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Shannon's Theorem

links: AC1 TOC - Security & Cryptography - Modern Cryptography MOC - Index

Shannon provided a characterization of perfectly secret encryption schemes.

We have an encryption scheme with \(|M| = |K| = |C|\), the scheme is perfectly secret iff:

  1. Every key \(k \in K\) is chosen with equal probability \(1/|K|\) by \(Gen\)
  2. For every \(m \in M\) and every \(c \in C\), there is a unique key \(k \in K\) such that \(Enc_k(m)\) outputs \(c\)

Given that \(M, K\) and \(C\) represent spaces (Message-, key- and ciphertextspace) and not concrete expressions/terms (as also stated in Shannon Cipher).

links: AC1 TOC - Security & Cryptography - Modern Cryptography MOC - Index