Cryptology ePrint Archive: Report 2015/777

Arithmetic Walsh Transform of Boolean Functions with Linear Structures

Qinglan Zhao and Dong Zheng and 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.

Category / Keywords: Boolean functions; arithmetic Walsh transform; Walsh-Hadamard transform; linear structure

Date: received 3 Aug 2015, last revised 3 Aug 2015, withdrawn 13 Jun 2016

Contact author: zhaoqinglan at foxmail com

Available format(s): (-- withdrawn --)

Version: 20160614:053041 (All versions of this report)

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