Journal of Advances in Mathematics and Computer Science

The Recursive Equivalent Formula of Quadratic Rotation Symmetric Functions Which Contain Two MRS Functions

Hongli-liu . *

School of Mathematics and Statistics, Zhejiang University of Finance and Economics 18 XueYuan Street, Xiasha Higher Education Zone , Hangzhou , China.

*Author to whom correspondence should be addressed.

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Abstract

The equivalent form of quadratic Boolean functions can determine the weight and nonlinearity. In order to obtain the equivalent form of odd variables quadratic rotation symmetric function which contains two MRS functions ƒ_n,i and ƒ_n,j , we discuss the recursive equivalent formula of ƒ_n,s + ƒ_n,s+j . First, we give the recursive formula of ƒ_n,s + ƒ_n,s+j for j = 1, 2, 3, 4 by corresponding nonsingular affine transformation. Furthermore, we also give the recursive formula of ƒ_n,s + ƒ_n,s+t if t satisfies s ≡ 1 (mod t).

Keywords: Boolean function, Rotation symmetric Boolean function, Recursive formula, Affine equivalent, MRS function

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