Cryptology ePrint Archive: Report 2007/058
The simplest method for constructing APN polynomials EA-inequivalent to power functions
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.
 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.
 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.
Category / Keywords: secret-key cryptography / Affine equivalence, Almost bent, Almost perfect nonlinear, CCZ-equivalence, Differential uniformity, Nonlinearity, S-box, Vectorial Boolean function
Date: received 17 Feb 2007
Contact author: lilya at science unitn it
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Version: 20070220:101744 (All versions of this report)
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