Further Results on the Relation Between Nonlinearity and Resiliency for Boolean Functions
A good design of a Boolean function used in a stream cipher requires that the function satisfies certain criteria in order to resist different attacks. In this paper we study the tradeoff between two such criteria, the nonlinearity and the resiliency. The results are twofold. Firstly, we establish the maximum nonlinearity for a fixed resiliency in certain cases. Secondly, we present a simple search algorithm for finding Boolean functions with good nonlinearity and some fixed resiliency.
KeywordsBoolean Function Stream Cipher Bend Function Hadamard Matrix Algebraic Degree
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- 1.P. Camion, C. Carlet, P. Charpin and N. Sendrier, “On Correlation-Immune functions”, Advances in Cryptology-CRYPTO’91, Lecture Notes in Computer Science, 1233, pp. 422–33, Springer-Verlag, 1997.Google Scholar
- 3.L.E. Dickson (1900), Linear Groups with an Exposition of the Galois Field Theory, Teubner, Leipzig 1900; Dover, New York, 1958.Google Scholar
- 5.R. Gallager, Information theory and reliable communication, 1968.Google Scholar
- 7.B. Kolman and R.E. Beck, Elementary Linear Programming with Applications, Academic Press, 1995.Google Scholar
- 8.S. Maitra and P. Sarkar, “Highly Nonlinear Resilient Functions Optimizing Siegen-thaler’s Inequality” Advances in Cryptology-CRYPTO’99, Lecture Notes in Computer Science, 1666, pp. 198–215, Springer-Verlag, 1999.Google Scholar
- 9.W. Meier, and O. Staffelbach, “Fast correlation attacks on certain stream ciphers”, Advances in Cryptology-EUROCRYPT’88, Lecture Notes in Computer Science, 330, pp. 301–314, Springer-Verlag, 1988.Google Scholar
- 10.A. Menezes, P. van Oorschot, S. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997.Google Scholar
- 12.W. Millan, A. Clark and E. Dawson, “An effective genetic algorithm for finding highly nonlinear Boolean functions”, In First International Conference on Information and Communications Security, Lecture Notes in Computer Science, 1334, pp. 149–158, 1997.Google Scholar