International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 04 August 2015

Qinglan Zhao, Dong Zheng, Xiangxue Li, Xiaoli Dong
ePrint Report ePrint Report
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.

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