Cryptology ePrint Archive: Report 2007/290

Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on Odd Number of Variables

Sumanta Sarkar and Subhamoy Maitra

Abstract: In this paper we present a theoretical construction of Rotation Symmetric Boolean Functions (RSBFs) on odd number of variables with maximum possible \ai and further these functions are not symmetric. Our RSBFs are of better nonlinearity than the existing theoretical constructions with maximum possible \ai. To get very good nonlinearity, which is important for practical cryptographic design, we generalize our construction to a construction cum search technique in the RSBF class. We find 7, 9, 11 variable RSBFs with maximum possible \ai having nonlinearities 56, 240, 984 respectively with very small amount of search after our basic construction.

Category / Keywords: secret-key cryptography / Algebraic Immunity, Boolean Function, Nonlinearity, Nonsingular Matrix, Rotational Symmetry, Walsh Spectrum.

Date: received 28 Jul 2007

Contact author: subho at isical ac in

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Version: 20070807:153513 (All versions of this report)

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