使用 Python 在 RSA 算法中将文本转换为数字时无法修复错误

Question

我的老师给我布置了一项任务，要求我编写一个 python 程序，该程序可以使用 RSA 算法加密消息。所以要做到这一点，我必须创建将文本转换为数字的函数，然后能够操纵这些数字并对其进行加密。但是为了测试我是否正确加密了它，我还设计了一个解密函数，我也在底部做了这个函数。加密函数和 Ascii 函数之间的所有函数都可以在其他函数中使用（此时你会意识到我喜欢将我的代码划分为函数）。我的代码的问题是当我运行它

时我不断收到这个错误

    Traceback (most recent call last):
  File "D:/Applications/Python/Ziad/RSA algotrithim V2.py", line 127, in <module>
    print(decrypt(Phi_N, e, encrypted))
  File "D:/Applications/Python/Ziad/RSA algotrithim V2.py", line 115, in decrypt
    return Num2Text(message)
  File "D:/Applications/Python/Ziad/RSA algotrithim V2.py", line 58, in Num2Text
    return Ascii2Text(Num2Ascii(message))
  File "D:/Applications/Python/Ziad/RSA algotrithim V2.py", line 17, in Ascii2Text
    text = text + chr(int(char))
ValueError: invalid literal for int() with base 10: '1.0'
>>> ================================ RESTART =================

我单独测试了所有功能，看看它们是否有效。我重新检查了我的加密和解密功能，它们应该可以工作。出于某种原因，我认为我的问题出在我的解密函数上，因为我认为它给了我十进制数，但是我在互联网上搜索了算法，我看到的所有网站都使用相同的算法。请帮助我找到问题所在，我通常不会向其他人寻求帮助（这是我在 Whosebug 上的第一个问题）并且我已经为此伤脑筋 3 周了。

import math

def Text2Ascii(message):
    Ascii = ""
    for count in range(len(message)):
        if len(str(ord(message[count]))) <= 2:
            Ascii = Ascii + "0" +str(ord(message[count])) + " "
        else:
            Ascii = Ascii + str(ord(message[count])) + " "
    return Ascii

def Ascii2Text(message):
    text = ""
    char = ""
    for count in range(len(message)):
        if message[count] == " ":
            text = text + chr(int(char))
            char = ""
        else:
            char = char + message[count]
    text = text + chr(int(char))
    return text

def Ascii2Num(message):
    Num = ""
    for count in range(len(message)):
        if message[count] != " ":
            Num = Num + message[count]
    return int(Num)

def Num2Ascii(message):
    Ascii = ""
    char = ""
    message = str(message)
    if len(message)%3 == 0:
        for count in range(len(message)):
            if (count+1)%3 == 0:
                char = char + message[count]
                Ascii = Ascii + char + " "
                char = ""
            else:
                char = char + message[count]
    else:
        Ascii = "0"
        for count in range(len(message)):
            if (count+2)%3 == 0:
                char = char + message[count]
                Ascii = Ascii + char + " "
                char = ""
            else:
                char = char + message[count]
    return Ascii

def Text2Num(message):
    return Ascii2Num(Text2Ascii(message))

def Num2Text(message):
    return Ascii2Text(Num2Ascii(message))

def exponent(number, power):
    answer = 1
    for count in range(power):
        answer = number*answer
    return answer

def primeCheck(number):
    if number == 2:
        prime = True
    elif number <= 1:
        prime = False
    else:
        n = math.sqrt(number)
        n = math.ceil(n)
        for count in range(2,n+1):
            if number%count == 0:
                prime = False
                break
            else:
                prime = True
    return prime


def factors(number):
    answer = []
    if primeCheck(number)== True:
        answer = [number,1]
    else:
        for count in range(1,number+1):
            if number%count == 0:
                answer.append(count)
    return answer

def phi(number):
    answer = number
    if primeCheck(number) == True:
        answer = number - 1
    else:
        factor = factors(number)
        for count in factor:
            for count2 in factors(count):
                if count2 == count:
                    answer = answer -1
                    break   
    return answer
def encrypt(N,e):
    message = input("What is the message you need encrypted?\n")
    message = Text2Num(message)
    encrypted = (message ** e)%N
    return encrypted

def decrypt(Phi_N, e,encrypted):
    k = 3
    d = (Phi_N*k + 1)/e
    message = encrypted ** d
    return Num2Text(message)

p = int(input("Give me a prime number: "))
while primeCheck(p) == False:
    p = int(input("Give me a prime number: "))
q = int(input("Give me a prime number: "))
while primeCheck(q) == False:
    q = int(input("Give me a prime number: "))
N = q*p
Phi_N = (q-1)*(p-1)
e = int(input("Enter your encryption key: "))
encrypted = encrypt(N,e)
print(decrypt(Phi_N, e, encrypted))

Answer 1

您遇到的特定错误是由两个因素共同造成的：

第一个也是最容易解决的问题是您在 Ascii2Text 中分解字符串的方式：

def Ascii2Text(message):
text = ""
char = ""
for count in range(len(message)):
    **if message[count] == " ":**      #<-- This line is not robust
        text = text + chr(int(char))
        char = ""
    else:
        char = char + message[count]
text = text + chr(int(char))
return text

问题是，随着 Num2Ascii 的实现方式，您最终会得到一个尾随 space，这会导致您在循环结束时尝试将空字符串转换为 int，并且ascii 化消息中前面的非 space 个字符。我建议要么大声扼杀无效字符，要么至少不要尝试将它们附加到您尝试在下一行转换为 int 的 "char" 字符串。

这给我们带来了下一个问题：您甚至一开始就有非数字字符。导致您看到的失败的小数点来自 d 的错误计算。 d 应该是 modular multiplicative inverse of e, and it will always be an integer when calculated correctly. Yours, however, was coming up as a decimal more often than not when I ran this code. This is one of the bits of RSA that people choke on most often, since it involves manipulating the modulo operator in ways that people without a math background aren't typically taught. One of the more common, efficient ways to calculate this value is to use the Extended Euclidean algorithm.

关于您在解决上述两个问题后可能运行的事情的更多注意事项：

e 应与 Phi_N 互质且小于 Phi_N，您目前尚未验证。如果不这样做，可能无法正确计算 d（只有少数几对数字具有模乘逆）。最简单（虽然不是严格正确）的方法是在 e 下面使用一个 while 循环，就像您对素数所做的那样，它会检查 False == primeCheck(e) or e >= Phi_N。更准确地说，你必须编写一个包含 Phi_N 和 e 的互质检查，并断言它们除了 1 之外没有共同因子。
您消息的填充版本 m 必须小于 N。如果不这样做，当您尝试在解密期间反转取幂时，可能会导致某些消息无法恢复。为了更容易地验证这一点，您可能希望在用户 select P 和 Q （他们是更有可能改变他们的数字而不是他们想要发送的消息），然后在提供两个素数后添加一个额外的门来检查 N > m.

使用 Python 在 RSA 算法中将文本转换为数字时无法修复错误

Error I can't fix while converting text to number in RSA algorithm using Python

python

algorithm

encryption

cryptography

rsa