密碼學：基於python的rsa算法

#n=p和q隨機生成
#課本以兩個字母爲一組，此處以每一個字母爲一組，故必須n=p*q>2

import math
import random
dict1={'a':0,'b':1,'c':2,'d':3,'e':4,'f':5,'g':6,'h':7,'i':8,'j':9,'k':10,'l':11,'m':12,'n':13,'o':14,'p':15,'q':16,'r':17,'s':18,'t':19,'u':20,'v':21,'w':22,'x':23,'y':24,'z':25}

#字典鍵值轉換
dict2 = dict(zip(dict1.values(),dict1))

#生成100以內的素數數組
def prime_array():
    array = []
    for i in range(2,1000):
        x = prime(i,2)
        if x :
            array.append(i)
    return array

   
#判斷素數
def prime(n,div):
    if math.sqrt(n) < div:
        return True
    if n % div == 0:
        return False
    else :
        return prime(n,div + 1)

#求最大公約數
def gcd(a,b):
    if b == 0:
        return a
    else :
        return gcd(b,a%b)

#找出與（p-1）*(p+1)互質的素數e
def co_prime(s):
    while True:
        e = random.choice(range(100))
        x = gcd(e,s)
        if x == 1:
            break
    return e

#找出d
def find_d(e,s):
    d = 0
    while(True):
        d += 1
        x = (e * d) % s
        if x == 1:
            return d

#加密
def encryption(m,ku):
    C = pow(m,ku[0]) % ku[1]
    return C

#解密
def decode(c,kr):
    M = pow(c,kr[0]) % kr[1]
    return M

#主函數
if __name__ == '__main__':
   # print("字典1：",dict1,"\n"+"字典2",dict2)
    print('請輸入明文(只支持小寫字母)：')
    M = input()
    C = ""
    iC = []
    print("p,q的取值範圍：")
    array = prime_array()
    print(array)

#n不能小於25
    while True:
        p = random.choice(array)
        q = random.choice(array)
        n = p * q
        if n>25:
            break
    print('p爲{},q爲{}'.format(p,q))

    s = (p-1) * (q-1)
    e = co_prime(s)
    d = find_d(e,s)
    KU = [e,n]
    KR = [d,n]
#加密結果
    for ch in M:
        iC.append(encryption(dict1[ch],KU))
    for i in iC:
        C += str(i)
    print("加密後密文爲：",C)
#解密結果
    M = ''
    for i in iC:
        M += dict2[decode(i,KR)]
    print('解密後明文爲：',M)