Detecting Affine Equivalence Of Boolean Functions And Circuit Transformation

Author:

Zeng Xiao1,Yang Guowu2,Song Xiaoyu2,Perkowski Marek A2,Chen Gang3

Affiliation:

1. University of Electronic Science and Technology of China , Chengdu 611731 , China

2. Department of Electrical and Computer Engineering , Portland State University, Portland, OR 97201 USA

3. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics , Jiangjun Rd. Campus: 29 Jiangjun Ave., Nanjing 211100, Nanjing , China

Abstract

Abstract Affine equivalence of Boolean functions has various applications in computer science and modern cryptography, such as circuit design and S-boxes. Existing methods for detecting affine equivalence of Boolean functions work in some cases but not when the truth table of a Boolean function is sparse. To improve previous methods and overcome this limitation, we propose a method by transforming the Boolean function to a function with the property that its function values at the orthonormal basis are all equal to 1 or 0, which narrows down the search space of affine transformations. Our first algorithm has the advantage of getting a smaller search space than previous methods and is especially useful for sparse functions. Specifically, when the Boolean functions are sparse, the search space can be reduced exponentially in average and experiments show the efficiency of our first algorithm. We then present another algorithm to transform one circuit into its equivalent affine circuit by synthesizing a reversible circuit and inserting it in front of the original circuit. To our knowledge, this is the first work to automatically synthesize an affine equivalent circuit for any given circuit and the first to do this by combining reversible circuit and non-reversible circuit.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Guangxi Province

Publisher

Oxford University Press (OUP)

Subject

General Computer Science

Reference28 articles.

1. A canonical representation for piecewise-affine maps and its applications to circuit analysis;Guzelis;IEEE Transactions on Circuits and Systems,1991

2. Circuit implementation of piecewise-affine functions based on a binary search tree

3. Solving Circuit Optimisation Problems in Cryptography and Cryptanalysis;Courtois;IACR Cryptol. ePrint Arch.,2011

4. Classification of cosets of the Reed-Muller code R(m−3,m)

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