G-Perfect Nonlinear Functions

Authors

James A. Davis, University of RichmondFollow
Laurent Poinsot

DOI

10.1007/s10623-007-9137-7

Abstract

Perfect nonlinear functions are used to construct DES-like cryptosystems that are resistant to differential attacks. We present generalized DES-like cryptosystems where the XOR operation is replaced by a general group action. The new cryptosystems, when combined with G-perfect nonlinear functions (similar to classical perfect nonlinear functions with one XOR replaced by a general group action), allow us to construct systems resistant to modified differential attacks. The more general setting enables robust cryptosystems with parameters that would not be possible in the classical setting. We construct several examples of G-perfect nonlinear functions, both Z₂ -valued and Z^a₂ -valued. Our final constructions demonstrate G-perfect nonlinear planar permutations (from Z^a₂ to itself), thus providing an alternative implementation to current uses of almost perfect nonlinear functions.

Document Type

Post-print Article

Publication Date

1-2008

Publisher Statement

Copyright © 2008 Springer.

The definitive version is available at: http://link.springer.com/article/10.1007/s10623-007-9137-7

DOI: 10.1007/s10623-007-9137-7

Full Citation:

Davis, James A., and Laurent Poinsot. "G-Perfect Nonlinear Functions."Designs, Codes, and Cryptography 46, no. 1 (January 2008): 83-96. doi: 10.1007/s10623-007-9137-7.

Recommended Citation

Davis, James A. and Poinsot, Laurent, "G-Perfect Nonlinear Functions" (2008). Department of Math & Statistics Faculty Publications. 141.
https://scholarship.richmond.edu/mathcs-faculty-publications/141