On the constructing of highly nonlinear resilient Boolean functions by means of special matrices

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2247, Issue , 2001, Pages 254-266

  Fedorova, Maria ^a   Tarannikov, Yuriy ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Boolean function; Correlation immunity; Nonlinear combining function; Nonlinearity; Resiliency; Special matrices; Stream cipher

Indexed keywords

CRYPTOGRAPHY;

CORRELATION IMMUNITY; NONLINEARITY; RESILIENCY; SPECIAL MATRICES; STREAM CIPHERS;

BOOLEAN FUNCTIONS;

EID: 84974705196     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45311-3_24     Document Type: Conference Paper

References (12)

1. P. Camion, C. Carlet, P. Charpin, N. Sendrier, On correlation-immune functions, Advances in Cryptology: Crypto '91, Proceedings, Lecture Notes in Computer Science, V. 576, 1991, pp. 86-100.
2. R. Canetti, Y. Dodis, S. Halevi, E. Kushilevitz, A. Sahai, Exposure-resilient functions and all-or-nothing transforms, In Advanced in Cryptology: Eurocrypt 2000, Proceedings, Lecture Notes in Computer Science, V. 1807, 2000, pp. 453-469.
3. B. Chor, O. Goldreich, J. Hastad, J. Friedman, S. Rudich, R. Smolensky, The bit extraction problem or t-resilient functions, IEEE Symposium on Foundations of Computer Science, V. 26, 1985, pp. 396-407.
4. C. Ding, G. Xiao, W. Shan, The stability theory of stream ciphers, Lecture Notes in Computer Science, V. 561, Springer-Verlag, 1991.
5. E. Pasalic, T. Johansson, Further results on the relation between nonlinearity and resiliency for Boolean functions, IMA Conference on Cryptography and Coding, Lecture Notes in Computer Science, Vol. 1746, 1999, pp. 35-44.
6. E. Pasalic, S. Maitra, T. Johansson, P. Sarkar, New constructions of resilient and correlation immune Boolean functions achieving upper bounds on nonlinearity, WCC2001 International Workshop on Coding and Cryptography, Paris, January 8-12, 2001, Electronic Notes in Discrete Mathematics, Volume 6, Elsevier Science, 2001.
7. P. Sarkar, S. Maitra, Construction of nonlinear Boolean functions with important cryptographic properties, In Advanced in Cryptology: Eurocrypt 2000, Lecture Notes in Computer Science, V. 1807, 2000, pp. 485-506.
8. P. Sarkar, S. Maitra, Nonlinearity bounds and constructions of resilient Boolean functions, In Advanced in Cryptology: Crypto 2000, Proceedings, Lecture Notes in Computer Science, V. 1880, 2000, pp. 515-532.
9. T. Siegenthaler, Correlation-immunity of nonlinear combining functions for cryptographic applications, IEEE Transactions on Information theory, V. IT-30, No 5, 1984, p. 776-780.
10. Yu. Tarannikov. On resilient Boolean functions with maximal possible nonlinearity, Proceedings of Indocrypt 2000, Lecture Notes in Computer Science, V. 1977, pp. 19-30, Springer-Verlag, 2000.
11. Yu. Tarannikov. New constructions of resilient Boolean functions with maximal nonlinearity, Preproceedings of 8th Fast Software Encryption Workshop, Yokohama, Japan, April 2-4, 2001, pp. 70-81, also available at Cryptology ePrint archive (http://eprint.iacr.org/), Report 2000/069, December 2000, 11 pp.
12. Y. Zheng, X. M. Zhang, Improved upper bound on the nonlinearity of high order correlation immune functions, Selected Areas in Cryptography, 7th Annual International Workshop, SAC2000, Lecture Notes in Computer Science, V. 2012, pp. 264-274, Springer-Verlag, 2001.