Strict avalanche criterion over finite fields

Abstract

Boolean functions which satisfy the Strict Avalanche Criterion (SAC) play an important role in the art of information security. In this paper, we extend the concept of SAC to finite fields GF(p). A necessary and sufficient condition is given by using spectral analysis. Also, based on an interesting permutation polynomial theorem, we prove various facts about (n – 1)-th order SAC functions on GF(p). We also construct many such functions.

Keywords

• fourier transform,
• cryptography,
• boolean functions,
• algebraic normal form,
• strict avalanche criterion,
• resilience,
• bent functions,
• permutation polynomials,
• finite field,
• quadratic residue,
• legendre symbol