A class of Boolean functions with four-valued Walsh spectra
Yonghong Xie, Lei Hu, Wenfeng Jiang, Xiangyong Zeng · 2009
In this paper, we propose an infinite class of Boolean functions with four-valued Walsh spectra. These functions have a simple trace expression of the form f(x) = trn1(¿d(2n+1)) + tr2n1(bx) for b ¿ F22nand d satisfying d(2l+1) = 2i(mod 2n-1) with integers I and i, where x ¿ F22n. Their cryptographic properties, including balancedness, spectrum distribution, nonlinearity, algebraic degree and algebraic immunity, are investigated. We prove that the proposed functions have high nonlinearity, and algebraic degrees n - gcd(n, I) + 2. Our computer simulation shows these functions have optimal or suboptimal algebraic immunity.