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

The Strict Avalanche Criterion (SAC) for functions f : Z>2n → Z2 was introduced by Webster and Tavares in 1986 [4] in a study of cryptographic design criteria. A function is said to satisfy the SAC if complementing any input bit changes the output bit with probability one half. In [3], OʹConnor gave bounds for the number of functions satisfying the SAC. This study was continued in [1,2,5], motivated partially by a conjecture presented by Cusick in [1] concerning the asymptotic behavior of the number of functions satisfying the SAC. We present a lower bound on the number of such functions, and as a consequence disprove the limit conjectured by Cusick.