Paper 2021/1571 Original: eprint.iacr.org/2021/1571 ↗
Tight Security for Key-Alternating Ciphers with Correlated Sub-Keys
Abstract
A substantial effort has been devoted to proving optimal bounds for the security of key-alternating ciphers with independent sub-keys in the random permutation model (e.g., Chen and Steinberger, EUROCRYPT '14; Hoang and Tessaro, CRYPTO '16). While common in the study of multi-round constructions, the assumption that sub-keys are truly independent is not realistic, as these are generally highly correlated and generated from shorter keys. In this paper, we show the existence of non-trivial distributions of limited independence for which a t-round key-alternating cipher achieves optimal security. Our work is a natural continuation of the work of Chen et al. (CRYPTO '14) which considered the case of t = 2 when all-subkeys are identical. Here, we show that key-alternating ciphers remain secure for a large class of (t-1)-wise and (t-2)-wise independent distribution of sub-keys. Our proofs proceed by generalizations of the so-called Sum-Capture Theorem, which we prove using Fourier-analytic techniques.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2021-12-10: last updated
- 2021-12-03: published
- Short URL
- https://ia.cr/2021/1571
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/1571,
author = {Stefano Tessaro and Xihu Zhang},
title = {Tight Security for Key-Alternating Ciphers with Correlated Sub-Keys},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1571},
year = {2021},
url = {https://eprint.iacr.org/2021/1571}
}