Paper 2018/713
On CCZ-Equivalence, Extended-Affine Equivalence, and Function Twisting
Anne Canteaut and Léo Perrin
Abstract
Two vectorial Boolean functions are ``CCZ-equivalent'' if there exists an affine permutation mapping the graph of one to the other. It preserves many of the cryptographic properties of a function such as its differential and Walsh spectra, which is why it could be used by Dillon et al. to find the first APN permutation on an even number of variables. However, the meaning of this form of equivalence remains unclear. In fact, to the best of our knowledge, it is not known how to partition a CCZ-equivalence class into its Extended-Affine (EA) equivalence classes; EA-equivalence being a simple particular case of CCZ-equivalence.
In this paper, we characterize CCZ-equivalence as a property of the zeroes in the Walsh spectrum of a function
Note: Updated to take into account the comments of the FFA reviewers and of Christof Beierle.
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Published elsewhere. Minor revision. Finite Fields and their Applications
- Keywords
- Boolean functionsCCZ-EquivalenceEA-equivalenceTwistAPNButterfly
- Contact author(s)
- perrin leo @ gmail com
- History
- 2018-12-05: revised
- 2018-08-01: received
- See all versions
- Short URL
- https://ia.cr/2018/713
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2018/713, author = {Anne Canteaut and Léo Perrin}, title = {On {CCZ}-Equivalence, Extended-Affine Equivalence, and Function Twisting}, howpublished = {Cryptology {ePrint} Archive, Paper 2018/713}, year = {2018}, url = {https://eprint.iacr.org/2018/713} }