Compulsory Assignment (Tuesday 8 September)
Problem 3.1 Consider the affine cipher on ,
with key . Encrypt the message
For he’s a jolly good fellow, for he’s a jolly good fellow.
Problem 3.2 Consider a polyalphabetic Cæsar (additive) cipher with key . Encrypt the message
For he’s a jolly good fellow, for he’s a jolly good fellow.
Problem 3.3 Compare the ciphertexts in Exercises 3.2 and 3.1. What do you see? Is the affine cipher monoalphabetic, polyalphabetic, or neither? Why?
Problem 3.4 Consider the ring . Write down a complete multiplication table, i.e. a where cell gives the product for . For each number identify the inverse such that .
Problem 3.5 Consider a polyalphabetic Cæsar (additive) cipher with a block length of . What is the keyspace ? What is the size ? Give reasons for your answers.
Problem 3.6 Consider the affine cipher applied to the 29-letter Scandinavian alphabet:
Which (if any) are the zero divisors of ? What is the size of the keyspace for the affine cipher modulo 29?