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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2007/427}},
      url = {https://eprint.iacr.org/2007/427}
}
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