summary and document of this namespace. This caused by a bug of jsdoc2.
     * @name KJUR
     * @namespace kjur‘s class library name space
     */
    var KJUR = {};
    /**
     * kjur‘s ASN.1 class library name space
     * <p>
     * This is ITU-T X.690 ASN.1 DER encoder class library and
     * class structure and methods is very similar to
     * org.bouncycastle.asn1 package of
     * well known BouncyCaslte Cryptography Library.
     * <h4>PROVIDING ASN.1 PRIMITIVES</h4>
     * Here are ASN.1 DER primitive classes.
     * <ul>
     * <li>0x01 {@link KJUR.asn1.DERBoolean}</li>
     * <li>0x02 {@link KJUR.asn1.DERInteger}</li>
     * <li>0x03 {@link KJUR.asn1.DERBitString}</li>
     * <li>0x04 {@link KJUR.asn1.DEROctetString}</li>
     * <li>0x05 {@link KJUR.asn1.DERNull}</li>
     * <li>0x06 {@link KJUR.asn1.DERObjectIdentifier}</li>
     * <li>0x0a {@link KJUR.asn1.DEREnumerated}</li>
     * <li>0x0c {@link KJUR.asn1.DERUTF8String}</li>
     * <li>0x12 {@link KJUR.asn1.DERNumericString}</li>
     * <li>0x13 {@link KJUR.asn1.DERPrintableString}</li>
     * <li>0x14 {@link KJUR.asn1.DERTeletexString}</li>
     * <li>0x16 {@link KJUR.asn1.DERIA5String}</li>
     * <li>0x17 {@link KJUR.asn1.DERUTCTime}</li>
     * <li>0x18 {@link KJUR.asn1.DERGeneralizedTime}</li>
     * <li>0x30 {@link KJUR.asn1.DERSequence}</li>
     * <li>0x31 {@link KJUR.asn1.DERSet}</li>
     * </ul>
     * <h4>OTHER ASN.1 CLASSES</h4>
     * <ul>
     * <li>{@link KJUR.asn1.ASN1Object}</li>
     * <li>{@link KJUR.asn1.DERAbstractString}</li>
     * <li>{@link KJUR.asn1.DERAbstractTime}</li>
     * <li>{@link KJUR.asn1.DERAbstractStructured}</li>
     * <li>{@link KJUR.asn1.DERTaggedObject}</li>
     * </ul>
     * <h4>SUB NAME SPACES</h4>
     * <ul>
     * <li>{@link KJUR.asn1.cades} - CAdES long term signature format</li>
     * <li>{@link KJUR.asn1.cms} - Cryptographic Message Syntax</li>
     * <li>{@link KJUR.asn1.csr} - Certificate Signing Request (CSR/PKCS#10)</li>
     * <li>{@link KJUR.asn1.tsp} - RFC 3161 Timestamping Protocol Format</li>
     * <li>{@link KJUR.asn1.x509} - RFC 5280 X.509 certificate and CRL</li>
     * </ul>
     * </p>
     * NOTE: Please ignore method summary and document of this namespace.
     * This caused by a bug of jsdoc2.
     * @name KJUR.asn1
     * @namespace
     */
    if (typeof KJUR.asn1 == "undefined" || !KJUR.asn1) KJUR.asn1 = {};
    /**
     * ASN1 utilities class
     * @name KJUR.asn1.ASN1Util
     * @class ASN1 utilities class
     * @since asn1 1.0.2
     */
    KJUR.asn1.ASN1Util = new function() {
        this.integerToByteHex = function(i) {
            var h = i.toString(16);
            if ((h.length % 2) == 1) h = ‘0‘ + h;
            return h;
        };
        this.bigIntToMinTwosComplementsHex = function(bigIntegerValue) {
            var h = bigIntegerValue.toString(16);
            if (h.substr(0, 1) != ‘-‘) {
                if (h.length % 2 == 1) {
                    h = ‘0‘ + h;
                } else {
                    if (! h.match(/^[0-7]/)) {
                        h = ‘00‘ + h;
                    }
                }
            } else {
                var hPos = h.substr(1);
                var xorLen = hPos.length;
                if (xorLen % 2 == 1) {
                    xorLen += 1;
                } else {
                    if (! h.match(/^[0-7]/)) {
                        xorLen += 2;
                    }
                }
                var hMask = ‘‘;
                for (var i = 0; i < xorLen; i++) {
                    hMask += ‘f‘;
                }
                var biMask = new BigInteger(hMask, 16);
                var biNeg = biMask.xor(bigIntegerValue).add(BigInteger.ONE);
                h = biNeg.toString(16).replace(/^-/, ‘‘);
            }
            return h;
        };
        /**
         * get PEM string from hexadecimal data and header string
         * @name getPEMStringFromHex
         * @memberOf KJUR.asn1.ASN1Util
         * @function
         * @param {String} dataHex hexadecimal string of PEM body
         * @param {String} pemHeader PEM header string (ex. ‘RSA PRIVATE KEY‘)
         * @return {String} PEM formatted string of input data
         * @description
         * This method converts a hexadecimal string to a PEM string with
         * a specified header. Its line break will be CRLF("\r\n").
         * @example
         * var pem  = KJUR.asn1.ASN1Util.getPEMStringFromHex(‘616161‘, ‘RSA PRIVATE KEY‘);
         * // value of pem will be:
         * -----BEGIN PRIVATE KEY-----
         * YWFh
         * -----END PRIVATE KEY-----
         */
        this.getPEMStringFromHex = function(dataHex, pemHeader) {
            return hextopem(dataHex, pemHeader);
        };
        /**
         * generate ASN1Object specifed by JSON parameters
         * @name newObject
         * @memberOf KJUR.asn1.ASN1Util
         * @function
         * @param {Array} param JSON parameter to generate ASN1Object
         * @return {KJUR.asn1.ASN1Object} generated object
         * @since asn1 1.0.3
         * @description
         * generate any ASN1Object specified by JSON param
         * including ASN.1 primitive or structured.
         * Generally ‘param‘ can be described as follows:
         * <blockquote>
         * {TYPE-OF-ASNOBJ: ASN1OBJ-PARAMETER}
         * </blockquote>
         * ‘TYPE-OF-ASN1OBJ‘ can be one of following symbols:
         * <ul>
         * <li>‘bool‘ - DERBoolean</li>
         * <li>‘int‘ - DERInteger</li>
         * <li>‘bitstr‘ - DERBitString</li>
         * <li>‘octstr‘ - DEROctetString</li>
         * <li>‘null‘ - DERNull</li>
         * <li>‘oid‘ - DERObjectIdentifier</li>
         * <li>‘enum‘ - DEREnumerated</li>
         * <li>‘utf8str‘ - DERUTF8String</li>
         * <li>‘numstr‘ - DERNumericString</li>
         * <li>‘prnstr‘ - DERPrintableString</li>
         * <li>‘telstr‘ - DERTeletexString</li>
         * <li>‘ia5str‘ - DERIA5String</li>
         * <li>‘utctime‘ - DERUTCTime</li>
         * <li>‘gentime‘ - DERGeneralizedTime</li>
         * <li>‘seq‘ - DERSequence</li>
         * <li>‘set‘ - DERSet</li>
         * <li>‘tag‘ - DERTaggedObject</li>
         * </ul>
         * @example
         * newObject({‘prnstr‘: ‘aaa‘});
         * newObject({‘seq‘: [{‘int‘: 3}, {‘prnstr‘: ‘aaa‘}]})
         * // ASN.1 Tagged Object
         * newObject({‘tag‘: {‘tag‘: ‘a1‘,
         *                    ‘explicit‘: true,
         *                    ‘obj‘: {‘seq‘: [{‘int‘: 3}, {‘prnstr‘: ‘aaa‘}]}}});
         * // more simple representation of ASN.1 Tagged Object
         * newObject({‘tag‘: [‘a1‘,
         *                    true,
         *                    {‘seq‘: [
         *                      {‘int‘: 3},
         *                      {‘prnstr‘: ‘aaa‘}]}
         *                   ]});
         */
        this.newObject = function(param) {
            var _KJUR = KJUR,
                _KJUR_asn1 = _KJUR.asn1,
                _DERBoolean = _KJUR_asn1.DERBoolean,
                _DERInteger = _KJUR_asn1.DERInteger,
                _DERBitString = _KJUR_asn1.DERBitString,
                _DEROctetString = _KJUR_asn1.DEROctetString,
                _DERNull = _KJUR_asn1.DERNull,
                _DERObjectIdentifier = _KJUR_asn1.DERObjectIdentifier,
                _DEREnumerated = _KJUR_asn1.DEREnumerated,
                _DERUTF8String = _KJUR_asn1.DERUTF8String,
                _DERNumericString = _KJUR_asn1.DERNumericString,
                _DERPrintableString = _KJUR_asn1.DERPrintableString,
                _DERTeletexString = _KJUR_asn1.DERTeletexString,
                _DERIA5String = _KJUR_asn1.DERIA5String,
                _DERUTCTime = _KJUR_asn1.DERUTCTime,
                _DERGeneralizedTime = _KJUR_asn1.DERGeneralizedTime,
                _DERSequence = _KJUR_asn1.DERSequence,
                _DERSet = _KJUR_asn1.DERSet,
                _DERTaggedObject = _KJUR_asn1.DERTaggedObject,
                _newObject = _KJUR_asn1.ASN1Util.newObject;
            var keys = Object.keys(param);
            if (keys.length != 1)
                throw "key of param shall be only one.";
            var key = keys[0];
            if (":bool:int:bitstr:octstr:null:oid:enum:utf8str:numstr:prnstr:telstr:ia5str:utctime:gentime:seq:set:tag:".indexOf(":" + key + ":") == -1)
                throw "undefined key: " + key;
            if (key == "bool")    return new _DERBoolean(param[key]);
            if (key == "int")     return new _DERInteger(param[key]);
            if (key == "bitstr")  return new _DERBitString(param[key]);
            if (key == "octstr")  return new _DEROctetString(param[key]);
            if (key == "null")    return new _DERNull(param[key]);
            if (key == "oid")     return new _DERObjectIdentifier(param[key]);
            if (key == "enum")    return new _DEREnumerated(param[key]);
            if (key == "utf8str") return new _DERUTF8String(param[key]);
            if (key == "numstr")  return new _DERNumericString(param[key]);
            if (key == "prnstr")  return new _DERPrintableString(param[key]);
            if (key == "telstr")  return new _DERTeletexString(param[key]);
            if (key == "ia5str")  return new _DERIA5String(param[key]);
            if (key == "utctime") return new _DERUTCTime(param[key]);
            if (key == "gentime") return new _DERGeneralizedTime(param[key]);
            if (key == "seq") {
                var paramList = param[key];
                var a = [];
                for (var i = 0; i < paramList.length; i++) {
                    var asn1Obj = _newObject(paramList[i]);
                    a.push(asn1Obj);
                }
                return new _DERSequence({‘array‘: a});
            }
            if (key == "set") {
                var paramList = param[key];
                var a = [];
                for (var i = 0; i < paramList.length; i++) {
                    var asn1Obj = _newObject(paramList[i]);
                    a.push(asn1Obj);
                }
                return new _DERSet({‘array‘: a});
            }
            if (key == "tag") {
                var tagParam = param[key];
                if (Object.prototype.toString.call(tagParam) === ‘[object Array]‘ &&
                    tagParam.length == 3) {
                    var obj = _newObject(tagParam[2]);
                    return new _DERTaggedObject({tag: tagParam[0],
                        explicit: tagParam[1],
                        obj: obj});
                } else {
                    var newParam = {};
                    if (tagParam.explicit !== undefined)
                        newParam.explicit = tagParam.explicit;
                    if (tagParam.tag !== undefined)
                        newParam.tag = tagParam.tag;
                    if (tagParam.obj === undefined)
                        throw "obj shall be specified for ‘tag‘.";
                    newParam.obj = _newObject(tagParam.obj);
                    return new _DERTaggedObject(newParam);
                }
            }
        };
        /**
         * get encoded hexadecimal string of ASN1Object specifed by JSON parameters
         * @name jsonToASN1HEX
         * @memberOf KJUR.asn1.ASN1Util
         * @function
         * @param {Array} param JSON parameter to generate ASN1Object
         * @return hexadecimal string of ASN1Object
         * @since asn1 1.0.4
         * @description
         * As for ASN.1 object representation of JSON object,
         * please see {@link newObject}.
         * @example
         * jsonToASN1HEX({‘prnstr‘: ‘aaa‘});
         */
        this.jsonToASN1HEX = function(param) {
            var asn1Obj = this.newObject(param);
            return asn1Obj.getEncodedHex();
        };
    };
    /**
     * get dot noted oid number string from hexadecimal value of OID
     * @name oidHexToInt
     * @memberOf KJUR.asn1.ASN1Util
     * @function
     * @param {String} hex hexadecimal value of object identifier
     * @return {String} dot noted string of object identifier
     * @since jsrsasign 4.8.3 asn1 1.0.7
     * @description
     * This static method converts from hexadecimal string representation of
     * ASN.1 value of object identifier to oid number string.
     * @example
     * KJUR.asn1.ASN1Util.oidHexToInt(‘550406‘) &rarr; "2.5.4.6"
     */
    KJUR.asn1.ASN1Util.oidHexToInt = function(hex) {
        var s = "";
        var i01 = parseInt(hex.substr(0, 2), 16);
        var i0 = Math.floor(i01 / 40);
        var i1 = i01 % 40;
        var s = i0 + "." + i1;
        var binbuf = "";
        for (var i = 2; i < hex.length; i += 2) {
            var value = parseInt(hex.substr(i, 2), 16);
            var bin = ("00000000" + value.toString(2)).slice(- 8);
            binbuf = binbuf + bin.substr(1, 7);
            if (bin.substr(0, 1) == "0") {
                var bi = new BigInteger(binbuf, 2);
                s = s + "." + bi.toString(10);
                binbuf = "";
            }
        }
        return s;
    };
    /**
     * get hexadecimal value of object identifier from dot noted oid value
     * @name oidIntToHex
     * @memberOf KJUR.asn1.ASN1Util
     * @function
     * @param {String} oidString dot noted string of object identifier
     * @return {String} hexadecimal value of object identifier
     * @since jsrsasign 4.8.3 asn1 1.0.7
     * @description
     * This static method converts from object identifier value string.
     * to hexadecimal string representation of it.
     * @example
     * KJUR.asn1.ASN1Util.oidIntToHex("2.5.4.6") &rarr; "550406"
     */
    KJUR.asn1.ASN1Util.oidIntToHex = function(oidString) {
        var itox = function(i) {
            var h = i.toString(16);
            if (h.length == 1) h = ‘0‘ + h;
            return h;
        };
        var roidtox = function(roid) {
            var h = ‘‘;
            var bi = new BigInteger(roid, 10);
            var b = bi.toString(2);
            var padLen = 7 - b.length % 7;
            if (padLen == 7) padLen = 0;
            var bPad = ‘‘;
            for (var i = 0; i < padLen; i++) bPad += ‘0‘;
            b = bPad + b;
            for (var i = 0; i < b.length - 1; i += 7) {
                var b8 = b.substr(i, 7);
                if (i != b.length - 7) b8 = ‘1‘ + b8;
                h += itox(parseInt(b8, 2));
            }
            return h;
        };
        if (! oidString.match(/^[0-9.]+$/)) {
            throw "malformed oid string: " + oidString;
        }
        var h = ‘‘;
        var a = oidString.split(‘.‘);
        var i0 = parseInt(a[0]) * 40 + parseInt(a[1]);
        h += itox(i0);
        a.splice(0, 2);
        for (var i = 0; i < a.length; i++) {
            h += roidtox(a[i]);
        }
        return h;
    };
    // ********************************************************************
    //  Abstract ASN.1 Classes
    // ********************************************************************
    // ********************************************************************
    /**
     * base class for ASN.1 DER encoder object
     * @name KJUR.asn1.ASN1Object
     * @class base class for ASN.1 DER encoder object
     * @property {Boolean} isModified flag whether internal data was changed
     * @property {String} hTLV hexadecimal string of ASN.1 TLV
     * @property {String} hT hexadecimal string of ASN.1 TLV tag(T)
     * @property {String} hL hexadecimal string of ASN.1 TLV length(L)
     * @property {String} hV hexadecimal string of ASN.1 TLV value(V)
     * @description
     */
    KJUR.asn1.ASN1Object = function() {
        var hV = ‘‘;
        /**
         * get hexadecimal ASN.1 TLV length(L) bytes from TLV value(V)
         * @name getLengthHexFromValue
         * @memberOf KJUR.asn1.ASN1Object#
         * @function
         * @return {String} hexadecimal string of ASN.1 TLV length(L)
         */
        this.getLengthHexFromValue = function() {
            if (typeof this.hV == "undefined" || this.hV == null) {
                throw "this.hV is null or undefined.";
            }
            if (this.hV.length % 2 == 1) {
                throw "value hex must be even length: n=" + hV.length + ",v=" + this.hV;
            }
            var n = this.hV.length / 2;
            var hN = n.toString(16);
            if (hN.length % 2 == 1) {
                hN = "0" + hN;
            }
            if (n < 128) {
                return hN;
            } else {
                var hNlen = hN.length / 2;
                if (hNlen > 15) {
                    throw "ASN.1 length too long to represent by 8x: n = " + n.toString(16);
                }
                var head = 128 + hNlen;
                return head.toString(16) + hN;
            }
        };
        /**
         * get hexadecimal string of ASN.1 TLV bytes
         * @name getEncodedHex
         * @memberOf KJUR.asn1.ASN1Object#
         * @function
         * @return {String} hexadecimal string of ASN.1 TLV
         */
        this.getEncodedHex = function() {
            if (this.hTLV == null || this.isModified) {
                this.hV = this.getFreshValueHex();
                this.hL = this.getLengthHexFromValue();
                this.hTLV = this.hT + this.hL + this.hV;
                this.isModified = false;
                //alert("first time: " + this.hTLV);
            }
            return this.hTLV;
        };
        /**
         * get hexadecimal string of ASN.1 TLV value(V) bytes
         * @name getValueHex
         * @memberOf KJUR.asn1.ASN1Object#
         * @function
         * @return {String} hexadecimal string of ASN.1 TLV value(V) bytes
         */
        this.getValueHex = function() {
            this.getEncodedHex();
            return this.hV;
        };
        this.getFreshValueHex = function() {
            return ‘‘;
        };
    };
    // == BEGIN DERAbstractString ================================================
    /**
     * base class for ASN.1 DER string classes
     * @name KJUR.asn1.DERAbstractString
     * @class base class for ASN.1 DER string classes
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘aaa‘})
     * @property {String} s internal string of value
     * @extends KJUR.asn1.ASN1Object
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>str - specify initial ASN.1 value(V) by a string</li>
     * <li>hex - specify initial ASN.1 value(V) by a hexadecimal string</li>
     * </ul>
     * NOTE: ‘params‘ can be omitted.
     */
    KJUR.asn1.DERAbstractString = function(params) {
        KJUR.asn1.DERAbstractString.superclass.constructor.call(this);
        /**
         * get string value of this string object
         * @name getString
         * @memberOf KJUR.asn1.DERAbstractString#
         * @function
         * @return {String} string value of this string object
         */
        this.getString = function() {
            return this.s;
        };
        /**
         * set value by a string
         * @name setString
         * @memberOf KJUR.asn1.DERAbstractString#
         * @function
         * @param {String} newS value by a string to set
         */
        this.setString = function(newS) {
            this.hTLV = null;
            this.isModified = true;
            this.s = newS;
            this.hV = stohex(this.s);
        };
        /**
         * set value by a hexadecimal string
         * @name setStringHex
         * @memberOf KJUR.asn1.DERAbstractString#
         * @function
         * @param {String} newHexString value by a hexadecimal string to set
         */
        this.setStringHex = function(newHexString) {
            this.hTLV = null;
            this.isModified = true;
            this.s = null;
            this.hV = newHexString;
        };
        this.getFreshValueHex = function() {
            return this.hV;
        };
        if (typeof params != "undefined") {
            if (typeof params == "string") {
                this.setString(params);
            } else if (typeof params[‘str‘] != "undefined") {
                this.setString(params[‘str‘]);
            } else if (typeof params[‘hex‘] != "undefined") {
                this.setStringHex(params[‘hex‘]);
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERAbstractString, KJUR.asn1.ASN1Object);
    // == END   DERAbstractString ================================================
    // == BEGIN DERAbstractTime ==================================================
    /**
     * base class for ASN.1 DER Generalized/UTCTime class
     * @name KJUR.asn1.DERAbstractTime
     * @class base class for ASN.1 DER Generalized/UTCTime class
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘130430235959Z‘})
     * @extends KJUR.asn1.ASN1Object
     * @description
     * @see KJUR.asn1.ASN1Object - superclass
     */
    KJUR.asn1.DERAbstractTime = function(params) {
        KJUR.asn1.DERAbstractTime.superclass.constructor.call(this);
        // --- PRIVATE METHODS --------------------
        this.localDateToUTC = function(d) {
            utc = d.getTime() + (d.getTimezoneOffset() * 60000);
            var utcDate = new Date(utc);
            return utcDate;
        };
        /*
         * format date string by Data object
         * @name formatDate
         * @memberOf KJUR.asn1.AbstractTime;
         * @param {Date} dateObject
         * @param {string} type ‘utc‘ or ‘gen‘
         * @param {boolean} withMillis flag for with millisections or not
         * @description
         * ‘withMillis‘ flag is supported from asn1 1.0.6.
         */
        this.formatDate = function(dateObject, type, withMillis) {
            var pad = this.zeroPadding;
            var d = this.localDateToUTC(dateObject);
            var year = String(d.getFullYear());
            if (type == ‘utc‘) year = year.substr(2, 2);
            var month = pad(String(d.getMonth() + 1), 2);
            var day = pad(String(d.getDate()), 2);
            var hour = pad(String(d.getHours()), 2);
            var min = pad(String(d.getMinutes()), 2);
            var sec = pad(String(d.getSeconds()), 2);
            var s = year + month + day + hour + min + sec;
            if (withMillis === true) {
                var millis = d.getMilliseconds();
                if (millis != 0) {
                    var sMillis = pad(String(millis), 3);
                    sMillis = sMillis.replace(/[0]+$/, "");
                    s = s + "." + sMillis;
                }
            }
            return s + "Z";
        };
        this.zeroPadding = function(s, len) {
            if (s.length >= len) return s;
            return new Array(len - s.length + 1).join(‘0‘) + s;
        };
        // --- PUBLIC METHODS --------------------
        /**
         * get string value of this string object
         * @name getString
         * @memberOf KJUR.asn1.DERAbstractTime#
         * @function
         * @return {String} string value of this time object
         */
        this.getString = function() {
            return this.s;
        };
        /**
         * set value by a string
         * @name setString
         * @memberOf KJUR.asn1.DERAbstractTime#
         * @function
         * @param {String} newS value by a string to set such like "130430235959Z"
         */
        this.setString = function(newS) {
            this.hTLV = null;
            this.isModified = true;
            this.s = newS;
            this.hV = stohex(newS);
        };
        /**
         * set value by a Date object
         * @name setByDateValue
         * @memberOf KJUR.asn1.DERAbstractTime#
         * @function
         * @param {Integer} year year of date (ex. 2013)
         * @param {Integer} month month of date between 1 and 12 (ex. 12)
         * @param {Integer} day day of month
         * @param {Integer} hour hours of date
         * @param {Integer} min minutes of date
         * @param {Integer} sec seconds of date
         */
        this.setByDateValue = function(year, month, day, hour, min, sec) {
            var dateObject = new Date(Date.UTC(year, month - 1, day, hour, min, sec, 0));
            this.setByDate(dateObject);
        };
        this.getFreshValueHex = function() {
            return this.hV;
        };
    };
    YAHOO.lang.extend(KJUR.asn1.DERAbstractTime, KJUR.asn1.ASN1Object);
    // == END   DERAbstractTime ==================================================
    // == BEGIN DERAbstractStructured ============================================
    /**
     * base class for ASN.1 DER structured class
     * @name KJUR.asn1.DERAbstractStructured
     * @class base class for ASN.1 DER structured class
     * @property {Array} asn1Array internal array of ASN1Object
     * @extends KJUR.asn1.ASN1Object
     * @description
     * @see KJUR.asn1.ASN1Object - superclass
     */
    KJUR.asn1.DERAbstractStructured = function(params) {
        KJUR.asn1.DERAbstractString.superclass.constructor.call(this);
        /**
         * set value by array of ASN1Object
         * @name setByASN1ObjectArray
         * @memberOf KJUR.asn1.DERAbstractStructured#
         * @function
         * @param {array} asn1ObjectArray array of ASN1Object to set
         */
        this.setByASN1ObjectArray = function(asn1ObjectArray) {
            this.hTLV = null;
            this.isModified = true;
            this.asn1Array = asn1ObjectArray;
        };
        /**
         * append an ASN1Object to internal array
         * @name appendASN1Object
         * @memberOf KJUR.asn1.DERAbstractStructured#
         * @function
         * @param {ASN1Object} asn1Object to add
         */
        this.appendASN1Object = function(asn1Object) {
            this.hTLV = null;
            this.isModified = true;
            this.asn1Array.push(asn1Object);
        };
        this.asn1Array = new Array();
        if (typeof params != "undefined") {
            if (typeof params[‘array‘] != "undefined") {
                this.asn1Array = params[‘array‘];
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERAbstractStructured, KJUR.asn1.ASN1Object);
    // ********************************************************************
    //  ASN.1 Object Classes
    // ********************************************************************
    // ********************************************************************
    /**
     * class for ASN.1 DER Boolean
     * @name KJUR.asn1.DERBoolean
     * @class class for ASN.1 DER Boolean
     * @extends KJUR.asn1.ASN1Object
     * @description
     * @see KJUR.asn1.ASN1Object - superclass
     */
    KJUR.asn1.DERBoolean = function() {
        KJUR.asn1.DERBoolean.superclass.constructor.call(this);
        this.hT = "01";
        this.hTLV = "0101ff";
    };
    YAHOO.lang.extend(KJUR.asn1.DERBoolean, KJUR.asn1.ASN1Object);
    // ********************************************************************
    /**
     * class for ASN.1 DER Integer
     * @name KJUR.asn1.DERInteger
     * @class class for ASN.1 DER Integer
     * @extends KJUR.asn1.ASN1Object
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>int - specify initial ASN.1 value(V) by integer value</li>
     * <li>bigint - specify initial ASN.1 value(V) by BigInteger object</li>
     * <li>hex - specify initial ASN.1 value(V) by a hexadecimal string</li>
     * </ul>
     * NOTE: ‘params‘ can be omitted.
     */
    KJUR.asn1.DERInteger = function(params) {
        KJUR.asn1.DERInteger.superclass.constructor.call(this);
        this.hT = "02";
        /**
         * set value by Tom Wu‘s BigInteger object
         * @name setByBigInteger
         * @memberOf KJUR.asn1.DERInteger#
         * @function
         * @param {BigInteger} bigIntegerValue to set
         */
        this.setByBigInteger = function(bigIntegerValue) {
            this.hTLV = null;
            this.isModified = true;
            this.hV = KJUR.asn1.ASN1Util.bigIntToMinTwosComplementsHex(bigIntegerValue);
        };
        /**
         * set value by integer value
         * @name setByInteger
         * @memberOf KJUR.asn1.DERInteger
         * @function
         * @param {Integer} integer value to set
         */
        this.setByInteger = function(intValue) {
            var bi = new BigInteger(String(intValue), 10);
            this.setByBigInteger(bi);
        };
        /**
         * set value by integer value
         * @name setValueHex
         * @memberOf KJUR.asn1.DERInteger#
         * @function
         * @param {String} hexadecimal string of integer value
         * @description
         * <br/>
         * NOTE: Value shall be represented by minimum octet length of
         * two‘s complement representation.
         * @example
         * new KJUR.asn1.DERInteger(123);
         * new KJUR.asn1.DERInteger({‘int‘: 123});
         * new KJUR.asn1.DERInteger({‘hex‘: ‘1fad‘});
         */
        this.setValueHex = function(newHexString) {
            this.hV = newHexString;
        };
        this.getFreshValueHex = function() {
            return this.hV;
        };
        if (typeof params != "undefined") {
            if (typeof params[‘bigint‘] != "undefined") {
                this.setByBigInteger(params[‘bigint‘]);
            } else if (typeof params[‘int‘] != "undefined") {
                this.setByInteger(params[‘int‘]);
            } else if (typeof params == "number") {
                this.setByInteger(params);
            } else if (typeof params[‘hex‘] != "undefined") {
                this.setValueHex(params[‘hex‘]);
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERInteger, KJUR.asn1.ASN1Object);
    // ********************************************************************
    /**
     * class for ASN.1 DER encoded BitString primitive
     * @name KJUR.asn1.DERBitString
     * @class class for ASN.1 DER encoded BitString primitive
     * @extends KJUR.asn1.ASN1Object
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>bin - specify binary string (ex. ‘10111‘)</li>
     * <li>array - specify array of boolean (ex. [true,false,true,true])</li>
     * <li>hex - specify hexadecimal string of ASN.1 value(V) including unused bits</li>
     * <li>obj - specify {@link KJUR.asn1.ASN1Util.newObject}
     * argument for "BitString encapsulates" structure.</li>
     * </ul>
     * NOTE1: ‘params‘ can be omitted.<br/>
     * NOTE2: ‘obj‘ parameter have been supported since
     * asn1 1.0.11, jsrsasign 6.1.1 (2016-Sep-25).<br/>
     * @example
     * // default constructor
     * o = new KJUR.asn1.DERBitString();
     * // initialize with binary string
     * o = new KJUR.asn1.DERBitString({bin: "1011"});
     * // initialize with boolean array
     * o = new KJUR.asn1.DERBitString({array: [true,false,true,true]});
     * // initialize with hexadecimal string (04 is unused bits)
     * o = new KJUR.asn1.DEROctetString({hex: "04bac0"});
     * // initialize with ASN1Util.newObject argument for encapsulated
     * o = new KJUR.asn1.DERBitString({obj: {seq: [{int: 3}, {prnstr: ‘aaa‘}]}});
     * // above generates a ASN.1 data like this:
     * // BIT STRING, encapsulates {
     * //   SEQUENCE {
     * //     INTEGER 3
     * //     PrintableString ‘aaa‘
     * //     }
     * //   }
     */
    KJUR.asn1.DERBitString = function(params) {
        if (params !== undefined && typeof params.obj !== "undefined") {
            var o = KJUR.asn1.ASN1Util.newObject(params.obj);
            params.hex = "00" + o.getEncodedHex();
        }
        KJUR.asn1.DERBitString.superclass.constructor.call(this);
        this.hT = "03";
        /**
         * set ASN.1 value(V) by a hexadecimal string including unused bits
         * @name setHexValueIncludingUnusedBits
         * @memberOf KJUR.asn1.DERBitString#
         * @function
         * @param {String} newHexStringIncludingUnusedBits
         */
        this.setHexValueIncludingUnusedBits = function(newHexStringIncludingUnusedBits) {
            this.hTLV = null;
            this.isModified = true;
            this.hV = newHexStringIncludingUnusedBits;
        };
        /**
         * set ASN.1 value(V) by unused bit and hexadecimal string of value
         * @name setUnusedBitsAndHexValue
         * @memberOf KJUR.asn1.DERBitString#
         * @function
         * @param {Integer} unusedBits
         * @param {String} hValue
         */
        this.setUnusedBitsAndHexValue = function(unusedBits, hValue) {
            if (unusedBits < 0 || 7 < unusedBits) {
                throw "unused bits shall be from 0 to 7: u = " + unusedBits;
            }
            var hUnusedBits = "0" + unusedBits;
            this.hTLV = null;
            this.isModified = true;
            this.hV = hUnusedBits + hValue;
        };
        /**
         * set ASN.1 DER BitString by binary string<br/>
         * @name setByBinaryString
         * @memberOf KJUR.asn1.DERBitString#
         * @function
         * @param {String} binaryString binary value string (i.e. ‘10111‘)
         * @description
         * Its unused bits will be calculated automatically by length of
         * ‘binaryValue‘. <br/>
         * NOTE: Trailing zeros ‘0‘ will be ignored.
         * @example
         * o = new KJUR.asn1.DERBitString();
         * o.setByBooleanArray("01011");
         */
        this.setByBinaryString = function(binaryString) {
            binaryString = binaryString.replace(/0+$/, ‘‘);
            var unusedBits = 8 - binaryString.length % 8;
            if (unusedBits == 8) unusedBits = 0;
            for (var i = 0; i <= unusedBits; i++) {
                binaryString += ‘0‘;
            }
            var h = ‘‘;
            for (var i = 0; i < binaryString.length - 1; i += 8) {
                var b = binaryString.substr(i, 8);
                var x = parseInt(b, 2).toString(16);
                if (x.length == 1) x = ‘0‘ + x;
                h += x;
            }
            this.hTLV = null;
            this.isModified = true;
            this.hV = ‘0‘ + unusedBits + h;
        };
        /**
         * set ASN.1 TLV value(V) by an array of boolean<br/>
         * @name setByBooleanArray
         * @memberOf KJUR.asn1.DERBitString#
         * @function
         * @param {array} booleanArray array of boolean (ex. [true, false, true])
         * @description
         * NOTE: Trailing falses will be ignored in the ASN.1 DER Object.
         * @example
         * o = new KJUR.asn1.DERBitString();
         * o.setByBooleanArray([false, true, false, true, true]);
         */
        this.setByBooleanArray = function(booleanArray) {
            var s = ‘‘;
            for (var i = 0; i < booleanArray.length; i++) {
                if (booleanArray[i] == true) {
                    s += ‘1‘;
                } else {
                    s += ‘0‘;
                }
            }
            this.setByBinaryString(s);
        };
        /**
         * generate an array of falses with specified length<br/>
         * @name newFalseArray
         * @memberOf KJUR.asn1.DERBitString
         * @function
         * @param {Integer} nLength length of array to generate
         * @return {array} array of boolean falses
         * @description
         * This static method may be useful to initialize boolean array.
         * @example
         * o = new KJUR.asn1.DERBitString();
         * o.newFalseArray(3) &rarr; [false, false, false]
         */
        this.newFalseArray = function(nLength) {
            var a = new Array(nLength);
            for (var i = 0; i < nLength; i++) {
                a[i] = false;
            }
            return a;
        };
        this.getFreshValueHex = function() {
            return this.hV;
        };
        if (typeof params != "undefined") {
            if (typeof params == "string" && params.toLowerCase().match(/^[0-9a-f]+$/)) {
                this.setHexValueIncludingUnusedBits(params);
            } else if (typeof params[‘hex‘] != "undefined") {
                this.setHexValueIncludingUnusedBits(params[‘hex‘]);
            } else if (typeof params[‘bin‘] != "undefined") {
                this.setByBinaryString(params[‘bin‘]);
            } else if (typeof params[‘array‘] != "undefined") {
                this.setByBooleanArray(params[‘array‘]);
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERBitString, KJUR.asn1.ASN1Object);
    // ********************************************************************
    /**
     * class for ASN.1 DER OctetString<br/>
     * @name KJUR.asn1.DEROctetString
     * @class class for ASN.1 DER OctetString
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘aaa‘})
     * @extends KJUR.asn1.DERAbstractString
     * @description
     * This class provides ASN.1 OctetString simple type.<br/>
     * Supported "params" attributes are:
     * <ul>
     * <li>str - to set a string as a value</li>
     * <li>hex - to set a hexadecimal string as a value</li>
     * <li>obj - to set a encapsulated ASN.1 value by JSON object
     * which is defined in {@link KJUR.asn1.ASN1Util.newObject}</li>
     * </ul>
     * NOTE: A parameter ‘obj‘ have been supported
     * for "OCTET STRING, encapsulates" structure.
     * since asn1 1.0.11, jsrsasign 6.1.1 (2016-Sep-25).
     * @see KJUR.asn1.DERAbstractString - superclass
     * @example
     * // default constructor
     * o = new KJUR.asn1.DEROctetString();
     * // initialize with string
     * o = new KJUR.asn1.DEROctetString({str: "aaa"});
     * // initialize with hexadecimal string
     * o = new KJUR.asn1.DEROctetString({hex: "616161"});
     * // initialize with ASN1Util.newObject argument
     * o = new KJUR.asn1.DEROctetString({obj: {seq: [{int: 3}, {prnstr: ‘aaa‘}]}});
     * // above generates a ASN.1 data like this:
     * // OCTET STRING, encapsulates {
     * //   SEQUENCE {
     * //     INTEGER 3
     * //     PrintableString ‘aaa‘
     * //     }
     * //   }
     */
    KJUR.asn1.DEROctetString = function(params) {
        if (params !== undefined && typeof params.obj !== "undefined") {
            var o = KJUR.asn1.ASN1Util.newObject(params.obj);
            params.hex = o.getEncodedHex();
        }
        KJUR.asn1.DEROctetString.superclass.constructor.call(this, params);
        this.hT = "04";
    };
    YAHOO.lang.extend(KJUR.asn1.DEROctetString, KJUR.asn1.DERAbstractString);
    // ********************************************************************
    /**
     * class for ASN.1 DER Null
     * @name KJUR.asn1.DERNull
     * @class class for ASN.1 DER Null
     * @extends KJUR.asn1.ASN1Object
     * @description
     * @see KJUR.asn1.ASN1Object - superclass
     */
    KJUR.asn1.DERNull = function() {
        KJUR.asn1.DERNull.superclass.constructor.call(this);
        this.hT = "05";
        this.hTLV = "0500";
    };
    YAHOO.lang.extend(KJUR.asn1.DERNull, KJUR.asn1.ASN1Object);
    // ********************************************************************
    /**
     * class for ASN.1 DER ObjectIdentifier
     * @name KJUR.asn1.DERObjectIdentifier
     * @class class for ASN.1 DER ObjectIdentifier
     * @param {Array} params associative array of parameters (ex. {‘oid‘: ‘2.5.4.5‘})
     * @extends KJUR.asn1.ASN1Object
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>oid - specify initial ASN.1 value(V) by a oid string (ex. 2.5.4.13)</li>
     * <li>hex - specify initial ASN.1 value(V) by a hexadecimal string</li>
     * </ul>
     * NOTE: ‘params‘ can be omitted.
     */
    KJUR.asn1.DERObjectIdentifier = function(params) {
        var itox = function(i) {
            var h = i.toString(16);
            if (h.length == 1) h = ‘0‘ + h;
            return h;
        };
        var roidtox = function(roid) {
            var h = ‘‘;
            var bi = new BigInteger(roid, 10);
            var b = bi.toString(2);
            var padLen = 7 - b.length % 7;
            if (padLen == 7) padLen = 0;
            var bPad = ‘‘;
            for (var i = 0; i < padLen; i++) bPad += ‘0‘;
            b = bPad + b;
            for (var i = 0; i < b.length - 1; i += 7) {
                var b8 = b.substr(i, 7);
                if (i != b.length - 7) b8 = ‘1‘ + b8;
                h += itox(parseInt(b8, 2));
            }
            return h;
        };
        KJUR.asn1.DERObjectIdentifier.superclass.constructor.call(this);
        this.hT = "06";
        /**
         * set value by a hexadecimal string
         * @name setValueHex
         * @memberOf KJUR.asn1.DERObjectIdentifier#
         * @function
         * @param {String} newHexString hexadecimal value of OID bytes
         */
        this.setValueHex = function(newHexString) {
            this.hTLV = null;
            this.isModified = true;
            this.s = null;
            this.hV = newHexString;
        };
        /**
         * set value by a OID string<br/>
         * @name setValueOidString
         * @memberOf KJUR.asn1.DERObjectIdentifier#
         * @function
         * @param {String} oidString OID string (ex. 2.5.4.13)
         * @example
         * o = new KJUR.asn1.DERObjectIdentifier();
         * o.setValueOidString("2.5.4.13");
         */
        this.setValueOidString = function(oidString) {
            if (! oidString.match(/^[0-9.]+$/)) {
                throw "malformed oid string: " + oidString;
            }
            var h = ‘‘;
            var a = oidString.split(‘.‘);
            var i0 = parseInt(a[0]) * 40 + parseInt(a[1]);
            h += itox(i0);
            a.splice(0, 2);
            for (var i = 0; i < a.length; i++) {
                h += roidtox(a[i]);
            }
            this.hTLV = null;
            this.isModified = true;
            this.s = null;
            this.hV = h;
        };
        /**
         * set value by a OID name
         * @name setValueName
         * @memberOf KJUR.asn1.DERObjectIdentifier#
         * @function
         * @param {String} oidName OID name (ex. ‘serverAuth‘)
         * @since 1.0.1
         * @description
         * OID name shall be defined in ‘KJUR.asn1.x509.OID.name2oidList‘.
         * Otherwise raise error.
         * @example
         * o = new KJUR.asn1.DERObjectIdentifier();
         * o.setValueName("serverAuth");
         */
        this.setValueName = function(oidName) {
            var oid = KJUR.asn1.x509.OID.name2oid(oidName);
            if (oid !== ‘‘) {
                this.setValueOidString(oid);
            } else {
                throw "DERObjectIdentifier oidName undefined: " + oidName;
            }
        };
        this.getFreshValueHex = function() {
            return this.hV;
        };
        if (params !== undefined) {
            if (typeof params === "string") {
                if (params.match(/^[0-2].[0-9.]+$/)) {
                    this.setValueOidString(params);
                } else {
                    this.setValueName(params);
                }
            } else if (params.oid !== undefined) {
                this.setValueOidString(params.oid);
            } else if (params.hex !== undefined) {
                this.setValueHex(params.hex);
            } else if (params.name !== undefined) {
                this.setValueName(params.name);
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERObjectIdentifier, KJUR.asn1.ASN1Object);
    // ********************************************************************
    /**
     * class for ASN.1 DER Enumerated
     * @name KJUR.asn1.DEREnumerated
     * @class class for ASN.1 DER Enumerated
     * @extends KJUR.asn1.ASN1Object
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>int - specify initial ASN.1 value(V) by integer value</li>
     * <li>hex - specify initial ASN.1 value(V) by a hexadecimal string</li>
     * </ul>
     * NOTE: ‘params‘ can be omitted.
     * @example
     * new KJUR.asn1.DEREnumerated(123);
     * new KJUR.asn1.DEREnumerated({int: 123});
     * new KJUR.asn1.DEREnumerated({hex: ‘1fad‘});
     */
    KJUR.asn1.DEREnumerated = function(params) {
        KJUR.asn1.DEREnumerated.superclass.constructor.call(this);
        this.hT = "0a";
        /**
         * set value by Tom Wu‘s BigInteger object
         * @name setByBigInteger
         * @memberOf KJUR.asn1.DEREnumerated#
         * @function
         * @param {BigInteger} bigIntegerValue to set
         */
        this.setByBigInteger = function(bigIntegerValue) {
            this.hTLV = null;
            this.isModified = true;
            this.hV = KJUR.asn1.ASN1Util.bigIntToMinTwosComplementsHex(bigIntegerValue);
        };
        /**
         * set value by integer value
         * @name setByInteger
         * @memberOf KJUR.asn1.DEREnumerated#
         * @function
         * @param {Integer} integer value to set
         */
        this.setByInteger = function(intValue) {
            var bi = new BigInteger(String(intValue), 10);
            this.setByBigInteger(bi);
        };
        /**
         * set value by integer value
         * @name setValueHex
         * @memberOf KJUR.asn1.DEREnumerated#
         * @function
         * @param {String} hexadecimal string of integer value
         * @description
         * <br/>
         * NOTE: Value shall be represented by minimum octet length of
         * two‘s complement representation.
         */
        this.setValueHex = function(newHexString) {
            this.hV = newHexString;
        };
        this.getFreshValueHex = function() {
            return this.hV;
        };
        if (typeof params != "undefined") {
            if (typeof params[‘int‘] != "undefined") {
                this.setByInteger(params[‘int‘]);
            } else if (typeof params == "number") {
                this.setByInteger(params);
            } else if (typeof params[‘hex‘] != "undefined") {
                this.setValueHex(params[‘hex‘]);
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DEREnumerated, KJUR.asn1.ASN1Object);
    // ********************************************************************
    /**
     * class for ASN.1 DER UTF8String
     * @name KJUR.asn1.DERUTF8String
     * @class class for ASN.1 DER UTF8String
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘aaa‘})
     * @extends KJUR.asn1.DERAbstractString
     * @description
     * @see KJUR.asn1.DERAbstractString - superclass
     */
    KJUR.asn1.DERUTF8String = function(params) {
        KJUR.asn1.DERUTF8String.superclass.constructor.call(this, params);
        this.hT = "0c";
    };
    YAHOO.lang.extend(KJUR.asn1.DERUTF8String, KJUR.asn1.DERAbstractString);
    // ********************************************************************
    /**
     * class for ASN.1 DER NumericString
     * @name KJUR.asn1.DERNumericString
     * @class class for ASN.1 DER NumericString
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘aaa‘})
     * @extends KJUR.asn1.DERAbstractString
     * @description
     * @see KJUR.asn1.DERAbstractString - superclass
     */
    KJUR.asn1.DERNumericString = function(params) {
        KJUR.asn1.DERNumericString.superclass.constructor.call(this, params);
        this.hT = "12";
    };
    YAHOO.lang.extend(KJUR.asn1.DERNumericString, KJUR.asn1.DERAbstractString);
    // ********************************************************************
    /**
     * class for ASN.1 DER PrintableString
     * @name KJUR.asn1.DERPrintableString
     * @class class for ASN.1 DER PrintableString
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘aaa‘})
     * @extends KJUR.asn1.DERAbstractString
     * @description
     * @see KJUR.asn1.DERAbstractString - superclass
     */
    KJUR.asn1.DERPrintableString = function(params) {
        KJUR.asn1.DERPrintableString.superclass.constructor.call(this, params);
        this.hT = "13";
    };
    YAHOO.lang.extend(KJUR.asn1.DERPrintableString, KJUR.asn1.DERAbstractString);
    // ********************************************************************
    /**
     * class for ASN.1 DER TeletexString
     * @name KJUR.asn1.DERTeletexString
     * @class class for ASN.1 DER TeletexString
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘aaa‘})
     * @extends KJUR.asn1.DERAbstractString
     * @description
     * @see KJUR.asn1.DERAbstractString - superclass
     */
    KJUR.asn1.DERTeletexString = function(params) {
        KJUR.asn1.DERTeletexString.superclass.constructor.call(this, params);
        this.hT = "14";
    };
    YAHOO.lang.extend(KJUR.asn1.DERTeletexString, KJUR.asn1.DERAbstractString);
    // ********************************************************************
    /**
     * class for ASN.1 DER IA5String
     * @name KJUR.asn1.DERIA5String
     * @class class for ASN.1 DER IA5String
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘aaa‘})
     * @extends KJUR.asn1.DERAbstractString
     * @description
     * @see KJUR.asn1.DERAbstractString - superclass
     */
    KJUR.asn1.DERIA5String = function(params) {
        KJUR.asn1.DERIA5String.superclass.constructor.call(this, params);
        this.hT = "16";
    };
    YAHOO.lang.extend(KJUR.asn1.DERIA5String, KJUR.asn1.DERAbstractString);
    // ********************************************************************
    /**
     * class for ASN.1 DER UTCTime
     * @name KJUR.asn1.DERUTCTime
     * @class class for ASN.1 DER UTCTime
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘130430235959Z‘})
     * @extends KJUR.asn1.DERAbstractTime
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>str - specify initial ASN.1 value(V) by a string (ex.‘130430235959Z‘)</li>
     * <li>hex - specify initial ASN.1 value(V) by a hexadecimal string</li>
     * <li>date - specify Date object.</li>
     * </ul>
     * NOTE: ‘params‘ can be omitted.
     * <h4>EXAMPLES</h4>
     * @example
     * d1 = new KJUR.asn1.DERUTCTime();
     * d1.setString(‘130430125959Z‘);
     *
     * d2 = new KJUR.asn1.DERUTCTime({‘str‘: ‘130430125959Z‘});
     * d3 = new KJUR.asn1.DERUTCTime({‘date‘: new Date(Date.UTC(2015, 0, 31, 0, 0, 0, 0))});
     * d4 = new KJUR.asn1.DERUTCTime(‘130430125959Z‘);
     */
    KJUR.asn1.DERUTCTime = function(params) {
        KJUR.asn1.DERUTCTime.superclass.constructor.call(this, params);
        this.hT = "17";
        /**
         * set value by a Date object<br/>
         * @name setByDate
         * @memberOf KJUR.asn1.DERUTCTime#
         * @function
         * @param {Date} dateObject Date object to set ASN.1 value(V)
         * @example
         * o = new KJUR.asn1.DERUTCTime();
         * o.setByDate(new Date("2016/12/31"));
         */
        this.setByDate = function(dateObject) {
            this.hTLV = null;
            this.isModified = true;
            this.date = dateObject;
            this.s = this.formatDate(this.date, ‘utc‘);
            this.hV = stohex(this.s);
        };
        this.getFreshValueHex = function() {
            if (typeof this.date == "undefined" && typeof this.s == "undefined") {
                this.date = new Date();
                this.s = this.formatDate(this.date, ‘utc‘);
                this.hV = stohex(this.s);
            }
            return this.hV;
        };
        if (params !== undefined) {
            if (params.str !== undefined) {
                this.setString(params.str);
            } else if (typeof params == "string" && params.match(/^[0-9]{12}Z$/)) {
                this.setString(params);
            } else if (params.hex !== undefined) {
                this.setStringHex(params.hex);
            } else if (params.date !== undefined) {
                this.setByDate(params.date);
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERUTCTime, KJUR.asn1.DERAbstractTime);
    // ********************************************************************
    /**
     * class for ASN.1 DER GeneralizedTime
     * @name KJUR.asn1.DERGeneralizedTime
     * @class class for ASN.1 DER GeneralizedTime
     * @param {Array} params associative array of parameters (ex. {‘str‘: ‘20130430235959Z‘})
     * @property {Boolean} withMillis flag to show milliseconds or not
     * @extends KJUR.asn1.DERAbstractTime
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>str - specify initial ASN.1 value(V) by a string (ex.‘20130430235959Z‘)</li>
     * <li>hex - specify initial ASN.1 value(V) by a hexadecimal string</li>
     * <li>date - specify Date object.</li>
     * <li>millis - specify flag to show milliseconds (from 1.0.6)</li>
     * </ul>
     * NOTE1: ‘params‘ can be omitted.
     * NOTE2: ‘withMillis‘ property is supported from asn1 1.0.6.
     */
    KJUR.asn1.DERGeneralizedTime = function(params) {
        KJUR.asn1.DERGeneralizedTime.superclass.constructor.call(this, params);
        this.hT = "18";
        this.withMillis = false;
        /**
         * set value by a Date object
         * @name setByDate
         * @memberOf KJUR.asn1.DERGeneralizedTime#
         * @function
         * @param {Date} dateObject Date object to set ASN.1 value(V)
         * @example
         * When you specify UTC time, use ‘Date.UTC‘ method like this:<br/>
         * o1 = new DERUTCTime();
         * o1.setByDate(date);
         *
         * date = new Date(Date.UTC(2015, 0, 31, 23, 59, 59, 0)); #2015JAN31 23:59:59
         */
        this.setByDate = function(dateObject) {
            this.hTLV = null;
            this.isModified = true;
            this.date = dateObject;
            this.s = this.formatDate(this.date, ‘gen‘, this.withMillis);
            this.hV = stohex(this.s);
        };
        this.getFreshValueHex = function() {
            if (this.date === undefined && this.s === undefined) {
                this.date = new Date();
                this.s = this.formatDate(this.date, ‘gen‘, this.withMillis);
                this.hV = stohex(this.s);
            }
            return this.hV;
        };
        if (params !== undefined) {
            if (params.str !== undefined) {
                this.setString(params.str);
            } else if (typeof params == "string" && params.match(/^[0-9]{14}Z$/)) {
                this.setString(params);
            } else if (params.hex !== undefined) {
                this.setStringHex(params.hex);
            } else if (params.date !== undefined) {
                this.setByDate(params.date);
            }
            if (params.millis === true) {
                this.withMillis = true;
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERGeneralizedTime, KJUR.asn1.DERAbstractTime);
    // ********************************************************************
    /**
     * class for ASN.1 DER Sequence
     * @name KJUR.asn1.DERSequence
     * @class class for ASN.1 DER Sequence
     * @extends KJUR.asn1.DERAbstractStructured
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>array - specify array of ASN1Object to set elements of content</li>
     * </ul>
     * NOTE: ‘params‘ can be omitted.
     */
    KJUR.asn1.DERSequence = function(params) {
        KJUR.asn1.DERSequence.superclass.constructor.call(this, params);
        this.hT = "30";
        this.getFreshValueHex = function() {
            var h = ‘‘;
            for (var i = 0; i < this.asn1Array.length; i++) {
                var asn1Obj = this.asn1Array[i];
                h += asn1Obj.getEncodedHex();
            }
            this.hV = h;
            return this.hV;
        };
    };
    YAHOO.lang.extend(KJUR.asn1.DERSequence, KJUR.asn1.DERAbstractStructured);
    // ********************************************************************
    /**
     * class for ASN.1 DER Set
     * @name KJUR.asn1.DERSet
     * @class class for ASN.1 DER Set
     * @extends KJUR.asn1.DERAbstractStructured
     * @description
     * <br/>
     * As for argument ‘params‘ for constructor, you can specify one of
     * following properties:
     * <ul>
     * <li>array - specify array of ASN1Object to set elements of content</li>
     * <li>sortflag - flag for sort (default: true). ASN.1 BER is not sorted in ‘SET OF‘.</li>
     * </ul>
     * NOTE1: ‘params‘ can be omitted.<br/>
     * NOTE2: sortflag is supported since 1.0.5.
     */
    KJUR.asn1.DERSet = function(params) {
        KJUR.asn1.DERSet.superclass.constructor.call(this, params);
        this.hT = "31";
        this.sortFlag = true; // item shall be sorted only in ASN.1 DER
        this.getFreshValueHex = function() {
            var a = new Array();
            for (var i = 0; i < this.asn1Array.length; i++) {
                var asn1Obj = this.asn1Array[i];
                a.push(asn1Obj.getEncodedHex());
            }
            if (this.sortFlag == true) a.sort();
            this.hV = a.join(‘‘);
            return this.hV;
        };
        if (typeof params != "undefined") {
            if (typeof params.sortflag != "undefined" &&
                params.sortflag == false)
                this.sortFlag = false;
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERSet, KJUR.asn1.DERAbstractStructured);
    // ********************************************************************
    /**
     * class for ASN.1 DER TaggedObject
     * @name KJUR.asn1.DERTaggedObject
     * @class class for ASN.1 DER TaggedObject
     * @extends KJUR.asn1.ASN1Object
     * @description
     * <br/>
     * Parameter ‘tagNoNex‘ is ASN.1 tag(T) value for this object.
     * For example, if you find ‘[1]‘ tag in a ASN.1 dump,
     * ‘tagNoHex‘ will be ‘a1‘.
     * <br/>
     * As for optional argument ‘params‘ for constructor, you can specify *ANY* of
     * following properties:
     * <ul>
     * <li>explicit - specify true if this is explicit tag otherwise false
     *     (default is ‘true‘).</li>
     * <li>tag - specify tag (default is ‘a0‘ which means [0])</li>
     * <li>obj - specify ASN1Object which is tagged</li>
     * </ul>
     * @example
     * d1 = new KJUR.asn1.DERUTF8String({‘str‘:‘a‘});
     * d2 = new KJUR.asn1.DERTaggedObject({‘obj‘: d1});
     * hex = d2.getEncodedHex();
     */
    KJUR.asn1.DERTaggedObject = function(params) {
        KJUR.asn1.DERTaggedObject.superclass.constructor.call(this);
        this.hT = "a0";
        this.hV = ‘‘;
        this.isExplicit = true;
        this.asn1Object = null;
        /**
         * set value by an ASN1Object
         * @name setString
         * @memberOf KJUR.asn1.DERTaggedObject#
         * @function
         * @param {Boolean} isExplicitFlag flag for explicit/implicit tag
         * @param {Integer} tagNoHex hexadecimal string of ASN.1 tag
         * @param {ASN1Object} asn1Object ASN.1 to encapsulate
         */
        this.setASN1Object = function(isExplicitFlag, tagNoHex, asn1Object) {
            this.hT = tagNoHex;
            this.isExplicit = isExplicitFlag;
            this.asn1Object = asn1Object;
            if (this.isExplicit) {
                this.hV = this.asn1Object.getEncodedHex();
                this.hTLV = null;
                this.isModified = true;
            } else {
                this.hV = null;
                this.hTLV = asn1Object.getEncodedHex();
                this.hTLV = this.hTLV.replace(/^../, tagNoHex);
                this.isModified = false;
            }
        };
        this.getFreshValueHex = function() {
            return this.hV;
        };
        if (typeof params != "undefined") {
            if (typeof params[‘tag‘] != "undefined") {
                this.hT = params[‘tag‘];
            }
            if (typeof params[‘explicit‘] != "undefined") {
                this.isExplicit = params[‘explicit‘];
            }
            if (typeof params[‘obj‘] != "undefined") {
                this.asn1Object = params[‘obj‘];
                this.setASN1Object(this.isExplicit, this.hT, this.asn1Object);
            }
        }
    };
    YAHOO.lang.extend(KJUR.asn1.DERTaggedObject, KJUR.asn1.ASN1Object);
    /**
     * Create a new JSEncryptRSAKey that extends Tom Wu‘s RSA key object.
     * This object is just a decorator for parsing the key parameter
     * @param {string|Object} key - The key in string format, or an object containing
     * the parameters needed to build a RSAKey object.
     * @constructor
     */
    var JSEncryptRSAKey = /** @class */ (function (_super) {
        __extends(JSEncryptRSAKey, _super);
        function JSEncryptRSAKey(key) {
            var _this = _super.call(this) || this;
            // Call the super constructor.
            //  RSAKey.call(this);
            // If a key key was provided.
            if (key) {
                // If this is a string...
                if (typeof key === "string") {
                    _this.parseKey(key);
                }
                else if (JSEncryptRSAKey.hasPrivateKeyProperty(key) ||
                    JSEncryptRSAKey.hasPublicKeyProperty(key)) {
                    // Set the values for the key.
                    _this.parsePropertiesFrom(key);
                }
            }
            return _this;
        }
        /**
         * Method to parse a pem encoded string containing both a public or private key.
         * The method will translate the pem encoded string in a der encoded string and
         * will parse private key and public key parameters. This method accepts public key
         * in the rsaencryption pkcs #1 format (oid: 1.2.840.113549.1.1.1).
         *
         * @todo Check how many rsa formats use the same format of pkcs #1.
         *
         * The format is defined as:
         * PublicKeyInfo ::= SEQUENCE {
         *   algorithm       AlgorithmIdentifier,
         *   PublicKey       BIT STRING
         * }
         * Where AlgorithmIdentifier is:
         * AlgorithmIdentifier ::= SEQUENCE {
         *   algorithm       OBJECT IDENTIFIER,     the OID of the enc algorithm
         *   parameters      ANY DEFINED BY algorithm OPTIONAL (NULL for PKCS #1)
         * }
         * and PublicKey is a SEQUENCE encapsulated in a BIT STRING
         * RSAPublicKey ::= SEQUENCE {
         *   modulus           INTEGER,  -- n
         *   publicExponent    INTEGER   -- e
         * }
         * it‘s possible to examine the structure of the keys obtained from openssl using
         * an asn.1 dumper as the one used here to parse the components: http://lapo.it/asn1js/
         * @argument {string} pem the pem encoded string, can include the BEGIN/END header/footer
         * @private
         */
        JSEncryptRSAKey.prototype.parseKey = function (pem) {
            try {
                var modulus = 0;
                var public_exponent = 0;
                var reHex = /^\s*(?:[0-9A-Fa-f][0-9A-Fa-f]\s*)+$/;
                var der = reHex.test(pem) ? Hex.decode(pem) : Base64.unarmor(pem);
                var asn1 = ASN1.decode(der);
                // Fixes a bug with OpenSSL 1.0+ private keys
                if (asn1.sub.length === 3) {
                    asn1 = asn1.sub[2].sub[0];
                }
                if (asn1.sub.length === 9) {
                    // Parse the private key.
                    modulus = asn1.sub[1].getHexStringValue(); // bigint
                    this.n = parseBigInt(modulus, 16);
                    public_exponent = asn1.sub[2].getHexStringValue(); // int
                    this.e = parseInt(public_exponent, 16);
                    var private_exponent = asn1.sub[3].getHexStringValue(); // bigint
                    this.d = parseBigInt(private_exponent, 16);
                    var prime1 = asn1.sub[4].getHexStringValue(); // bigint
                    this.p = parseBigInt(prime1, 16);
                    var prime2 = asn1.sub[5].getHexStringValue(); // bigint
                    this.q = parseBigInt(prime2, 16);
                    var exponent1 = asn1.sub[6].getHexStringValue(); // bigint
                    this.dmp1 = parseBigInt(exponent1, 16);
                    var exponent2 = asn1.sub[7].getHexStringValue(); // bigint
                    this.dmq1 = parseBigInt(exponent2, 16);
                    var coefficient = asn1.sub[8].getHexStringValue(); // bigint
                    this.coeff = parseBigInt(coefficient, 16);
                }
                else if (asn1.sub.length === 2) {
                    // Parse the public key.
                    var bit_string = asn1.sub[1];
                    var sequence = bit_string.sub[0];
                    modulus = sequence.sub[0].getHexStringValue();
                    this.n = parseBigInt(modulus, 16);
                    public_exponent = sequence.sub[1].getHexStringValue();
                    this.e = parseInt(public_exponent, 16);
                }
                else {
                    return false;
                }
                return true;
            }
            catch (ex) {
                return false;
            }
        };
        /**
         * Translate rsa parameters in a hex encoded string representing the rsa key.
         *
         * The translation follow the ASN.1 notation :
         * RSAPrivateKey ::= SEQUENCE {
         *   version           Version,
         *   modulus           INTEGER,  -- n
         *   publicExponent    INTEGER,  -- e
         *   privateExponent   INTEGER,  -- d
         *   prime1            INTEGER,  -- p
         *   prime2            INTEGER,  -- q
         *   exponent1         INTEGER,  -- d mod (p1)
         *   exponent2         INTEGER,  -- d mod (q-1)
         *   coefficient       INTEGER,  -- (inverse of q) mod p
         * }
         * @returns {string}  DER Encoded String representing the rsa private key
         * @private
         */
        JSEncryptRSAKey.prototype.getPrivateBaseKey = function () {
            var options = {
                array: [
                    new KJUR.asn1.DERInteger({ int: 0 }),
                    new KJUR.asn1.DERInteger({ bigint: this.n }),
                    new KJUR.asn1.DERInteger({ int: this.e }),
                    new KJUR.asn1.DERInteger({ bigint: this.d }),
                    new KJUR.asn1.DERInteger({ bigint: this.p }),
                    new KJUR.asn1.DERInteger({ bigint: this.q }),
                    new KJUR.asn1.DERInteger({ bigint: this.dmp1 }),
                    new KJUR.asn1.DERInteger({ bigint: this.dmq1 }),
                    new KJUR.asn1.DERInteger({ bigint: this.coeff })
                ]
            };
            var seq = new KJUR.asn1.DERSequence(options);
            return seq.getEncodedHex();
        };
        /**
         * base64 (pem) encoded version of the DER encoded representation
         * @returns {string} pem encoded representation without header and footer
         * @public
         */
        JSEncryptRSAKey.prototype.getPrivateBaseKeyB64 = function () {
            return hex2b64(this.getPrivateBaseKey());
        };
        /**
         * Translate rsa parameters in a hex encoded string representing the rsa public key.
         * The representation follow the ASN.1 notation :
         * PublicKeyInfo ::= SEQUENCE {
         *   algorithm       AlgorithmIdentifier,
         *   PublicKey       BIT STRING
         * }
         * Where AlgorithmIdentifier is:
         * AlgorithmIdentifier ::= SEQUENCE {
         *   algorithm       OBJECT IDENTIFIER,     the OID of the enc algorithm
         *   parameters      ANY DEFINED BY algorithm OPTIONAL (NULL for PKCS #1)
         * }
         * and PublicKey is a SEQUENCE encapsulated in a BIT STRING
         * RSAPublicKey ::= SEQUENCE {
         *   modulus           INTEGER,  -- n
         *   publicExponent    INTEGER   -- e
         * }
         * @returns {string} DER Encoded String representing the rsa public key
         * @private
         */
        JSEncryptRSAKey.prototype.getPublicBaseKey = function () {
            var first_sequence = new KJUR.asn1.DERSequence({
                array: [
                    new KJUR.asn1.DERObjectIdentifier({ oid: "1.2.840.113549.1.1.1" }),
                    new KJUR.asn1.DERNull()
                ]
            });
            var second_sequence = new KJUR.asn1.DERSequence({
                array: [
                    new KJUR.asn1.DERInteger({ bigint: this.n }),
                    new KJUR.asn1.DERInteger({ int: this.e })
                ]
            });
            var bit_string = new KJUR.asn1.DERBitString({
                hex: "00" + second_sequence.getEncodedHex()
            });
            var seq = new KJUR.asn1.DERSequence({
                array: [
                    first_sequence,
                    bit_string
                ]
            });
            return seq.getEncodedHex();
        };
        /**
         * base64 (pem) encoded version of the DER encoded representation
         * @returns {string} pem encoded representation without header and footer
         * @public
         */
        JSEncryptRSAKey.prototype.getPublicBaseKeyB64 = function () {
            return hex2b64(this.getPublicBaseKey());
        };
        /**
         * wrap the string in block of width chars. The default value for rsa keys is 64
         * characters.
         * @param {string} str the pem encoded string without header and footer
         * @param {Number} [width=64] - the length the string has to be wrapped at
         * @returns {string}
         * @private
         */
        JSEncryptRSAKey.wordwrap = function (str, width) {
            width = width || 64;
            if (!str) {
                return str;
            }
            var regex = "(.{1," + width + "})( +|$\n?)|(.{1," + width + "})";
            return str.match(RegExp(regex, "g")).join("\n");
        };
        /**
         * Retrieve the pem encoded private key
         * @returns {string} the pem encoded private key with header/footer
         * @public
         */
        JSEncryptRSAKey.prototype.getPrivateKey = function () {
            var key = "-----BEGIN RSA PRIVATE KEY-----\n";
            key += JSEncryptRSAKey.wordwrap(this.getPrivateBaseKeyB64()) + "\n";
            key += "-----END RSA PRIVATE KEY-----";
            return key;
        };
        /**
         * Retrieve the pem encoded public key
         * @returns {string} the pem encoded public key with header/footer
         * @public
         */
        JSEncryptRSAKey.prototype.getPublicKey = function () {
            var key = "-----BEGIN PUBLIC KEY-----\n";
            key += JSEncryptRSAKey.wordwrap(this.getPublicBaseKeyB64()) + "\n";
            key += "-----END PUBLIC KEY-----";
            return key;
        };
        /**
         * Check if the object contains the necessary parameters to populate the rsa modulus
         * and public exponent parameters.
         * @param {Object} [obj={}] - An object that may contain the two public key
         * parameters
         * @returns {boolean} true if the object contains both the modulus and the public exponent
         * properties (n and e)
         * @todo check for types of n and e. N should be a parseable bigInt object, E should
         * be a parseable integer number
         * @private
         */
        JSEncryptRSAKey.hasPublicKeyProperty = function (obj) {
            obj = obj || {};
            return (obj.hasOwnProperty("n") &&
                obj.hasOwnProperty("e"));
        };
        /**
         * Check if the object contains ALL the parameters of an RSA key.
         * @param {Object} [obj={}] - An object that may contain nine rsa key
         * parameters
         * @returns {boolean} true if the object contains all the parameters needed
         * @todo check for types of the parameters all the parameters but the public exponent
         * should be parseable bigint objects, the public exponent should be a parseable integer number
         * @private
         */
        JSEncryptRSAKey.hasPrivateKeyProperty = function (obj) {
            obj = obj || {};
            return (obj.hasOwnProperty("n") &&
                obj.hasOwnProperty("e") &&
                obj.hasOwnProperty("d") &&
                obj.hasOwnProperty("p") &&
                obj.hasOwnProperty("q") &&
                obj.hasOwnProperty("dmp1") &&
                obj.hasOwnProperty("dmq1") &&
                obj.hasOwnProperty("coeff"));
        };
        /**
         * Parse the properties of obj in the current rsa object. Obj should AT LEAST
         * include the modulus and public exponent (n, e) parameters.
         * @param {Object} obj - the object containing rsa parameters
         * @private
         */
        JSEncryptRSAKey.prototype.parsePropertiesFrom = function (obj) {
            this.n = obj.n;
            this.e = obj.e;
            if (obj.hasOwnProperty("d")) {
                this.d = obj.d;
                this.p = obj.p;
                this.q = obj.q;
                this.dmp1 = obj.dmp1;
                this.dmq1 = obj.dmq1;
                this.coeff = obj.coeff;
            }
        };
        return JSEncryptRSAKey;
    }(RSAKey));
    /**
     *
     * @param {Object} [options = {}] - An object to customize JSEncrypt behaviour
     * possible parameters are:
     * - default_key_size        {number}  default: 1024 the key size in bit
     * - default_public_exponent {string}  default: ‘010001‘ the hexadecimal representation of the public exponent
     * - log                     {boolean} default: false whether log warn/error or not
     * @constructor
     */
    var JSEncrypt = /** @class */ (function () {
        function JSEncrypt(options) {
            options = options || {};
            this.default_key_size = parseInt(options.default_key_size, 10) || 1024;
            this.default_public_exponent = options.default_public_exponent || "010001"; // 65537 default openssl public exponent for rsa key type
            this.log = options.log || false;
            // The private and public key.
            this.key = null;
        }
        /**
         * Method to set the rsa key parameter (one method is enough to set both the public
         * and the private key, since the private key contains the public key paramenters)
         * Log a warning if logs are enabled
         * @param {Object|string} key the pem encoded string or an object (with or without header/footer)
         * @public
         */
        JSEncrypt.prototype.setKey = function (key) {
            if (this.log && this.key) {
                console.warn("A key was already set, overriding existing.");
            }
            this.key = new JSEncryptRSAKey(key);
        };
        /**
         * Proxy method for setKey, for api compatibility
         * @see setKey
         * @public
         */
        JSEncrypt.prototype.setPrivateKey = function (privkey) {
            // Create the key.
            this.setKey(privkey);
        };
        /**
         * Proxy method for setKey, for api compatibility
         * @see setKey
         * @public
         */
        JSEncrypt.prototype.setPublicKey = function (pubkey) {
            // Sets the public key.
            this.setKey(pubkey);
        };
        /**
         * Proxy method for RSAKey object‘s decrypt, decrypt the string using the private
         * components of the rsa key object. Note that if the object was not set will be created
         * on the fly (by the getKey method) using the parameters passed in the JSEncrypt constructor
         * @param {string} str base64 encoded crypted string to decrypt
         * @return {string} the decrypted string
         * @public
         */
        JSEncrypt.prototype.decrypt = function (str) {
            // Return the decrypted string.
            try {
                return this.getKey().decrypt(b64tohex(str));
            }
            catch (ex) {
                return false;
            }
        };
        /**
         * Proxy method for RSAKey object‘s encrypt, encrypt the string using the public
         * components of the rsa key object. Note that if the object was not set will be created
         * on the fly (by the getKey method) using the parameters passed in the JSEncrypt constructor
         * @param {string} str the string to encrypt
         * @return {string} the encrypted string encoded in base64
         * @public
         */
        JSEncrypt.prototype.encrypt = function (str) {
            // Return the encrypted string.
            try {
                return hex2b64(this.getKey().encrypt(str));
            }
            catch (ex) {
                return false;
            }
        };
        /**
         * Proxy method for RSAKey object‘s sign.
         * @param {string} str the string to sign
         * @param {function} digestMethod hash method
         * @param {string} digestName the name of the hash algorithm
         * @return {string} the signature encoded in base64
         * @public
         */
        JSEncrypt.prototype.sign = function (str, digestMethod, digestName) {
            // return the RSA signature of ‘str‘ in ‘hex‘ format.
            try {
                return hex2b64(this.getKey().sign(str, digestMethod, digestName));
            }
            catch (ex) {
                return false;
            }
        };
        /**
         * Proxy method for RSAKey object‘s verify.
         * @param {string} str the string to verify
         * @param {string} signature the signature encoded in base64 to compare the string to
         * @param {function} digestMethod hash method
         * @return {boolean} whether the data and signature match
         * @public
         */
        JSEncrypt.prototype.verify = function (str, signature, digestMethod) {
            // Return the decrypted ‘digest‘ of the signature.
            try {
                return this.getKey().verify(str, b64tohex(signature), digestMethod);
            }
            catch (ex) {
                return false;
            }
        };
        /**
         * Getter for the current JSEncryptRSAKey object. If it doesn‘t exists a new object
         * will be created and returned
         * @param {callback} [cb] the callback to be called if we want the key to be generated
         * in an async fashion
         * @returns {JSEncryptRSAKey} the JSEncryptRSAKey object
         * @public
         */
        JSEncrypt.prototype.getKey = function (cb) {
            // Only create new if it does not exist.
            if (!this.key) {
                // Get a new private key.
                this.key = new JSEncryptRSAKey();
                if (cb && {}.toString.call(cb) === "[object Function]") {
                    this.key.generateAsync(this.default_key_size, this.default_public_exponent, cb);
                    return;
                }
                // Generate the key.
                this.key.generate(this.default_key_size, this.default_public_exponent);
            }
            return this.key;
        };
        /**
         * Returns the pem encoded representation of the private key
         * If the key doesn‘t exists a new key will be created
         * @returns {string} pem encoded representation of the private key WITH header and footer
         * @public
         */
        JSEncrypt.prototype.getPrivateKey = function () {
            // Return the private representation of this key.
            return this.getKey().getPrivateKey();
        };
        /**
         * Returns the pem encoded representation of the private key
         * If the key doesn‘t exists a new key will be created
         * @returns {string} pem encoded representation of the private key WITHOUT header and footer
         * @public
         */
        JSEncrypt.prototype.getPrivateKeyB64 = function () {
            // Return the private representation of this key.
            return this.getKey().getPrivateBaseKeyB64();
        };
        /**
         * Returns the pem encoded representation of the public key
         * If the key doesn‘t exists a new key will be created
         * @returns {string} pem encoded representation of the public key WITH header and footer
         * @public
         */
        JSEncrypt.prototype.getPublicKey = function () {
            // Return the private representation of this key.
            return this.getKey().getPublicKey();
        };
        /**
         * Returns the pem encoded representation of the public key
         * If the key doesn‘t exists a new key will be created
         * @returns {string} pem encoded representation of the public key WITHOUT header and footer
         * @public
         */
        JSEncrypt.prototype.getPublicKeyB64 = function () {
            // Return the private representation of this key.
            return this.getKey().getPublicBaseKeyB64();
        };
        JSEncrypt.version = "3.0.0-rc.1";
        return JSEncrypt;
    }());
    window.JSEncrypt = JSEncrypt;
    obj.JSEncrypt = JSEncrypt;
    obj.default = JSEncrypt;
    Object.defineProperty(obj, ‘__esModule‘, { value: true });
    return obj
    }

    b. 测试:
    test.html

    <!DOCTYPE html>
    <html>
    <head>
        <meta charset="UTF-8">
        <title>rsa加密/解密测试</title>
    </head>
    <!--引入jsencrypt.js-->
    <script src="./rsa.js"></script>
    <script type="text/javascript">
        //公钥
        var PUBLIC_KEY = ‘-----BEGIN PUBLIC KEY-----MIGfMA0GCSqGSIb3DQEBAQUAA4GNADCBiQKBgQCoZZ8iUBprOIc0kGckr5ax6/Fd9IKKMc/XHayKEAvqpS0oz0b1ojEkpkdZBk0OWNhp73YNV+YLKBwwxOwb3u3hl8nBLoG/RilEbBMdCf55cUzNsfn/XF5CiLr/aci/OHuTe6ULvXs280T5M+nUh3iKdiT6z9XrFbH69C+xFoNInwIDAQAB-----END PUBLIC KEY-----‘;
        //私钥
        var PRIVATE_KEY = ‘-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----‘;
        var obj = rsa()
        var crypt = new obj.JSEncrypt();
        crypt.setPublicKey(PUBLIC_KEY);
        crypt.setPrivateKey(PRIVATE_KEY);
        //使用公钥加密
        var encrypted = crypt.encrypt(‘hello world‘);
        //使用私钥解密
        var decrypted = crypt.decrypt(encrypted);
        console.log(encrypted);
        console.log(decrypted);
    </script>
    </html>

    c. 输出:

    C3r7m03r2ykaKVeggguYj0pSw0mqsludH2nk1DlQRzuTVi7gslQ3m0E1Cbyp6SOnWreui/08bVraCMJeAiGtUHweBBVQ2TwtWE2cAFIkdGA1HtVKP3TJvuBjjSnCG5wKiUddYwfR/rlAtbKpjWqGsQDsSwjidL6faahWvoWmXa8=
    test.html:23 hello world

    技术分享图片

  • php、javascript使用rsa进行加密/解密

    标签:water   work   begin   lower   tab   images   _id   owb   extract   

    原文地址:http://blog.51cto.com/12173069/2308624

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