Paper 2019/881
On the Boomerang Uniformity of some Permutation Polynomials
Marco Calderini and Irene Villa
Abstract
The boomerang attack, introduced by Wagner in 1999, is a cryptanalysis technique against block ciphers based on differential cryptanalysis. In particular it takes into consideration two differentials, one for the upper part of the cipher and one for the lower part, and it exploits the dependency of these two differentials. At Eurocrypt'18, Cid et al. introduced a new tool, called the Boomerang Connectivity Table (BCT) that permits to simplify this analysis. Next, Boura and Canteaut introduced an important parameter for cryptographic S-boxes called boomerang uniformity, that is the maximum value in the BCT. Very recently, the boomerang uniformity of some classes of permutations (in particular quadratic functions) have been studied by Li, Qu, Sun and Li, and by Mesnager, Chunming and Maosheng. In this paper we further study the boomerang uniformity of some non-quadratic differentially 4-uniform functions. In particular, we consider the case of the Bracken-Leander cubic function and three classes of 4-uniform functions constructed by Li, Wang and Yu, obtained from modifying the inverse functions.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Vectorial Boolean functionsBoomerang uniformityBoomerang connectivity tableBoomerang attack
- Contact author(s)
- irene villa @ uib no
- History
- 2020-03-02: last of 2 revisions
- 2019-08-01: received
- See all versions
- Short URL
- https://ia.cr/2019/881
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/881,
author = {Marco Calderini and Irene Villa},
title = {On the Boomerang Uniformity of some Permutation Polynomials},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/881},
year = {2019},
url = {https://eprint.iacr.org/2019/881}
}
