Plain versus Randomized Cascading-Based Key-Length Extension for Block Ciphers
Peter Gaži
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 $2^{k+\frac{l-1}{l+1}n}$ (resp. $2^{k+\frac{l-2}{l}n}$) 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 $2^{k+\frac{l-1}{l+1}n}$ (resp. $2^{k+\frac{l-2}{l}n}$) queries and also an improved bound $2^{k+\frac{l-1}{l}n}$ for the special case $l\in\{3,4\}$ 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 $2^{k+\frac{l-1}{l}n}$ queries. Since XOR-cascades are sequential, this proves tightness of our above result for XOR-cascades of length $l\in\{3,4\}$ 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.
BibTeX Citation
@inproceedings{Gazi13,
author = {Peter Gaži},
title = {Plain versus Randomized Cascading-Based Key-Length Extension for Block Ciphers},
booktitle = {Advances in Cryptology --- CRYPTO 2013},
pages = 551--570,
series = {Lecture Notes in Computer Science},
volume = 8042,
year = 2013,
month = 8,
note = {to appear},
publisher = {Springer-Verlag},
}