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Breaking the Shift Cipher

A private-key encryption scheme consists of a set of all possible messages, called the message space M, and three algorithms, namely,

  • (a) Gen
  • (b) Enc
  • (c) Dec

The algorithm for key generation Gen is used to choose a key k at random from the set of all possible secert keys, denoted by the key space K.

The algorithm for encryption Enc takes as inputs the message m and the secret key k and outputs the ciphertext c.

The algorithm for decryption Dec inputs the ciphertext c and the key k and outputs the message m.

About the experiment:

Apparently, the system is easily broken if the total number of distinct secret keys is small, that is the key space K is small.

In this experiment, we work with a well-known historical encryption scheme, namely the shift cipher, that has a very small key space.

Your task is to break the shift cipher. Specifically, given (only) the ciphertext in some instance of a shift cipher, you need to find the plaintext and the secret key.