Abstract
Boolean functions that satisfy higher order propagation criteria are studied. A complete characterization is given of the autocorrelation function and Walsh spectrum of second order functions. The number of second order functions satisfying PC(k) is related to a problem in coding theory and can be computed explicitly for k = 1, n − 1 and n. A new interpretation of the number of balanced second order functions is given and a class of functions showing interesting properties is discussed.
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References
R. Forré, “The strict avalanche criterion: spectral properties of Boolean functions and an extended definition”, Advances in Cryptology, Proc. Crypto 88, Springer Verlag, 1990, p. 450–468.
H.J. Helgert and R.D. Stinaff, “Minimum-Distance bounds for binary linear codes”, IEEE Trans. Inform. Theory, Vol. IT-19, p. 344–356, May 1973.
F.J. MacWilliams and N.J.A. Sloane, “The theory of error-correcting codes”, North-Holland Publishing Company, Amsterdam, 1977.
W. Meier and O. Staffelbach, “Nonlinearity criteria for cryptographic functions”, Advances in Cryptology, Proc. Eurocrypt 89, Springer Verlag, 1990, pp. 549–562.
B. Preneel, W. Van Leekwijck, L. Van Linden, R. Govaerts and J. Vandewalle, “Propagation Characteristics of Boolean Functions”, Advances in Cryptology, Proc. Eurocrypt 90, Lecture Notes in Computer Science 473, Springer Verlag, 1991, pp. 161–173.
R.A. Rueppel, “Stream Ciphers”, in Contemporary Cryptology: The Science of Information Integrity, G. Simmons, ed., IEEE Press, to appear.
T. Siegenthaler, “Correlation immunity of non-linear combining functions for cryptographic applications”, IEEE Trans. Inform. Theory, Vol. IT-30, p. 776–780, Oct. 1984.
W. Van Leekwijck and L. Van Linden, “Cryptographic properties of Boolean functions — in Dutch, Cryptografische eigenschappen van Booleaanse functies”, ESAT Katholieke Universiteit Leuven, Thesis grad. eng., 1990.
G.-Z. Xiao and J.L. Massey, “A spectral characterization of correlation-immune combining functions”, IEEE Trans. Inform. Theory, Vol. IT-34, p. 569–571, May 1988.
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© 1991 Springer-Verlag Berlin Heidelberg
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Preneel, B., Govaerts, R., Vandewalle, J. (1991). Boolean Functions Satisfying Higher Order Propagation Criteria. In: Davies, D.W. (eds) Advances in Cryptology — EUROCRYPT ’91. EUROCRYPT 1991. Lecture Notes in Computer Science, vol 547. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46416-6_12
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DOI: https://doi.org/10.1007/3-540-46416-6_12
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