仿射密码的实现
仿射密码是一种单字母替换密码，其中字母表中的每个字母都映射到其等效数字，使用简单的数学函数加密，然后转换回字母。使用的公式意味着每个字母加密到另一个字母，然后再加密，这意味着密码本质上是一种标准替换密码，具有控制哪个字母去哪个字母的规则。
整个过程依赖于工作模 m（使用的字母的长度）。在仿射密码中，大小为 m 的字母表中的字母首先映射到 0 ... m-1 范围内的整数。
仿射密码的“密钥”由 2 个数字组成，我们称它们为 a 和 b。以下讨论假设使用 26 个字符的字母表 (m = 26)。 a 应该被选择为与 m 互质（即 a 应该与 m 没有共同因子）。
加密
它使用模运算将每个明文字母对应的整数转换为另一个密文字母对应的整数。单个字母的加密函数是
E ( x ) = ( a x + b ) mod m
modulus m: size of the alphabet
a and b: key of the cipher.
a must be chosen such that a and m are coprime.解密
在解密密文时，我们必须对密文执行相反的（或逆向）函数来检索明文。再一次，第一步是将每个密文字母转换为它们的整数值。解密函数为
D ( x ) = a^-1 ( x - b ) mod m
a^-1 : modular multiplicative inverse of a modulo m. i.e., it satisfies the equation
1 = a a^-1 mod m .求乘法逆
我们需要找到一个数 x 使得：
如果我们找到数 x 使得等式成立，则 x 是 a 的倒数，我们称其为 a^-1。求解这个方程的最简单方法是搜索 1 到 25 中的每一个数字，看看哪一个满足方程。
[g,x,d] = gcd(a,m); % we can ignore g and d, we dont need them
x = mod(x,m); 如果现在将 x 和 a 相乘并减少结果（模 26），您将得到答案 1。请记住，这只是逆的定义，即如果 a*x = 1（模 26），则 x 是逆a 的（并且 a 是 x 的倒数）
例子：
C++
//CPP program to illustrate Affine Cipher
#include
using namespace std;
//Key values of a and b
const int a = 17;
const int b = 20;
string encryptMessage(string msg)
{
///Cipher Text initially empty
string cipher = "";
for (int i = 0; i < msg.length(); i++)
{
// Avoid space to be encrypted
if(msg[i]!=' ')
/* applying encryption formula ( a x + b ) mod m
{here x is msg[i] and m is 26} and added 'A' to
bring it in range of ascii alphabet[ 65-90 | A-Z ] */
cipher = cipher +
(char) ((((a * (msg[i]-'A') ) + b) % 26) + 'A');
else
//else simply append space character
cipher += msg[i];
}
return cipher;
}
string decryptCipher(string cipher)
{
string msg = "";
int a_inv = 0;
int flag = 0;
//Find a^-1 (the multiplicative inverse of a
//in the group of integers modulo m.)
for (int i = 0; i < 26; i++)
{
flag = (a * i) % 26;
//Check if (a*i)%26 == 1,
//then i will be the multiplicative inverse of a
if (flag == 1)
{
a_inv = i;
}
}
for (int i = 0; i < cipher.length(); i++)
{
if(cipher[i]!=' ')
/*Applying decryption formula a^-1 ( x - b ) mod m
{here x is cipher[i] and m is 26} and added 'A'
to bring it in range of ASCII alphabet[ 65-90 | A-Z ] */
msg = msg +
(char) (((a_inv * ((cipher[i]+'A' - b)) % 26)) + 'A');
else
//else simply append space character
msg += cipher[i];
}
return msg;
}
//Driver Program
int main(void)
{
string msg = "AFFINE CIPHER";
//Calling encryption function
string cipherText = encryptMessage(msg);
cout << "Encrypted Message is : " << cipherText< Java
// Java program to illustrate Affine Cipher
class GFG
{
// Key values of a and b
static int a = 17;
static int b = 20;
static String encryptMessage(char[] msg)
{
/// Cipher Text initially empty
String cipher = "";
for (int i = 0; i < msg.length; i++)
{
// Avoid space to be encrypted
/* applying encryption formula ( a x + b ) mod m
{here x is msg[i] and m is 26} and added 'A' to
bring it in range of ascii alphabet[ 65-90 | A-Z ] */
if (msg[i] != ' ')
{
cipher = cipher
+ (char) ((((a * (msg[i] - 'A')) + b) % 26) + 'A');
} else // else simply append space character
{
cipher += msg[i];
}
}
return cipher;
}
static String decryptCipher(String cipher)
{
String msg = "";
int a_inv = 0;
int flag = 0;
//Find a^-1 (the multiplicative inverse of a
//in the group of integers modulo m.)
for (int i = 0; i < 26; i++)
{
flag = (a * i) % 26;
// Check if (a*i)%26 == 1,
// then i will be the multiplicative inverse of a
if (flag == 1)
{
a_inv = i;
}
}
for (int i = 0; i < cipher.length(); i++)
{
/*Applying decryption formula a^-1 ( x - b ) mod m
{here x is cipher[i] and m is 26} and added 'A'
to bring it in range of ASCII alphabet[ 65-90 | A-Z ] */
if (cipher.charAt(i) != ' ')
{
msg = msg + (char) (((a_inv *
((cipher.charAt(i) + 'A' - b)) % 26)) + 'A');
}
else //else simply append space character
{
msg += cipher.charAt(i);
}
}
return msg;
}
// Driver code
public static void main(String[] args)
{
String msg = "AFFINE CIPHER";
// Calling encryption function
String cipherText = encryptMessage(msg.toCharArray());
System.out.println("Encrypted Message is : " + cipherText);
// Calling Decryption function
System.out.println("Decrypted Message is: " + decryptCipher(cipherText));
}
}
// This code contributed by Rajput-JiPython
# Implementation of Affine Cipher in Python
# Extended Euclidean Algorithm for finding modular inverse
# eg: modinv(7, 26) = 15
def egcd(a, b):
x,y, u,v = 0,1, 1,0
while a != 0:
q, r = b//a, b%a
m, n = x-u*q, y-v*q
b,a, x,y, u,v = a,r, u,v, m,n
gcd = b
return gcd, x, y
def modinv(a, m):
gcd, x, y = egcd(a, m)
if gcd != 1:
return None # modular inverse does not exist
else:
return x % m
# affine cipher encryption function
# returns the cipher text
def affine_encrypt(text, key):
'''
C = (a*P + b) % 26
'''
return ''.join([ chr((( key[0]*(ord(t) - ord('A')) + key[1] ) % 26)
+ ord('A')) for t in text.upper().replace(' ', '') ])
# affine cipher decryption function
# returns original text
def affine_decrypt(cipher, key):
'''
P = (a^-1 * (C - b)) % 26
'''
return ''.join([ chr((( modinv(key[0], 26)*(ord(c) - ord('A') - key[1]))
% 26) + ord('A')) for c in cipher ])
# Driver Code to test the above functions
def main():
# declaring text and key
text = 'AFFINE CIPHER'
key = [17, 20]
# calling encryption function
affine_encrypted_text = affine_encrypt(text, key)
print('Encrypted Text: {}'.format( affine_encrypted_text ))
# calling decryption function
print('Decrypted Text: {}'.format
( affine_decrypt(affine_encrypted_text, key) ))
if __name__ == '__main__':
main()
# This code is contributed by
# Bhushan BoroleC#
// C# program to illustrate Affine Cipher
using System;
class GFG
{
// Key values of a and b
static int a = 17;
static int b = 20;
static String encryptMessage(char[] msg)
{
/// Cipher Text initially empty
String cipher = "";
for (int i = 0; i < msg.Length; i++)
{
// Avoid space to be encrypted
/* applying encryption formula ( a x + b ) mod m
{here x is msg[i] and m is 26} and added 'A' to
bring it in range of ascii alphabet[ 65-90 | A-Z ] */
if (msg[i] != ' ')
{
cipher = cipher
+ (char) ((((a * (msg[i] - 'A')) + b) % 26) + 'A');
} else // else simply append space character
{
cipher += msg[i];
}
}
return cipher;
}
static String decryptCipher(String cipher)
{
String msg = "";
int a_inv = 0;
int flag = 0;
//Find a^-1 (the multiplicative inverse of a
//in the group of integers modulo m.)
for (int i = 0; i < 26; i++)
{
flag = (a * i) % 26;
// Check if (a*i)%26 == 1,
// then i will be the multiplicative inverse of a
if (flag == 1)
{
a_inv = i;
}
}
for (int i = 0; i < cipher.Length; i++)
{
/*Applying decryption formula a^-1 ( x - b ) mod m
{here x is cipher[i] and m is 26} and added 'A'
to bring it in range of ASCII alphabet[ 65-90 | A-Z ] */
if (cipher[i] != ' ')
{
msg = msg + (char) (((a_inv *
((cipher[i] + 'A' - b)) % 26)) + 'A');
}
else //else simply append space character
{
msg += cipher[i];
}
}
return msg;
}
// Driver code
public static void Main(String[] args)
{
String msg = "AFFINE CIPHER";
// Calling encryption function
String cipherText = encryptMessage(msg.ToCharArray());
Console.WriteLine("Encrypted Message is : " + cipherText);
// Calling Decryption function
Console.WriteLine("Decrypted Message is: " + decryptCipher(cipherText));
}
}
/* This code contributed by PrinciRaj1992 */输出：
Encrypted Message is : UBBAHK CAPJKX
Decrypted Message is : AFFINE CIPHER