Question

If it helps the marginal PMF is

Problem 6.2 In this proble, we wi look at a simple application of probability to cryptog- raphy. Alice would like to communicate a message to Bob but docs not want Eve to learn the message. The difficulty is that Eve can hear everything that Alice says. However, Alice and Bob both have access to a shared random key, which will allow Alice to hide the message from Eve. The block diagram below should help you visualize the scenario. Random Key Generator MAlice Bob M Eve? To be more precise, let's say Alice's message is represented by a discrete random variable M and the random key is represented by a discrete random variable K. Let M and K be independent with PMFs Pr(m)m-1 k - 0,1,2,3 otherwise. 0 0 otherwise Determine the conditional PMF PMIx (mr) and write it as a table. Are M and X independent? Briefly argue that Bob can recover M from X and K, but Eve can do no better than randomly guessing M since she only sees X P, (fora 0, 1,2,3 Ootherwise

Answer 1

Solubiont conch' Hond 1 드, Tte X70 (m, K Mcm hey

A vando myany vaama