Constructing Odd-Variable Rotation Symmetric Boolean Functions With Optimal AI and Higher Nonlinearity

Abstract

As a part of the field of cryptography, rotation symmetric Boolean functions have rich cryptographic significance. In this paper, based on the knowledge of integer compositions, we present a new construction of odd-variable rotation symmetric Boolean functions with optimal algebraic immunity. The nonlinearity of the new rotation symmetric Boolean functions is much better than that of the previously ones with optimal algebraic immunity. And the algebraic degree of the function class is also much high. Moreover, it is shown that our new functions have almost optimal fast algebraic immunity within the range of variable numbers that ordinary computers can calculate.

Constructing Two Classes of Boolean Functions With Good Cryptographic Properties

“…Researchers can construct Boolean functions with good properties or special properties, such as rotationally symmetric Boolean functions [5]- [9]. Liu summarized the recent work on Boolean functions constructed by decomposition methods based on additive or multiplicative groups over finite fields, which can effectively resist fast algebraic attacks in [10].…”