By Boris Youssin

ISBN-10: 0821824953

ISBN-13: 9780821824955

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Rose. Rewriting variables: the complexity of fast algebraic attacks on stream ciphers. Cryptology ePrint Archive, Report 2004/081, 2004. org/2004/081. 37. -D. Hou. New constructions of bent functions, International Conference on Combinatorics, Information Theory and Statistics; Journal of Combinatorics, Information and System Sciences, Vol. 24, Nos. 3-4, pp. 275-291, 1999. 38. -D. Hou. Group actions on binary resilient functions. Appl. Algebra Eng. Commun. Comput. 14(2), pp. 97-115, 2003. 39. -D.

Proof. If p (x) = p (y), then dH (M x, M y) ≥ 2. , dH (x, y) = dH (M x, M y). As we shall see below, for q = 2 and q = 3 all GPC’s are monomially equivalent, but the next theorem guarantees that for most values of q, there exist more than one monomial equivalence class. 2. If G and H are nonisomorphic groups of order q, then for k ≥ 2, pG and pH are not monomially equivalent. Proof. Omitted. Let us denote by N (k, q) the number of nonisomorphic (k, q) GPC’s. The following table summarizes what we know about this number.

C. Carlet. More correlation-immune and resilient functions over Galois ﬁelds and Galois rings. Advances in Cryptology, EUROCRYPT’ 97, Lecture Notes in Computer Science 1233, 422-433, Springer Verlag, 1997. 10. C. Carlet. Recent results on binary bent functions. International Conference on Combinatorics, Information Theory and Statistics; Journal of Combinatorics, Information and System Sciences, Vol. 24, Nos. 3-4, pp. 275-291, 1999. 26 C. Carlet 11. C. Carlet. On the coset weight divisibility and nonlinearity of resilient and correlation-immune functions, Proceedings of SETA’01 (Sequences and their Applications 2001), Discrete Mathematics and Theoretical Computer Science, Springer, pp.

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