Abstract
Almost Perfect Nonlinear (APN) S-boxes are used in block ciphers to prevent differential attacks. The non-evidence of permutation APN S-box on even number of variables and the efficiency of power functions bring the importance of power APN S-boxes to use in block ciphers. We present a special class of 3-to-1 S-box (named as S3-to-1 S-box) on even number of variables. The power APN S-boxes on even number of variables fall in this class. Further, another important class of APN functions X 3 + tr(X 9) too falls in this class. We study some results of S3-to-1 S-boxes. In another section we present a necessary condition for power functions to be APN. Using this necessary condition we can filter out some non-APN power functions. Specifically, if the number of variables is multiple of small primes, then one can filter out many non-APN functions.
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Dalai, D.K. (2008). On 3-to-1 and Power APN S-Boxes. In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds) Sequences and Their Applications - SETA 2008. SETA 2008. Lecture Notes in Computer Science, vol 5203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85912-3_33
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DOI: https://doi.org/10.1007/978-3-540-85912-3_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85911-6
Online ISBN: 978-3-540-85912-3
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