Paper 2010/589
Higher-order differential properties of Keccak and Luffa
Christina Boura, Anne Canteaut, and Christophe De Cannière
Abstract
In this paper, we identify higher-order differential and zero-sum properties in the full Keccak-f permutation, in the Luffa v1 hash function, and in components of the Luffa v2 algorithm. These structural properties rely on a new bound on the degree of iterated permutations with a nonlinear layer composed of parallel applications of smaller balanced Sboxes. These techniques yield zero-sum partitions of size $2^{1590}$ for the full Keccak-f permutation and several observations on the Luffa hash family. We first show that Luffa v1 applied to one-block messages is a function of 255 variables with degree at most 251. This observation leads to the construction of a higher-order differential distinguisher for the full Luffa v1 hash function, similar to the one presented by Watanabe et al. on a reduced version. We show that similar techniques can be used to find all-zero higher-order differentials in the Luffa v2 compression function, but the additional blank round destroys this property in the hash function.
Note: Correction on the typo in the ANF of the Sbox in Luffa v2 (first line of Page 9)
Metadata
- Available format(s)
-
PDF
PS
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Hash functionsdegreehigher-order differentialszero-sumsSHA-3
- Contact author(s)
- Anne Canteaut @ inria fr
- History
- 2010-11-24: last of 2 revisions
- 2010-11-20: received
- See all versions
- Short URL
- https://ia.cr/2010/589
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2010/589,
author = {Christina Boura and Anne Canteaut and Christophe De Cannière},
title = {Higher-order differential properties of Keccak and Luffa},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/589},
year = {2010},
url = {https://eprint.iacr.org/2010/589}
}
