Highly Nonlinear Balanced Boolean Functions with very good Autocorrelation Property

Subhamoy Maitra

Paper 2000/047

Highly Nonlinear Balanced Boolean Functions with very good Autocorrelation Property

Subhamoy Maitra

Abstract

Constructing highly nonlinear balanced Boolean functions with very good autocorrelation property is an interesting open question. In this direction we use the measure $Δ_{f}$ for a function $f$ proposed by Zhang and Zheng (1995). We provide balanced functions $f$ with currently best known nonlinearity and $Δ_{f}$ values together. Our results for 15-variable functions disprove the conjecture proposed by Zhang and Zheng (1995), where our constructions are based on modifications of Patterson-Wiedemann (1983) functions. Also we propose a simple bent based construction technique to get functions with very good values for odd number of variables. This construction has a root in Kerdock Codes. Moreover, our construction on even number of variables is a recursive one and we conjecture (similar to Dobbertin's conjecture (1994) with respect to nonlinearity) that this provides minimum possible value of for a function on even number of variables.

Metadata

Available format(s): PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: boolean function
Contact author(s): subho @ isical ac in
History: 2001-06-06: revised; 2000-09-26: received; See all versions
Short URL: https://ia.cr/2000/047
License: CC BY

BibTeX

@misc{cryptoeprint:2000/047,
      author = {Subhamoy Maitra},
      title = {Highly Nonlinear Balanced Boolean Functions with very good Autocorrelation Property},
      howpublished = {Cryptology {ePrint} Archive, Paper 2000/047},
      year = {2000},
      url = {https://eprint.iacr.org/2000/047}
}