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Solutions

Table of Contents

Shift Ciphers

Question 1

Part A :

Given some character, we are able to map it to a numerical value in the set {0, 1, ..., 25}. Knowing that the key of 13 is utilized, we can state that two operations results in 13 + 13 shifts, which results in a shift of 26 modulo 26. This is equivalent to zero, meaning that for any number n 0-25, two shifts is equivalent to n + 0. While one shift encrypts, this shows that two shifts is the same as doing nothing, making the second shift function as $D_{k}$.

Part B :

K = 17. This can be enumerated via brute force. This was done to show how simple it is to break a shift cipher, and why they are no longer utilized.

Question 2: