NDLI: Computing Partial Walsh Transform From the Algebraic Normal Form of a Boolean Function

Content Provider	IEEE Xplore Digital Library
Author	Chand Gupta, K. Sarkar, P.
Copyright Year	1963
Abstract	We study the relationship between the Walsh transform and the algebraic normal form (ANF) of a Boolean function. In the first part of the paper, we obtain a formula for the Walsh transform at a certain point in terms of parameters derived from the algebraic normal form. We use previous results by Carlet and Guillot to obtain an explicit expression for the Walsh transform at a point in terms of parameters derived from the ANF. The second part of the paper is devoted to simplify this formula and develop an algorithm to evaluate it. This algorithm can be applied in situations where it is practically impossible to use the fast Walsh transform algorithm. Experimental results show that under certain conditions it is possible to execute our algorithm to evaluate the Walsh transform (at a small set of points) of functions on a few scores of variables having a few hundred terms in the algebraic normal form.
Sponsorship	IEEE Information Theory Society
Starting Page	1354
Ending Page	1359
Page Count	6
File Size	238236
File Format	PDF
ISSN	00189448
Volume Number	55
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Boolean functions Data structures Fourier transforms Polynomials Computer science Statistics Cryptography Galois fields Probes Walsh transform Algebraic normal form Boolean function
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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