Paper 2015/777

Arithmetic Walsh Transform of Boolean Functions with Linear Structures

Qinglan Zhao, Dong Zheng, Xiangxue Li, and Xiaoli Dong

Abstract

Arithmetic Walsh transform(AWT) of Boolean function caught our attention due to their arithmetic analogs of Walsh-Hadamard transform(WHT) recently. We present new results on AWT in this paper. Firstly we characterize the existence of linear structure of Boolean functions in terms of AWT. Secondly we show that the relation between AWT and WHT of a balanced Boolean function with a linear structure 1^n is sectionally linear. Carlet and Klapper's recent work showed that the AWT of a diagonal Boolean function can be expressed in terms of the AWT of a diagonal Boolean function of algebraic degree at most 3 in a larger number of variables.However their proof is right only when c has even weight.We complement their proof by considering the case of c with odd weight.

Metadata
Available format(s)
-- withdrawn --
Publication info
Preprint. MINOR revision.
Keywords
Boolean functionsarithmetic Walsh transformWalsh-Hadamard transformlinear structure
Contact author(s)
zhaoqinglan @ foxmail com
History
2016-06-14: withdrawn
2015-08-04: received
See all versions
Short URL
https://ia.cr/2015/777
License
Creative Commons Attribution
CC BY
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