Paper 2011/503
On the influence of the algebraic degree of $F^{−1}$ on the algebraic degree of $G \circ F$
Christina Boura and Anne Canteaut
Abstract
We present a study on the algebraic degree of iterated permutations seen as multivari- ate polynomials. Our main result shows that this degree depends on the algebraic degree of the inverse of the permutation which is iterated. This result is also extended to non-injective balanced vectorial functions where the relevant quantity is the minimal degree of the inverse of a permutation expanding the function. This property has consequences in symmetric cryptography since several attacks or distinguishers exploit a low algebraic degree, like higher-order differential attacks, cube attacks and cube testers, or algebraic attacks. Here, we present some applications of this improved bound to a higher-degree variant of the block cipher KN , to the block cipher Rijndael-256 and to the inner permutations of the hash functions ECHO and JH.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Unknown where it was published
- Contact author(s)
- christina boura @ inria fr
- History
- 2011-09-18: revised
- 2011-09-18: received
- See all versions
- Short URL
- https://ia.cr/2011/503
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2011/503,
author = {Christina Boura and Anne Canteaut},
title = {On the influence of the algebraic degree of $F^{−1}$ on the algebraic degree of $G \circ F$},
howpublished = {Cryptology {ePrint} Archive, Paper 2011/503},
year = {2011},
url = {https://eprint.iacr.org/2011/503}
}
