A substitution cipher (see Example 10.16) is a simple cryptographic scheme in which we choose a…

 

A substitution cipher (see Example 10.16) is a simple cryptographic scheme in which we choose a permutation π of the alphabet, and replace each letter i with πi . (Decryption is the same process, but backward: replace πi by i.) However, substitution ciphers are susceptible to frequency analysis, in which an eavesdropper who observes the encrypted message (the ciphertext) infers that the most common letter in the ciphertext probably corresponds to the most common letter in English text (the letter E), the second-most common to the second-most common (T), and so on

1. (programming required) Write a program that generates a random permutation π of the alphabet, and encrypts a given input text using π. (Leave all non-alphabetic characters unchanged.)

2. (programming required) Write a program that takes a text as input, converts it to upper case, and produces as output a vector hfA, fB, . . . , fZi, where f• is the fraction of letters in the input text that are the letter •. (So f will be a probability distribution over the alphabet.)

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