Abstract
The enumeration of m-resilient Boolean functions in n variables would be a quite useful information for cryptography. But it seems to be an intractable open problem. Upper and lower bounds have appeared in the literature in the mid 80’s. Since then, improving them has been the goal of several papers. In this paper, we give a new upper bound which partially improves upon all the known bounds.
Chapter PDF
Similar content being viewed by others
References
Carlet, C., Klapper, A.: Upper bounds on the number of resilient functions and of bent functions. Proceedings of 23rd Symposium on Information Theory in the Benelux (2002)
Chor, B., Goldreich, O., Hastad, J., Rudich, S., Smolensky, R.: The bit extraction problem or t-resilient functions. In 26th IEEE Symposium on Foundations of Computer Science (1985) 396–407
Denisov, O.: An asymptotic formula for the number of correlation-immune of order k Boolean functions. Discrete Mathematics and Applications 2(4) (1992) 407–426
Guo-Zhen, X., Massey, J. L.: A spectral characterization of correlation-immune combining functions. IEEE Transaction on Information Theory 34(3) (1988) 569–571
Maitra, S., Sarkar, P.: Enumeration of correlation-immune Boolean functions. ACISP (1999) 12–25
Massey, J. L.: Shift-register synthesis and BCH decoding. IEEE Transactions on Information Theory 15 (1969) 122–127
Mitchell, C. J.: Enumerating Boolean functions of cryptographic signifiance. Journal of Cryptology 2(3) (1990) 155–170
Park, S. M., Lee, S., Sung, S. H., Kim, K.: Improving bounds for the number of correlation-immune Boolean functions. Information Processing Letters 61 (1997) 209–212
Sarkar, P., Maitra, S.: Nonlinearity bounds and constructions of resilient Boolean functions. Crypto 2000 (2000) 515–532
Schneider, M.: A note on the construction and upper bounds of correlation-immune functions. 6th IMA Conference (1997) 295–306
Siegenthaler, T.: Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Transactions on Information Theory 30(5) (1984) 776–780
Siegenthaler, T.: Decrypting a class of stream cipher using ciphertext only. IEEE Transactions on Computers 34(1) (1985) 81–85
Vernam, G.: Cipher printing telegraph systems for secret wire and radio telegraphic communication. Journal of the American Institute of Electrical Engineers 45 (1926) 109–115
Yang, Y. X., Guo, B.: Further enumerating Boolean functions of cryptographic signifiance. Journal of Cryptology 8(3) (1995) 115–122
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carlet, C., Gouget, A. (2002). An Upper Bound on the Number of m-Resilient Boolean Functions. In: Zheng, Y. (eds) Advances in Cryptology — ASIACRYPT 2002. ASIACRYPT 2002. Lecture Notes in Computer Science, vol 2501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36178-2_30
Download citation
DOI: https://doi.org/10.1007/3-540-36178-2_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00171-3
Online ISBN: 978-3-540-36178-7
eBook Packages: Springer Book Archive