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

Sumanta Sarkar; Subhamoy Maitra

Paper 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.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Algebraic Immunity Boolean Function Nonlinearity Nonsingular Matrix Rotational Symmetry Walsh Spectrum.
Contact author(s): subho @ isical ac in
History: 2007-08-07: received
Short URL: https://ia.cr/2007/290
License: CC BY

BibTeX

@misc{cryptoeprint:2007/290,
      author = {Sumanta Sarkar and Subhamoy Maitra},
      title = {Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity on Odd Number of Variables},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/290},
      year = {2007},
      url = {https://eprint.iacr.org/2007/290}
}