RSA算法原理及实现

  1 # -*- coding:utf-8 -*-
  2 
  3 import math
  4 import random
  5 
  6 #this function is for a^b%n
  7 def fast_mul(a,b,n):
  8     c=1
  9     while b!=0:
 10         if b%2==0:
 11             b=b/2
 12             a=(a*a)%n
 13         elif b%2!=0:
 14             b=b-1
 15             c=(c*a)%n
 16 
 17     return c
 18 
 19 def ExtendedEuclid(n,u):
 20     x1=y2=1
 21     x2=y1=0
 22     if n>u:
 23         x3,y3=[n,u]
 24     else:
 25         x3,y3=[u,n]
 26 
 27     while 1:
 28         if y3==0:
 29             return x3
 30         elif y3==1:
 31             return y2
 32 
 33         q=x3/y3
 34         t1,t2,t3=[x1-q*y1,x2-q*y2,x3-q*y3]
 35         x1,x2,x3=[y1,y2,y3]
 36         y1,y2,y3=[t1,t2,t3]
 37 
 38 def MillerRabin(n):
 39     m=n-1
 40     k=a=b=0
 41     while m/2*2 == m:
 42         k+=1
 43         m=m/2
 44     a=random.random()%n
 45     while a<1:
 46         a+=1
 47     b=fast_mul(a,m,n)
 48     if 1==b:
 49         return 1
 50     for x in range(k):
 51         if(b==n-1):
 52             return 1
 53         else:
 54             b=b*b%n
 55     return 0
 56 
 57 def get_prime(max_num):
 58     prime_num=[]
 59     for i in xrange(2,max_num):
 60         temp=0
 61         sqrt_max_num=int(math.sqrt(i))+1
 62         for j in xrange(2,sqrt_max_num):
 63             if 0==i%j:
 64                 temp=j
 65                 break
 66         if temp==0:
 67             prime_num.append(i)
 68 
 69     return prime_num
 70 
 71 def get_key():
 72     prime=get_prime(500)
 73     print prime[-80:-1]
 74     while 1:
 75         prime_str=raw_input("please choose two prime number from above x1,x2: ").split(",")
 76         p,q=[int(x) for x in prime_str]
 77         if (p in prime) and (q in prime):
 78             break
 79         else:
 80             print "the number you enter is not prime number."
 81 
 82     N=p*q
 83     r=(p-1)*(q-1)
 84     r_prime=get_prime(r)
 85     r_len=len(r_prime)
 86     e=r_prime[int(random.uniform(0,r_len))]
 87     d=(ExtendedEuclid(e,r)+r)%r;
 88 
 89     return ((N,e),(N,d))
 90 
 91 def encode(pub_key,origal):
 92     N,e=pub_key
 93     return fast_mul(origal,e,N)
 94 
 95 def decode(pri_key,encry):
 96     N,d=pri_key
 97     return fast_mul(encry,d,N)
 98 
 99 if __name__==‘__main__‘:
100     pub_key,pri_key=get_key()
101     print "public key: ",pub_key
102     print "private key: ",pri_key
103 
104     origal_text=raw_input("please input the origal text: ")
105     encode_text=[encode(pub_key,ord(x)) for x in origal_text]
106     decode_text=[chr(decode(pri_key,x)) for x in encode_text]
107 
108     encode_show=",".join([str(x) for x in encode_text])
109     decode_show="".join(decode_text)
110     print "encode text: ",encode_show
111     print "decode text: ",decode_show