Abstract
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.
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