Cryptology ePrint Archive: Report 2009/272

A Conjecture on Binary String and Its Applications on Constructing Boolean Functions of Optimal Algebraic Immunity

Ziran Tu and Yingpu Deng

Abstract: In this paper, we propose a combinatoric conjecture on binary string, on the premise that our conjecture is correct we mainly obtain two classes of functions which are both algebraic immunity optimal: the first class of functions are also bent, moreover, from this fact we conclude that the algebraic immunity of bent functions can take all possible values except one. The second class are balanced functions, which have optimal algebraic degree and the best nonlinearity up to now.

Category / Keywords: secret-key cryptography / boolean function, algebraic immunity, bent function, balanced,nonlinearity, algebraic degree

Date: received 8 Jun 2009

Contact author: naturetu at gmail com,dengyp@amss ac cn

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Version: 20090609:145606 (All versions of this report)

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