Abstract
The Strict Avalanche Criterion (SAC) for Boolean functions was introduced by Webster and Tavares in connection with a study of the design of S-boxes. Later Forré extended this notion by defining strict avalanche criteria of order k for Boolean functions of n variables, where 0 ≤ k ≤ n − 2; the case k = 0 is the original SAC Recent work by Lloyd, Preneel and others has been concerned with the problem of counting the functions which satisfy SAC of various orders. If the order is n − 2 or n − 3, this problem has been completely solved; the work in these cases is made easier by the fact that only quadratic Boolean functions occur. In this paper, we give good estimates for the number of Boolean functions which satisfy the SAC of order n − 4. We also give a detailed description of the functions which satisfy SAC of order n − 4, so the actual construction of these functions for cryptographic applications is made easy.
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© 1994 Springer-Verlag Berlin Heidelberg
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Cusick, T.W. (1994). Boolean functions satisfying a higher order strict avalanche criterion. In: Helleseth, T. (eds) Advances in Cryptology — EUROCRYPT ’93. EUROCRYPT 1993. Lecture Notes in Computer Science, vol 765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48285-7_9
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DOI: https://doi.org/10.1007/3-540-48285-7_9
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