Question

What is the decryption function for an affine cipher if the encryption function is c=(15p+13)mod26 ?

Answer 1

The decryption function for the given affine cipher encryption function c=(15p+13) mod 26 is D(c) = 7(c-13) mod 26, where 7 is the modular inverse of 15 mod 26.

Step-by-step explanation:

The decryption function for an affine cipher, where the encryption function is given by c=(15p+13) mod 26, can be found by applying the modular inverse of the multiplication factor in the encryption function. In this case, 15 is the multiplication factor. We first need to find the modular inverse of 15 modulo 26, which is the number that when multiplied by 15, gives a product of 1 modulo 26. Using the extended Euclidean algorithm, we find that the modular inverse of 15 mod 26 is 7, since (15 * 7) mod 26 = 1. Therefore, the decryption function D(c) = 7(c-13) mod 26 can be used to decrypt a ciphertext c.

Answer 2

The decryption function for the given affine cipher encryption function 'c=(15p+13) mod 26' is 'p = 7(c - 13) mod 26', where 7 is the modular inverse of 15 modulo 26.

Step-by-step explanation:

The decryption function for an affine cipher, given the encryption function c=(15p+13) mod 26, is found by computing the modular inverse of the multiplication factor (which is 15 in this case) and then using it to reverse the encryption process.

An affine cipher is a type of substitution cipher in which each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and then converted back to a letter.

The general form of the affine cipher encryption function is c = (ap + b) mod m, where p is the plaintext letter, c is the ciphertext letter, a and b are keys, and m is the size of the alphabet.

To decrypt, we first need to find the modular inverse of a mod m, which is the number a-1 such that (a * a-1) mod m = 1. Once we have the modular inverse a-1, the decryption function is p = a-1(c - b) mod m.

In this case, we calculate the inverse of 15 mod 26. In practice, this can be done using the Extended Euclidean Algorithm, resulting in 15-1 = 7 mod 26. Thus, the decryption function would be p = 7(c - 13) mod 26.