On the distribution of Boolean function nonlinearity

Simon Litsyn; Alexander Shpunt

doi:10.1137/060665361

On the distribution of Boolean function nonlinearity

Simon Litsyn^*, Alexander Shpunt

^*Corresponding author for this work

School of Electrical Engineering

Massachusetts Institute of Technology

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

Nonlinearity is the number of bits which must change in the truth table of a Boolean function to reach the closest affine function. It may be expressed through the maximum of the absolute value of a component in the function's Walsh-Hadamard transform. Concentration of nonlinearity is proved. The derived bounds on the concentration point and tails of the distribution are tighter than the earlier known ones.

Original language	English
Pages (from-to)	79-95
Number of pages	17
Journal	SIAM Journal on Discrete Mathematics
Volume	23
Issue number	1
DOIs	https://doi.org/10.1137/060665361
State	Published - 2008

Keywords

Binomial sums
Boolean functions
Concentration of nonlinearity
Second moment method
Tails of binomial distribution
Walsh-Hadamard transform

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10.1137/060665361

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On the distribution of Boolean function nonlinearity

Abstract

Keywords

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