A Lower Bound for the Nonlinearity of Exponential Welch Costas Functions

Abstract : We study the nonlinearity of Exponential Welch Costas functions using the Fourier transform on Zn. Exponential Welch Costas functions are bijections from Zp-1 to Zp-1 defined using the exponential function of Zp, where p is an odd prime. Their linearity properties were recently studied by Drakakis, Requena, and McGuire, who conjectured that the absolute values of the Fourier coefficients of an Exponential Welch Costas function are bounded from above by O(p0,5+ ∈), where ∈ is a small constant. In this paper, we establish an upper bound of order O(√p log p), which is asymptotically strictly less than the bound conjectured by Drakakis et al.
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WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.397-404, 2011
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Risto Hakala. A Lower Bound for the Nonlinearity of Exponential Welch Costas Functions. WCC 2011 - Workshop on coding and cryptography, Apr 2011, Paris, France. pp.397-404, 2011. 〈inria-00614457〉

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