jekyll - 3 months ago 30

C Question

Here is my code. I tried to decrypt an affine cipher. My .txt files include two cipher: alpha and beta. Alpha is an odd number because gcd(alpha, 26)==1 but decryption doesnt work correctly. For example: the encrypted word **UVOVE**, when decrypted, turns out in the **AAAAA** word but it should be "BAHAR". Keys are: alpha:25 and beta:5

`fscanf(key_alpha, "%d", &alpha);`

fscanf(key_beta, "%d", &beta);

while((c = getc(cipher)) != EOF)

{

putc(((toupper(c) - 65 - beta) / alpha)% 26 + 65, decrypt); // 65 = the numeric value of A in ASCII

}

rewind(cipher);

Answer

E(x)=ax+b mod 26

D(x)=a^(-1)x-b mod 26

**a^(-1)** mod 26 is not just simply 1/26. It is a multiplicative inverse of a number **a**. It means that **a^(-1)** is such that a*a^(-1) = 1 mod 26.

If a=25 => a^(-1)=25.

Use euclidean algorithm to find multiplicative inverse mod 26.

If you want to avoid problem with negative numbers you can just use additive inverse of b mod 26. Additive inverse of b mod 26 is a number b' such that b + b' = 0 mod 26. In your case b'=21.

```
putc(((toupper(c) - 65 + add_inv_beta) * mul_inv_alpha) % 26 + 65, decrypt);
```