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

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 ƒn,i and ƒn,j , we discuss the recursive equivalent formula of ƒn,s + ƒn,s+j . First, we give the recursive formula of ƒn,s + ƒn,s+j for j = 1, 2, 3, 4 by corresponding nonsingular affine transformation. Furthermore, we also give the recursive formula of ƒn,s + ƒn,s+t if t satisfies s ≡ 1 (mod t).