Alice want to send a single bit of information (a yes or a no) to Bob by means o

Question

Alice want to send a single bit of information (a yes or a no) to Bob by means of a word of length 2. Alice and Bob have four possible keys available to perform message authentication. The following matrix shows the 2-bit word sent for each message under each key: a. The preceding matrix is in a useful form for Alice. Construct a matrix with the same information that would be more useful for Bob. b. What is the probability that someone else can successfully impersonate Alice? c. What is the probability that someone can replace an intercepted message with another message successfully?

Explanation / Answer

a. The matrix which can be useful for bob can be:

b. The probability would be 1/2. How? because only two of the four words in [00,01,11,10] are possible as trasmitted word as shared secret key of both Alice and Bob.

c. The probability would be 1/2. Let's take an example in this case: If John intercepts the message and receives 00 then he knows that either key 1 or 2 was used. If key 1 was used then 0 was sent otherwise 1 was sent. To replace the message, John can use either 01 for the first case and 10 for the second case giving us the probability of 1/2.

Key/Sent 00 01 10 11 1 0 1 - - 2 1 - 0 - 3 - 0 - 1 4 - - 1 0

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