Nonlinearly balanced Boolean functions and their propagation characteristics

摘要: Three of the most important criteria for cryptographically strong Boolean functions are balancedness, nonlinearity and propagation criterion. This paper studies systematic methods constructing satisfying some or all three criteria. We show that concatenating, splitting, modifying multiplying sequences can yield balanced with a very high nonlinearity. In particular, we obtained by achieve higher than attainable any previously known construction method. also present highly nonlinear criterion respect to but one vectors. A technique is developed transform vectors where not satisfied in such way constructed satisfy degree while preserving balancedness functions. The algebraic degrees discussed, together examples illustrating various constructions.