Boolean functions optimizing most of the cryptographic criteria
In this paper, we construct a class of 2k 2 k -variable Boolean functions which have optimal algebraic degree, very high nonlinearity, optimal algebraic immunity, and are 1 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 k ? 29 , so these functions have optimal algebraic immunity at least for k?29 k ? 29 .
boolean function algebraic degree nonlinearity algebraic immunity correlation immunity resiliency balancedness