Math Problem Statement
Consider shift cipher So here, we have K = {0,..., 25) with Pr[k +K]= 1/26 for each key k. Now, we are given the following distribution over M: Pr[M=a] = 0.7 and Pr[M= z) = 0.3. What is the probability that the ciphertext is B?
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Modular Arithmetic
Cryptography
Formulas
Ciphertext C = (M + k) mod 26
P(C = B) = P(C = B | M = a) + P(C = B | M = z)
P(C = B | M = a) = Pr[M = a] × Pr[k = 1]
P(C = B | M = z) = Pr[M = z] × Pr[k = 2]
Theorems
Bayes' Theorem
Modulo Operation
Suitable Grade Level
Grades 11-12, Undergraduate Level
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