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
-
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}
}
