Question

1. Assume the integers modulo 26 encode the standard 26 letter alphabet using 1 for a,2 for b, and so on. The ciphertext message, SPGH OLKN IGTX UQIB JEDI, was intercepted and known to be encrypted with a Hill cipher. Decipher the message into plain English using the decryption matrix

[1 3]
[2 5]

Answer 1

To decrypt the message encrypted with a Hill cipher, convert the ciphertext into numbers, apply the inverse decryption matrix, take the modulo 26, and then convert the numbers back to letters to reveal the plaintext.

Step-by-step explanation:

To decrypt the ciphertext SPGH OLKN IGTX UQIB JEDI encrypted using a Hill cipher and the decryption matrix [1 3][2 5], we first convert the letters to numbers using the standard 26 letter alphabet encoding (A=1, B=2,..., Z=26). Each pair of numbers is then multiplied by the inverse of the encryption matrix to get the original text back. However, we must find the inverse of the given decryption matrix first. The given decryption matrix is already the inverse matrix of the encryption matrix, so we can directly use it in our calculations.

For each 2-letter block of the ciphertext, we form a vector, multiply it by the inverse matrix, and then convert the resulting numeric vector back to letters. When calculating the modulus of a negative number, remember to add 26 until you get a positive result which is less than 26.

The steps to decrypt will include:

1. Converting ciphertext letters to numbers.
2. Grouping numbers into blocks of two and multiplying them by the decryption matrix.
3. Calculating the modulo 26 of the resulting matrix to get a number between 1 and 26.
4. Converting numbers back to letters to get the plaintext.