简单实现rsa加密算法

rsa的基本步骤如下：

# 1. 产生两个比较大的素数p,q
# 2. 计算 N = pq 和phi = (p-1) * (q - 1)
# 3. 找到一个整数e满足条件 (1 < e < phi)并且与phi是互质的： gcd(e, phi) = 1
# 4. 计算私钥 d, 满足条件1 < d <phi, 并且是e的模逆ed = 1 (mod phi)
# 5. 公共密钥就是(N, e),私钥就是(N, d)

# naive rsa implementation

# p  = 11 , q = 3

#

import math

import random

p = 11

q = 3

N = p * q

e = 3 # prime to ( p - 1)* (q - 1)



# public key: ( N, e ) = (33, 3)

# private key: d = 7

d = 7



# encrypt

#---------------



# message

m = 32



result = 1

exp = e

base = m

while (exp > 0):

    if ( exp & 1):

        result = result * base % N

    exp = exp >> 1

    base = (base * base) % N

c = result

print 'ciphertext:'

print c



# decrypt

#------------------

result = 1

exp = d

base = c

while (exp > 0):

    if ( exp & 1):

        result = result * base % N

    exp = exp >> 1

    base = (base * base) % N

dm = result

print 'decypher text:'

print dm