Alice is learning about the shift cipher. She chooses a random three-letter word (so all three-letter words in the dictionary have the same probability) and encrypts it using a shift cipher with a randomly chosen key (that is, each possible shift has probability 1/26). Eve intercepts the ciphertext mxp. (a) Compute P(M = cat | C = mxp). Show computational work. (b) Use the part (a) result to show that the shift cipher does not have perfect secrecy (this is also true because there are fewer keys than cipher texts). Show all work.

Alice is learning about the shift cipher. She chooses a random three-letter word (so all three-letter words in the dictionary have the same probability) and encrypts it using a shift cipher with a randomly chosen key (that is, each possible shift has probability 1/26). Eve intercepts the ciphertext mxp. (a) Compute P(M = cat | C = mxp). Show computational work. (b) Use the part (a) result to show that the shift cipher does not have perfect secrecy (this is also true because there are fewer keys than cipher texts). Show all work.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(a) Compute P(M = cat | C = mxp). Show computational work.

(b) Use the part (a) result to show that the shift cipher does not have perfect secrecy (this is also true because there are fewer keys than cipher texts). Show all work.

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