Bounds 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.

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

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...

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...

GAC | the Criterion for Global Avalanche Characteristics of Cryptographic Functions

We show that some widely accepted criteria for cryptographic functions, including the strict avalanche criterion (SAC) and the propagation criterion, have various limitations in capturing properties of vital importance to cryptographic algorithms, and propose a new criterion called GAC to measure the global avalanche characteristics of cryptographic functions. We also introduce two indicators r...