Idempotents in the Neighbourhood of Patterson-Wiedemann Functions having Walsh Spectra Zeros

Sumanta Sarkar; Subhamoy Maitra

Paper 2007/427

Idempotents in the Neighbourhood of Patterson-Wiedemann Functions having Walsh Spectra Zeros

Sumanta Sarkar and Subhamoy Maitra

Abstract

In this paper we study the neighbourhood of $15$ -variable Patterson-Wiedemann (PW) functions, i.e., the functions that differ by a small Hamming distance from the PW functions in terms of truth table representation. We exploit the idempotent structure of the PW functions and interpret them as Rotation Symmetric Boolean Functions (RSBFs). We present techniques to modify these RSBFs to introduce zeros in the Walsh spectra of the modified functions with minimum reduction in nonlinearity. Our technique demonstrates 15-variable balanced and $1$ -resilient functions with currently best known nonlinearities 16272 and 16264 respectively. In the process, we find functions for which the autocorrelation spectra and algebraic immunity parameters are best known till date.

Note: Correction of a typo.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Extended version (new results are included) of WCC 07.
Keywords: Boolean functions
Contact author(s): subho @ isical ac in
History: 2007-12-11: last of 5 revisions; 2007-11-18: received; See all versions
Short URL: https://ia.cr/2007/427
License: CC BY

BibTeX

@misc{cryptoeprint:2007/427,
      author = {Sumanta Sarkar and Subhamoy Maitra},
      title = {Idempotents in the Neighbourhood of Patterson-Wiedemann Functions having Walsh Spectra Zeros},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/427},
      year = {2007},
      url = {https://eprint.iacr.org/2007/427}
}