The spectral test of the Boolean function linearity

Piotr Porwik

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 4, page 567-575
  • ISSN: 1641-876X

Abstract

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The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be performed by means of other methods. In particular, the basic synthesis method described in the paper allows us to compute the spectral coefficients in an iterative manner. The method can be easily used in investigations of large Boolean functions (of many variables), which seems very attractive for modern digital technologies. Experimental results demonstrate the efficiency of the approach.

How to cite

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Porwik, Piotr. "The spectral test of the Boolean function linearity." International Journal of Applied Mathematics and Computer Science 13.4 (2003): 567-575. <http://eudml.org/doc/207668>.

@article{Porwik2003,
abstract = {The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be performed by means of other methods. In particular, the basic synthesis method described in the paper allows us to compute the spectral coefficients in an iterative manner. The method can be easily used in investigations of large Boolean functions (of many variables), which seems very attractive for modern digital technologies. Experimental results demonstrate the efficiency of the approach.},
author = {Porwik, Piotr},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {bent functions; Boolean functions; linearity measure of a Boolean function; coefficients distribution; Walsh coefficients},
language = {eng},
number = {4},
pages = {567-575},
title = {The spectral test of the Boolean function linearity},
url = {http://eudml.org/doc/207668},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Porwik, Piotr
TI - The spectral test of the Boolean function linearity
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 4
SP - 567
EP - 575
AB - The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be performed by means of other methods. In particular, the basic synthesis method described in the paper allows us to compute the spectral coefficients in an iterative manner. The method can be easily used in investigations of large Boolean functions (of many variables), which seems very attractive for modern digital technologies. Experimental results demonstrate the efficiency of the approach.
LA - eng
KW - bent functions; Boolean functions; linearity measure of a Boolean function; coefficients distribution; Walsh coefficients
UR - http://eudml.org/doc/207668
ER -

References

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  13. Porwik P. and Falkowski B.J. (1999): Informatics properties of the Walsh transform. - Proc. 2nd Int. Conf. Information Communications and Signal Processing, ICISC'99, Singapore, paper 2B2.4, pp .1-5. 
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