Plain versus randomized cascading-based key-length extension for block ciphers

Abstract

Cascading-based constructions represent the predominant approach to the problem of key-length extension for block ciphers. Besides the plain cascade, existing works also consider its modification containing key-whitening steps between the invocations of the block cipher, called randomized cascade or XOR-cascade. We contribute to the understanding of the security of these two designs by giving the following attacks and security proofs, assuming an underlying ideal block cipher with key length k and block length n: - For the plain cascade of odd (resp. even) length ℓ we present a generic attack requiring roughly 2k+ℓ-1/ℓ+1n (resp. 2 k+ℓ-2/ℓn) queries, being a generalization of both the meet-in-the-middle attack on double encryption and the best known attack on triple cascade. - For XOR-cascade of odd (resp. even) length ℓ we prove security up to 2k+ℓ-1/ℓ+1n (resp. 2 k+ℓ-2/ℓn) queries and also an improved bound 2 k+ℓ-1/ℓn for the special case ℓ ∈ {3,4} by relating the problem to the security of key-alternating ciphers in the random-permutation model. -Finally, for a natural class of sequential constructions where block-cipher encryptions are interleaved with key-dependent permutations, we show a generic attack requiring roughly 2k+ℓ-1/ℓn queries. Since XOR-cascades are sequential, this proves tightness of our above result for XOR-cascades of length ℓ ∈ {3,4} as well as their optimal security within the class of sequential constructions. These results suggest that XOR-cascades achieve a better security/efficiency trade-off than plain cascades and should be preferred. © 2013 International Association for Cryptologic Research.