Strict Avalanche Criterion Over Finite Fields

Boolean functions on $GF(2)$ which satisfy the Strict Avalanche Criterion ($SAC$) play an important role in the art of information security. In this paper, we extend the conception $SAC$ 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