Prove that the affine cipher over Z26 has perfect secrecy if every key is used with equal probability of 1/312.

Just some guidance/help with this problem would be greatly appreciated not sure how to start the proof. Many thanks!

  • 2
    $\begingroup$ Well, I'd start by reviewing the definition of perfect secrecy. $\endgroup$ – pg1989 Oct 17 '14 at 0:12
  • $\begingroup$ Note that such a cipher would have perfect secrecy only if the key is used only once. $\endgroup$ – poncho Mar 7 '16 at 16:41

This would usually I think be more suited as a comment, but you were looking for guidance instead of a complete answer as it were, and I don't have enough reputation to comment.

I'd highly recommend Claude Shannon's introduction (the literal introduction, he developed the concept) to the question you pose. Here’s the paper (PDF) and the section is Part 10 on Pg. 679. The more broad statement of your question is Theorem 6, but he does (as he always does) an incredibly good job of approaching both the motivation for the theorem as well as the proof, the latter of which he gives in relatively informal way.

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