🥥Python密码线性方程组和频率分析

本文将了解：模算术；最大公约数 (GCD) 的重要性；群论；伪随机数；创建用于频率分析的 Python 脚本。

模运算和最大公约数

商余定理指出，对于每个整数 $A$ 和正数 $B$，存在不同的整数 $Q$ 和 $R$，使得：$A=B^{*} Q+R, 0=<r=<b$。当 $a=95$ 且 $\vec{b}=10$ 时，$q$（商）和 $r$（余数）的唯一值是多少？你发现商等于 9，余数等于 5。

一旦你理解了商余定理，就更容易理解我们的密码数学的第一部分：模运算。

质数(素数)

密码学中的素数对于我们的加密方案的安全性至关重要。素数分解，也称为整数分解，是一个用于保护公钥加密方案的数学问题。这是通过使用极大的半素数来实现的，这些半素数是两个素数相乘的结果。您可能还记得，素数是任何只能被 1 和自身整除的数。第一个质数是2。

基本群论

在抽象代数和其他数学领域，群论研究称为群的代数结构。群的概念是抽象代数的核心：其他熟悉的代数结构，如向量空间、环和域，都可以作为具有附加运算和公理的群来执行。当您探索 Diffie-Hellman 和 RSA 加密系统时，群论开始发挥作用。

折叠目录

模逆

扩展最大公约数

欧拉定律

伪随机性

线性方程组

频率分析


test_str = "We hold these truths to be self-evident, that all men are
created equal, "
test_str += "that they are endowed by their Creator with certain
unalienable Rights, "
test_str += "that among these are Life, "
test_str += "Liberty and the pursuit of Happiness."

all_freq = {}
for i in test_str:
 if i in all_freq:
 all_freq[i] += 1
 else:
 all_freq[i] = 1

print()
print ("Count of all characters in the provided text is :\\n " + str(all_freq))

from collections import Counter

test_str = "We hold these truths to be self-evident, that all men are created equal, "
test_str += "that they are endowed by their Creator with certain unalienable Rights, "
test_str += "that among these are Life, "
test_str += "Liberty and the pursuit of Happiness."

res = Counter(test_str)

Python密码分析

Python密码协议释秘

示例

import binascii
def text2int(msg):
    print (msg)
    msg = msg.encode()
    hexstr = binascii.hexlify(msg)
    print (hexstr)

    back2hex = format(integer_m, 'x')
    print (back2hex)

    evenpad = ('0' * (len(back2hex) % 2)) + back2hex

    plaintext = binascii.unhexlify(evenpad)
    print (plaintext)

text2int("Hello World")

Python密码混淆数据

示例

import sys
import numpy as np

def cipher_encryption(plain, key):

    len_chk = 0
    if len(plain) % 2 != 0:
        plain += "0"
        len_chk = 1

    # msg to matrices
    row = 2
    col = int(len(plain)/2)
    msg2d = np.zeros((row, col), dtype=int)

    itr1 = 0
    itr2 = 0
    for i in range(len(plain)):
        if i%2 == 0:
            msg2d[0][itr1]= int(ord(plain[i]) - 65)
            itr1 += 1
        else:
            msg2d[1][itr2] = int(ord(plain[i]) - 65)
            itr2 += 1

    # finding multiplicative inverse
    for i in range(26):
        temp_inv = deter * i
        if temp_inv % 26 == 1:
            mul_inv = i
            break
        else:
            continue

    if mul_inv == -1:
        print("Invalid key")
        sys.exit()

    encryp_text = ""
    itr_count = int(len(plain)/2)
    if len_chk == 0:
        for i in range(itr_count):
            temp1 = msg2d[0][i] * key2d[0][0] + msg2d[1][i] * key2d[0][1]
            encryp_text += chr((temp1 % 26) + 65)
            temp2 = msg2d[0][i] * key2d[1][0] + msg2d[1][i] * key2d[1][1]
            encryp_text += chr((temp2 % 26) + 65)
    else:
        for i in range(itr_count-1):
            temp1 = msg2d[0][i] * key2d[0][0] + msg2d[1][i] * key2d[0][1]
            encryp_text += chr((temp1 % 26) + 65)
            temp2 = msg2d[0][i] * key2d[1][0] + msg2d[1][i] * key2d[1][1]
            encryp_text += chr((temp2 % 26) + 65)

    print("Encrypted text: {}".format(encryp_text))
    return encryp_text

def cipher_decryption(cipher, key):

    # if message length is an odd number, place a zero at the end.
    len_chk = 0
    if len(cipher) % 2 != 0:
        cipher += "0"
        len_chk = 1

    # msg to matrices
    row = 2
    col = int(len(cipher)/2)
    msg2d = np.zeros((row, col), dtype=int)

    itr1 = 0
    itr2 = 0
    for i in range(len(cipher)):
        if i%2 == 0:
            msg2d[0][itr1]= int(ord(cipher[i]) - 65)
            itr1 += 1
        else:
            msg2d[1][itr2] = int(ord(cipher[i]) - 65)
            itr2 += 1

Python流密码和分组密码

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Python PKI-RSA和ECC加密消息

🏈指点迷津 | Brief

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import sys import numpy as np def cipher_encryption(plain, key): len_chk = 0 if len(plain) % 2 != 0: plain += "0" len_chk = 1 # msg to matrices row = 2 col = int(len(plain)/2) msg2d = np.zeros((row, col), dtype=int) itr1 = 0 itr2 = 0 for i in range(len(plain)): if i%2 == 0: msg2d[0][itr1]= int(ord(plain[i]) - 65) itr1 += 1 else: msg2d[1][itr2] = int(ord(plain[i]) - 65) itr2 += 1 # finding multiplicative inverse for i in range(26): temp_inv = deter * i if temp_inv % 26 == 1: mul_inv = i break else: continue if mul_inv == -1: print("Invalid key") sys.exit() encryp_text = "" itr_count = int(len(plain)/2) if len_chk == 0: for i in range(itr_count): temp1 = msg2d[0][i] * key2d[0][0] + msg2d[1][i] * key2d[0][1] encryp_text += chr((temp1 % 26) + 65) temp2 = msg2d[0][i] * key2d[1][0] + msg2d[1][i] * key2d[1][1] encryp_text += chr((temp2 % 26) + 65) else: for i in range(itr_count-1): temp1 = msg2d[0][i] * key2d[0][0] + msg2d[1][i] * key2d[0][1] encryp_text += chr((temp1 % 26) + 65) temp2 = msg2d[0][i] * key2d[1][0] + msg2d[1][i] * key2d[1][1] encryp_text += chr((temp2 % 26) + 65) print("Encrypted text: {}".format(encryp_text)) return encryp_text def cipher_decryption(cipher, key): # if message length is an odd number, place a zero at the end. len_chk = 0 if len(cipher) % 2 != 0: cipher += "0" len_chk = 1 # msg to matrices row = 2 col = int(len(cipher)/2) msg2d = np.zeros((row, col), dtype=int) itr1 = 0 itr2 = 0 for i in range(len(cipher)): if i%2 == 0: msg2d[0][itr1]= int(ord(cipher[i]) - 65) itr1 += 1 else: msg2d[1][itr2] = int(ord(cipher[i]) - 65) itr2 += 1