Paper 2013/019

Plain versus Randomized Cascading-Based Key-Length Extension for Block Ciphers

Peter Gaźi

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 $$ and block length $$: - For the plain cascade of odd (resp. even) length $$ we present a generic attack requiring roughly $$ (resp. $$) queries, being a generalization of both the meet-in-the-middle attack on double encryption and the best known attack on triple cascade. - For XOR-cascade of odd (resp. even) length $$ we prove security up to $$ (resp. $$) queries and also an improved bound $$ for the special case $$ 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 $$ queries. Since XOR-cascades are sequential, this proves tightness of our above result for XOR-cascades of length $$ 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.