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代码如下：?
import random
from random import randint
import sys
sys.setrecursionlimit(100000)#修改默认递归深度为100000
'''
超大整数超大次幂然后对超大的整数取模
(base ^ exponent) mod n
'''
def exp_mode(base, exponent, n):
bin_array = bin(exponent)[2:][::-1]
r = len(bin_array)
base_array = []
pre_base = base
base_array.append(pre_base)
for _ in range(r - 1):
next_base = (pre_base * pre_base) % n
base_array.append(next_base)
pre_base = next_base
a_w_b = __multi(base_array, bin_array, n)
return a_w_b % n
def __multi(array, bin_array, n):
result = 1
for index in range(len(array)):
a = array[index]
if not int(bin_array[index]):
continue
result *= a
result = result % n # 加快连乘的速度
return result
# 求两个数字的最大公约数（欧几里得算法）
def gcd(a, b):
if b == 0:
return a
else:
return gcd(b, a % b)
'''
扩展欧几里的算法
计算 ax + by = 1中的x与y的整数解（a与b互质）
'''
def ext_gcd(a, b):
if b == 0:
x1 = 1
y1 = 0
x = x1
y = y1
r = a
return r, x, y
else:
r, x1, y1 = ext_gcd(b, a % b)
x = y1
y = x1 - a // b * y1
return r, x, y
def rabin_miller(num): # rabin_miller算法
s = num - 1
t = 0
while s % 2 == 0:
s = s // 2
t += 1
for trials in range(5):
a = random.randrange(2, num - 1)
v = pow(a, s, num)
if v != 1:
i = 0
while v != (num - 1):
if i == t - 1:
return False
else:
i = i + 1
v = (v ** 2) % num
return True
def is_prime(num): # 素数判断
# 排除0,1和负数
if num < 2:
return False
# 创建小素数的列表,可以大幅加快速度
# 如果是小素数,那么直接返回true
small_primes = [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]
if num in small_primes:
return True
# 如果大数是这些小素数的倍数,那么就是合数,返回false
for prime in small_primes:
if num % prime == 0:
return False
# 如果这样没有分辨出来,就一定是大整数,那么就调用rabin算法
return rabin_miller(num)
# 得到大整数,默认位数为1024
def get_prime(key_size=1024): # 此处设置素数位数
while True:
num = random.randrange(2 ** (key_size - 1), 2 ** key_size)
if is_prime(num):
return num
# 字符转换成asc
def Transfer_To_Ascii(messages):
result = []
for message in messages:
result.append(ord(message))
return result
def is_sushu(sushu):
for i in range(2, sushu):
if sushu % i == 0:
return False
return True
def Is_Huzhi(a, b):
while a % b: # 辗转相除法判断互质
a, b = b, a % b
if b > 1:
return False
else:
return True
def Creat_E(oula):
top = oula
while True:
i = randint(2, top)
for e in range(i, top):
if Is_Huzhi(e, oula):
return e
top = i
# 生成公钥私钥，p、q为两个超大质数
def gen_key(p, q):
n = p * q
fy = (p - 1) * (q - 1) # 计算与n互质的整数个数 欧拉函数
e = Creat_E(fy) # 选取e
a = e
b = fy
r, x, y = ext_gcd(a, b)
# 计算出的x不能是负数，如果是负数，说明p、q、e选取失败，不过可以把x加上fy，使x为正数，才能计算。
if x < 0:
x = x + fy
d = x
# 返回： 公钥 私钥
return (n, e), (n, d)
# 加密 m是被加密的信息 加密成为c
def encrypt(m, pubkey):
n = pubkey[0]
e = pubkey[1]
c = exp_mode(m, e, n)
return c
# 解密 c是密文，解密为明文m
def decrypt(c, selfkey):
n = selfkey[0]
d = selfkey[1]
m = exp_mode(c, d, n)
return m
if __name__ == "__main__":
p = get_prime()
q = p
while p == q:
q = get_prime()
'''生成公钥私钥'''
pubkey, selfkey = gen_key(p, q)
print('输入明文：')
text = input()
m1 = Transfer_To_Ascii(text)
length = len(m1)
c_list = []
for i in m1:
c_list.append(encrypt(i, pubkey))
print('密文：')
print(c_list)
b_list = []
for i in c_list:
b_list.append(decrypt(i, selfkey))
print('解密后：')
for i in b_list:
print(chr(i), end='')
参考博客：
RSA加密算法Python实现_feng锋～的博客-CSDN博客_rsa算法python实现
https://blog.csdn.net/qq_49597570/article/details/11378911425行代码实现完整的RSA算法（Python3.X版本）_※六边形战士※的博客-CSDN博客_rsa算法pythonhttps://blog.csdn.net/bian_h_f612701198412/article/details/87202462生成大素数(python实现),包含素性检测_钢琴线与小刀的博客-CSDN博客_python生成大素数https://blog.csdn.net/qq_38115310/article/details/88034676?ops_request_misc=&request_id=&biz_id=102&utm_term=python%20%E5%A4%A7%E6%95%B4%E6%95%B0%E7%B4%A0%E6%80%A7%E7%9B%91%E6%B5%8B&utm_medium=distribute.pc_search_result.none-task-blog-2~all~sobaiduweb~default-0-88034676.nonecase&spm=1018.2226.3001.4187
