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Paper: The simplest method for constructing APN polynomials EA-inequivalent to power functions

Authors:
Lilya Budaghyan
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URL: http://eprint.iacr.org/2007/058
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Abstract: The first APN polynomials EA-inequivalent to power functions have been constructed in [1,2] by applying CCZ-equivalence to the Gold APN functions. It is a natural question whether it is possible to construct APN polynomials EA-inequivalent to power functions by using only EA-equivalence and inverse transformation on a power APN function: this would be the simplest method to construct APN polynomials EA-inequivalent to power functions. In the present paper we prove that the answer to this question is positive. By this method we construct a class of APN polynomials EA-inequivalent to power functions. On the other hand it is shown that the APN polynomials from [1,2] cannot be obtained by the introduced method. [1] L. Budaghyan, C. Carlet, A. Pott. New Classes of Almost Bent and Almost Perfect Nonlinear Functions. IEEE Trans. Inform. Theory, vol. 52, no. 3, pp. 1141-1152, March 2006. [2] L. Budaghyan, C. Carlet, A. Pott. New Constructions of Almost Bent and Almost Perfect Nonlinear Functions. Proceedings of the Workshop on Coding and Cryptography 2005, pp. 306-315, 2005.
BibTeX
@misc{eprint-2007-13340,
  title={The simplest method for constructing APN polynomials EA-inequivalent to power functions},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / Affine equivalence, Almost bent, Almost perfect nonlinear, CCZ-equivalence, Differential uniformity, Nonlinearity, S-box, Vectorial Boolean function},
  url={http://eprint.iacr.org/2007/058},
  note={ lilya@science.unitn.it 13561 received 17 Feb 2007},
  author={Lilya Budaghyan},
  year=2007
}