Results on Algebraic Immunity for Cryptographically Significant Boolean Functions
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- Dalai D.K., Gupta K.C., Maitra S. (2004) Results on Algebraic Immunity for Cryptographically Significant Boolean Functions. In: Canteaut A., Viswanathan K. (eds) Progress in Cryptology - INDOCRYPT 2004. INDOCRYPT 2004. Lecture Notes in Computer Science, vol 3348. Springer, Berlin, Heidelberg
Recently algebraic attack has received a lot of attention in cryptographic literature. It has been observed that a Boolean function f, interpreted as a multivariate polynomial over GF(2), should not have low degree multiples when used as a cryptographic primitive. In this paper we show that high nonlinearity is a necessary condition to resist algebraic attack and explain how the Walsh spectra values are related to the algebraic immunity (resistance against algebraic attack) of a Boolean function. Next we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity.
KeywordsAlgebraic Attacks Annihilators Boolean Functions Nonlinearity Walsh Spectra
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