TY - GEN
T1 - Boolean functions satisfying a higher order strict avalanche criterion
AU - Cusick, Thomas W.
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1994.
PY - 1994
Y1 - 1994
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84858666096
U2 - 10.1007/3-540-48285-7_9
DO - 10.1007/3-540-48285-7_9
M3 - Conference contribution
AN - SCOPUS:84858666096
SN - 9783540576006
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 102
EP - 117
BT - Advances in Cryptology – EUROCRYPT 1993 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
A2 - Helleseth, Tor
PB - Springer Verlag
T2 - Workshop on Theory and Application of Cryptographic Techniques, EUROCRYPT 1993
Y2 - 23 May 1993 through 27 May 1993
ER -