Introduction to Cryptography with Coding Theory, 3rd Edition

4.6 Exercises

1. 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.

   1. Compute $P(M=cat\mid C=mxp)$. (Hint: Can mxp shift to cat?)

   2. Use your result from part (a) to show that the shift cipher does not have perfect secrecy (this is also true because there are fewer keys than ciphertexts; see the proposition at the end of the first section).

2. Alice is learning more advanced techniques for the shift cipher. She now chooses a random five-letter word (so all five-letter words in the dictionary have the same ...