AVALANCHE CHARACTERISTICS OF CRYPTOGRAPHIC FUNCTIONS OF TERNARY LOGIC

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...

Improving the Strict Avalanche Characteristics of Cryptographic Functions

This paper presents a simple yet e ective method for transforming Boolean functions that do not satisfy the strict avalanche criterion SAC into ones that satisfy the criterion Such a method has a wide range of applications in designing cryptographically strong functions including substitution boxes S boxes employed by common key block encryption algorithms The rst author was supported in part b...

Structures of Cryptographic Functions with Strong Avalanche Characteristics (Extended Abstract)

This paper studies the properties and constructions of non linear functions which are a core component of cryptographic primi tives including data encryption algorithms and one way hash functions A main contribution of this paper is to reveal the relationship between nonlinearity and propagation characteristic two critical indicators of the cryptographic strength of a Boolean function In partic...

A characterization of triple semigroup of ternary functions and Demorgan triple semigroup of ternary functions

Nonlinearity, local and global avalanche characteristics of balanced Boolean functions

For a Boolean function f , define ∆f (α) = ∑ x f̂(x)f̂(x⊕ α), f̂(x) = (−1)f(x), the absolute indicator ∆f = maxα6=0 |∆f (α)|, and the sum-of-squares indicator σf = ∑ α ∆ 2 f (α). We construct a class of functions with good local avalanche characteristics, but bad global avalanche characteristics, namely we show that 22n(1 + p) ≤ σf ≤ 2,∆f = 2n, where p is the number of linear structures (with even...