A lower bound on the number of functions satisfying the strict avalanche criterion

New Bounds on the Number of Functions Satisfying the Strict Avalanche Criterion

In this paper we present asymptotic expressions for the number of functions satisfying the Strict Avalanche Criterion (SAC) with respect to one and two variables, previously developed by O’Connor. Cusick recently gave a conjecture for a lower bound on the number of functions satisfying the SAC. Here, we give a constructive proof for this conjecture. Moreover, we provide an improved lower bound.

Highly Nonlinear 0-1 Balanced Boolean Functions Satisfying Strict Avalanche Criterion

Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 01 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k ≥ 1) having nonlinearit...

Bounds on the Number of Functions Satisfying the Strict Avalanche Criterion

On Relationships among Avalanche, Nonlinearity, and Correlation Immunity

We establish, for the first time, an explicit and simple lower bound on the nonlinearity Nf of a Boolean function f of n variables satisfying the avalanche criterion of degree p, namely, Nf ≥ 2n−1 − 2n−1− 1 2 . We also show that the lower bound is tight, and identify all the functions whose nonlinearity attains the lower bound. As a further contribution of this paper, we prove that except for v...

Highly Nonlinear 0 - 1 Balanced Boolean Functions Satisfying

Nonlinearity, 0-1 balancedness and strict avalanche criterion (SAC) are important criteria for cryptographic functions. Bent functions have maximum nonlinearity and satisfy SAC however they are not 0-1 balanced and hence cannot be directly used in many cryptosystems where 0-1 balancedness is needed. In this paper we construct (i) 0-1 balanced boolean functions on V2k+1 (k > = 1) having nonlinea...