## Cryptology ePrint Archive: Report 2010/518

Boolean functions with all main cryptographic properties

Ziran Tu and Yingpu Deng

Abstract: In this paper, we propose a class of $2k$-variable Boolean functions which have optimal algebraic degree, very high nonlinearity, and are $1$-resilient. Based on our newly proposed conjecture, it can be shown that the algebraic immunity of our functions is at least suboptimal. Moreover, when $k$ is odd, the algebraic immunity is actually optimal, and for even $k$, we find that the algebraic immunity is optimal at least for $k\leq 28$.

Category / Keywords: foundations /