Nonlinearly Balanced Boolean Functions and Their Propagation Characteristics (Extended Abstract)

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