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Cascade Ciphers Revisited: Indifferentiability Analysis

Shannon defined an ideal (κ, n)-blockcipher as a secrecy system consisting of 2 independent n-bit random permutations. This work revisits the following question: in the ideal cipher model, can a cascade of several ideal (κ, n)blockciphers realize 2 independent n-bit random permutations, i.e. an ideal (2κ, n)-blockcipher? The motivation goes back to Shannon’s theory on product secrecy systems, and similar question was considered by Even and Goldreich (CRYPTO ’83) in different settings. Towards giving an answer, this work analyzes cascading independent ideal (κ, n)-blockciphers with two alternated independent keys in the indifferentiability framework of Maurer et al. (TCC 2004), and proves that for such alternating-key cascade, four stages is necessary and sufficient to achieve indifferentiability from an ideal (2κ, n)-blockcipher. This shows cascade capable of achieving key-length extension in the settings where keys are not necessarily secret.