Boolean functions optimizing most of the cryptographic criteria

摘要

In this paper, we construct a class of 2k-variable Boolean functions which have optimal algebraic degree, very high nonlinearity, optimal algebraic immunity, and are 1-resilient. These properties are unconditional except the algebraic immunity property, which is optimal under some unproven assumptions. However, since the assumptions are verified to be true for k≥29, so these functions have optimal algebraic immunity at least for k≥29.