A Lower Bound for the Nonlinearity of Exponential Welch Costas Functions
| Autor: | Hakala, Risto |
|---|---|
| Přispěvatelé: | Trape, Marie, Department of Information and Computer Science, Aalto University |
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
ACM: E.: Data/E.4: CODING AND INFORMATION THEORY
[MATH.MATH-IT]Mathematics [math]/Information Theory [math.IT] exponential function [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM] [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR] [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM] [MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT] ACM: E.: Data/E.3: DATA ENCRYPTION ACM: G.: Mathematics of Computing/G.2: DISCRETE MATHEMATICS [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] Welch Costas functions Fourier transform [INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT] Nonlinearity Computer Science::Information Theory [INFO.INFO-CR] Computer Science [cs]/Cryptography and Security [cs.CR] |
| Zdroj: | WCC 2011-Workshop on coding and cryptography WCC 2011-Workshop on coding and cryptography, Apr 2011, Paris, France. pp.397-404 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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