Paper 2006/445

A class of quadratic APN binomials inequivalent to power functions

Lilya Budaghyan, Claude Carlet, and Gregor Leander

Abstract

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n (n12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-inequivalent to any known APN function, and in particular for n=12,24, they are therefore CCZ-inequivalent to any power function. It is also proven that, except in particular cases, the Gold mappings are CCZ-inequivalent to the Kasami and Welch functions.

Metadata
Available format(s)
PDF PS
Category
Secret-key cryptography
Publication info
Published elsewhere. Part of this paper was presented at ISIT 2006
Keywords
Affine equivalenceAlmost bentAlmost perfect nonlinearCCZ-equivalenceDifferential uniformityNonlinearityS-boxVectorial Boolean function
Contact author(s)
lilya @ science unitn it
History
2006-12-04: received
Short URL
https://ia.cr/2006/445
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2006/445,
      author = {Lilya Budaghyan and Claude Carlet and Gregor Leander},
      title = {A class of quadratic {APN} binomials inequivalent to power functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/445},
      year = {2006},
      url = {https://eprint.iacr.org/2006/445}
}
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