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 foreign Workshop, Wuyi Mountain, Fujian, China, 11-15 June 2007 (WS, 2008)(ISBN 9812832238)(O)(288s)
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Additional resources for Coding and cryptology: proceedings of the international workshop, Wuyi Mountain, Fujian, China 11-15 June 2007
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 . Since the introduction of algebraic attacks on stream ciphers (see ref. 19), the research of Boolean functions that can resist them has not given fully satisfactory results. It has produced only a small number of examples (excluding those results of ref.
Ding, G. Xiao, and W. Shan. The Stability Theory of Stream Ciphers. Number 561 in Lecture Notes in Computer Science. Springer-Verlag, 1991. 24. S. Fischer and W. Meier. Algebraic Immunity of S-boxes and Augmented Functions. Proceedings of Fast Software Encryption 2007. To appear. 25. P. Hawkes and G. G. Rose. Rewriting Variables: The Complexity of Fast Algebraic Attacks on Stream Ciphers. In M. K. Franklin, editor, Advances in Cryptology - CRYPTO 2004, LNCS 3152, pp. 390–406. Springer Verlag, 2004.
The positive definiteness condition of f can be proved using the Perron-Frobenius theorem; for this we must take f to be the eigenfunction that corresponds to the largest eigenvalue of Tk . This condition defines the range of code distances s in which the method is applicable. A variant of this calculation was performed in  to which we refer for details. The difference between  and the argument above is that there we May 23, 2008 13:28 WSPC - Proceedings Trim Size: 9in x 6in series 21 took ρk = ak pk+1 (1)/pk (1).
Coding and cryptology: proceedings of the international workshop, Wuyi Mountain, Fujian, China 11-15 June 2007 by Huaxiong Wang, Yongqing Li, Shengyuan Zhang