python代码利用素性测试算法和优化后的大数质因子分解算法高效地分解输入的公钥N,再结合输入的公钥e快速得到恢复得到明文的10进制txt串,再用hex(txt)将其转换为16进制,再将16进制txt(每四个字符为一组)转换为unidoce编码(即为本次实验所求文本): txt.encode('unicode_escape').decode().replace('\u','')
时间: 2024-02-12 10:09:27 浏览: 74
以下是一个实现示例:
```python
import math
def is_prime(n):
if n <= 1:
return False
if n <= 3:
return True
if n % 2 == 0 or n % 3 == 0:
return False
i = 5
while i*i <= n:
if n % i == 0 or n % (i+2) == 0:
return False
i += 6
return True
def prime_factors(n):
factors = []
while n % 2 == 0:
factors.append(2)
n //= 2
if n == 1:
return factors
while not is_prime(n):
a = math.ceil(math.sqrt(n))
b2 = a*a - n
while not math.sqrt(b2).is_integer():
a += 1
b2 = a*a - n
p = a + math.isqrt(b2)
q = a - math.isqrt(b2)
factors.extend(prime_factors(p))
factors.extend(prime_factors(q))
return factors
factors.append(n)
return factors
def decrypt(N, e, ciphertext):
factors = prime_factors(N)
phi = 1
for factor in set(factors):
phi *= (factor - 1)
d = pow(e, -1, phi)
plaintext = pow(ciphertext, d, N)
txt = str(plaintext)
hex_txt = hex(txt)[2:]
unicode_txt = ""
for i in range(0, len(hex_txt), 4):
unicode_txt += chr(int(hex_txt[i:i+4], 16))
return unicode_txt.encode('unicode_escape').decode().replace('\u','')
# 示例用法
N = 3233
e = 17
ciphertext = 855
plaintext = decrypt(N, e, ciphertext)
print(f"明文为: {plaintext}")
```
这个实现使用了素性测试和优化后的大数质因子分解算法来分解N,然后计算phi和d,最后使用RSA解密算法得到明文。最后,将明文转换为16进制字符串,然后按照每四个字符一组的方式分组,转换为unicode编码。
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