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 $\Delta_f$ for a function $f$ proposed by Zhang and Zheng (1995). We provide balanced functions $f$ with currently best known nonlinearity and $\Delta_f$ 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 $\Delta_f$ 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 $\Delta_f$ for a function $f$ 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2000/047}},
      url = {https://eprint.iacr.org/2000/047}
}
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