A construction of Boolean functions with good cryptographic properties

Abstract

Abstract.The two important qualities of a cipher is security and speed. Frequently, to satisfy the security of a Boolean function primitive, speed may be traded-off. In this paper we present a general construction that addresses both qualities. The idea of our construction is to manipulate a cryptographically strong base function and one of its affine equivalent functions, using concatenation and negation. We achieve security from the inherent qualities of the base function, which are preserved (or increased) and obtain speed by the simple Boolean operations. We present two applications of the construction to demonstrate the flexibility and efficiency of the construction.

Generalized Lexicographic MultiObjective Combinatorial Optimization. Application to Cryptography

“…For instance, [38,49] address only nonlinearity, [34] focuses on balancedness and autocorrelation (although nonlinearity, algebraic degree and algebraic immunity are also considered), [35] considers nonlinearity, balancedness, and autocorrelation (interestingly, they also look at resiliency and propagation as secondary criteria), while [19,36,18] address balancedness, nonlinearity, autocorrelation, and algebraic degree. Recently, in the context of stream ciphers, [52,14,54,51,16] take into account balancedness, nonlinearity, algebraic degree, algebraic immunity, and immunity to fast algebraic attacks; [14,54] focus on optimizing balancedness and algebraic immunity, [51] optimizes algebraic immunity and algebraic degree, whereas [16] additionally keeps track of correlation immunity order. In brief, very different optimization problems keep getting addressed, depending on the cipher specific application and the expected types of attacks.…”

“…These properties are characterized via several relevant criteria from the cryptographic perspective [43], usually posing a trade-off between them [19,36,11,54,51,16], so that the resultant design of robust Boolean functions looks for a compromise among these criteria [17,20,33,41,24,18,1,10,34,48,47,50,35,14,38,4,49,52]. The systematic selection of such criteria (not to mention the determination of their relative relevance) is an open issue in the existing literature on the subject matter.…”