Abstract
Highly nonlinear balanced Boolean functions both satisfying the propagation criterion and having almost uniform correlation values with all linear functions are very important in the design of hash functions, stream and block ciphers. In particular, the output uncorrelated properties between two Boolean functions are required to design permutations. We present, so called, semi-bent functions which satisfy all of these properties.
Preview
Unable to display preview. Download preview PDF.
References
C. Adams and S. Tavares, “The structured design of cryptographically good S-boxes”, Journal of Cryptology 3, no. 1, pp. 27–43, 1990.
E. Biham and A. Shamir, “Differential cryptanalysis of DES-like cryptosystems”, Journal of Cryptology 4, no. 1, pp. 3–72, 1991.
P. Camion, C. Carlet, P. Charpin and N. Sendrier, “On correlation-immune functions”, Advances in Cryptology — CRYPTO'91, Springer-Verlag, pp. 87–100, 1992.
S. Hirose and K. Ikeda, “A note on the propagation characteristics and the strict avalanche criteria”, The 1994 Symposium on Cryptography and Information Security, 1994.
M. Matsui, “Linear cryptanalysis method for DES cipher”, Advances in Cryptology — EUROCRYPT'93, Springer-Verlag, pp. 386–397, 1994.
W. Meier and O.Staffelbach, “Nonlinearity criteria for cryptographic functions”, Advances in Cryptology — EUROCRYPT'89, Springer-Verlag, pp. 549–562, 1990.
K. Nyberg, “On the construction of highly nonlinear permutations”, Advances in Cryptology — EUROCRYPT'92, Springer-Verlag, pp. 92–98, 1993.
K. Nyberg, “Differentially uniform mappings for cryptography”, Advances in Cryptology — EUROCRYPT'93, Springer-Verlag, pp. 55–64, 1994.
K. Nyberg and L.R. Knudsen, “Provable Security against Differential Cryptanalysis”, Advances in Cryptology — CRYPTO'92, Springer-Verlag, pp. 566–574, 1993.
J. Pieprzyk and G. Finkelstein, “Towards effective nonlinear cryptosystem design”, IEE Proceedings, Part E: Computers and Digital Techniques, Vol. 135, pp. 325–335, 1988.
B. Preneel, “Analysis and design of cryptographic hash functions”, Ph.D. Dissertation, Katholieke Universiteit Leuven, 1993.
B. Preneel, W. Van Leekwijck and L. Van Linden, “Propagation characteristics of Boolean functions”, Advances in Cryptology — EUROCRYPT'90, Springer-Verlag, pp. 161–173, 1991.
O.S. Rothaus, “On “bent” functions”, Journal of Combinatorial Theory (A), Vol. 20, pp. 300–305, 1976.
R.A. Rueppel, Stream Ciphers, in “Contemporary Cryptology: The Science of Information Integrity”, G.J. Simmons, Ed., IEEE Press, pp. 65–134, 1992.
J. Seberry, X. M. Zhang and Y. Zheng, “Systematic generation of cryptographically robust S-boxes”, In Proceedings of the first ACM Conference on Computer and Communications Security, pp. 172–182, 1993.
J. Seberry, X. M. Zhang and Y. Zheng, “On constructions and nonlinearity of correlation immune functions”, Advances in Cryptology — EUROCRYPT'93, Springer-Verlag, pp. 181–199, 1994.
J. Seberry, X. M. Zhang and Y. Zheng, “Nonlinearly balanced Boolean functions and their propagation characteristics”, Advances in Cryptology — CRYPTO'93, Springer-Verlag, pp. 49–60, 1994.
T. Siegenthaler, “Correlation immunity of non-linear combining functions for cryptographic applications”, IEEE Trans. Inform. Theory IT-30, pp. 776–780, 1984.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chee, S., Lee, S., Kim, K. (1995). Semi-bent functions. In: Pieprzyk, J., Safavi-Naini, R. (eds) Advances in Cryptology — ASIACRYPT'94. ASIACRYPT 1994. Lecture Notes in Computer Science, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000428
Download citation
DOI: https://doi.org/10.1007/BFb0000428
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59339-3
Online ISBN: 978-3-540-49236-8
eBook Packages: Springer Book Archive