Question

In the affine cipher, how do you decrypt the ciphertext, and what does a^-1 mean in the encryption formula?

A) Decrypt by reversing the operations.
B) Decrypt by using the multiplicative inverse.
C) Decrypt by using a Caesar cipher.
D) Decrypt by rearranging the letters.

Answer 1

To decrypt an affine cipher, one uses the multiplicative inverse of the number used in the encryption process. The symbol a^-1 denotes the multiplicative inverse of a, which is used in the decryption formula.

Step-by-step explanation:

To decrypt the ciphertext in an affine cipher, one must perform the inverse of the encryption process. This is typically done by using the multiplicative inverse of the number by which each letter's numerical value has been multiplied during encryption. The notation a^-1 refers to the multiplicative inverse of a in modular arithmetic, meaning a number which, when multiplied by a, gives a product of 1 modulo the size of the alphabet.

Therefore, the correct answer to how one decrypts ciphertext in an affine cipher would be Answer B): Decrypt by using the multiplicative inverse.

To illustrate with a mathematical example, if we have used the encryption function E(x) = (ax + b) mod m to encrypt a message, the decryption function will be D(y) = a^-1(y - b) mod m, where y is your ciphertext, b is the additive key, m is the size of the alphabet, and a^-1 is the multiplicative inverse of a modulo m.