Abstract
The conceptions of $\chi$-value and K-rotation symmetric Boolean functions are introduced by Cusick. K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the $k-th$ power of $\rho$.In this paper, we discuss cubic 2-value 2-rotation symmetric Boolean function with $2n$ variables, which denoted by $F^{2n}(x^{2n})$. We give the recursive formula of weight of $F^{2n}(x^{2n})$, and prove that the weight of $F^{2n}(x^{2n})$ is the same as its nonlinearity.
Highlights
Boolean functions have many applications in coding theory and cryptography
K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the k − th power of ρ
We give the recursive formula of weight of F2n(x2n), and prove that the weight of F2n(x2n) is the same as its nonlinearity
Summary
Boolean functions have many applications in coding theory and cryptography. Higher nonlinearity is a very important character of Boolean functions which are widely used in coding theory and S-box design. Rotation symmetric Boolean functions as a subclass of K − rotation symmetric have not higher nonlinearity. The applications of the k − rotation symmetric(k ≥ 2) to coding theory and S-box design can be found in some papers. Cusick gave the definition of cubic 2 − rotation symmetric Boolean functions and used the notation {2 − (1, r, s)2n : 2n ≥ s} as the cubic monomial 2-rotation symmetric functions (denoted by 2 − f unctions). Cusick described the affine equivalence of cubic MRS 2-rotation symmetric, and proved that the sequence of Hamming weights of {2 − (1, r, s)2n : 2n ≥ s} satisfies a linear recursion with integer coefficients. We will give the recursion formula of Hamming weight of {2 − [1, 2, 3]2n(2n ≥ 10)} and prove that the nonlinearity of {2 − [1, 2, 3]2n(2n ≥ 10)} is the same as its weight
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
