By Huaxiong Wang, Yongqing Li, Shengyuan Zhang
Li Y., Ling S., Niederreiter H., Wang H., Xing C. (eds.) Coding and Cryptology.. court cases of the overseas Workshop, Wuyi Mountain, Fujian, China, 11-15 June 2007 (WS, 2008)(ISBN 9812832238)(O)(288s)
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Extra resources for Coding and cryptology: proceedings of the international workshop, Wuyi Mountain, Fujian, China 11-15 June 2007
May 23, 2008 13:28 WSPC - Proceedings Trim Size: 9in x 6in series 26 This improvement of an idea due to C. Shannon  uses the existence of low degree multiples of the nonlinear function. It is called algebraic attack [4,16,19,30] and has deeply modified the situation with Boolean functions in stream ciphers. Given a Boolean function f on n variables, different kinds of scenarios related to low degree multiples of f have been studied in ref. 19,30. The core of the analysis is to find out minimum (or low) degree nonzero annihilators of f or of 1 + f , that is, functions g such that f ∗ g = 0 or (1 + f ) ∗ g = 0, where ”∗” is the multiplication of functions inheritated from the multiplication in F2 .
52, 2111–2126, (2006). fr. Because of the recent algebraic attacks, a high algebraic immunity is now an absolutely necessary (but not sufficient) property for Boolean functions used in stream ciphers. Very few examples of (balanced) functions with high algebraic immunity have been found so far. These examples seem to be isolated and no method for obtaining such functions is known. In this paper, we introduce a general method for proving that a given function, in any number of variables, has a prescribed algebraic immunity.
Gupta and S. Maitra. Algebraic Immunity for Cryptographically Significant Boolean Functions: Analysis and Construction. IEEE Transactions on Information Theory, vol. 52, no. 7, pp. 3105-3121, July 2006. 14. C. Carlet, X. Zeng, C. Li and L. HU. Further properties of several classes of Boolean functions with optimum algebraic immunity. IACR e-print archive 2007/370. 15. J. Y. Cho and J. Pieprzyk. Algebraic Attacks on SOBER-t32 and SOBER128. In FSE 2004, number 3017 in Lecture Notes in Computer Science, pp.