New Constructions of Resilient and Correlation Immune Boolean Functions Achieving Upper Bound on Nonlinearity

Electronic Notes in Discrete Mathematics

Volumn 6, Issue , 2001, Pages 158-167

  Pasalic, E ^a   Maitra, S ^b   Johansson, T ^a   Sarkar, P ^b  

^a LUND UNIVERSITY   (Sweden)

^b INDIAN STATISTICAL INSTITUTE   (India)

Author keywords

Boolean functions; Correlation Immunity; Nonlinearity; Resiliency; Stream Ciphers

Indexed keywords

EID: 34247148213     PISSN: 15710653     EISSN: 15710653     Source Type: Journal    
DOI: 10.1016/S1571-0653(04)00167-2     Document Type: Article

References (19)

1. Berlekamp E.R., and Welch L.R. Weight distributions of the cosets of the (32, 6) Reed-Muller code. IEEE Transactions on Information Theory IT-18 1 (January 1972) 203-207
2. P. Camion, C. Carlet, P. Charpin, and N. Sendrier. On correlation immune functions. In Advances in Cryptology - CRYPTO'91, pages 86-100. Springer-Verlag, 1992.
3. C. Carlet. On the coset weight divisibility and nonlinearity of resilient and correlation immune functions. Preprint, 2000.
4. Ding C., Xiao G., and Shan W. The Stability Theory of Stream Ciphers. Number 561 in Lecture Notes in Computer Science (1991), Springer-Verlag
5. Filiol E., and Fontaine C. Highly nonlinear balanced Boolean functions with a good correlation-immunity. Advances in Cryptology - Eurocrypt'98 (1998), Springer-Verlag
6. Guo-Zhen X., and Massey J. A spectral characterization of correlation immune combining functions. IEEE Transactions on Information Theory 34 3 (May 1988) 569-571
7. Hou X.-D. GL(m, 2) acting on R(r, m)/R(r - 1, m). Discrete Mathematics 149 (1996) 99-122
8. Hou X.-D. On the covering radius of R(1, m) in R(3, m). IEEE Trans-actions on Information Theory IT-42 3 (1996) 1035-1037
9. T. Johansson and F. Jonsson. Fast correlation attacks through reconstruction of linear polynomials. In Advances in Cryptology - CRYPTO 2000, number 1880 in Lecture Notes in Computer Science, pages 300-315. Springer Verlag, 2000.
10. Maiorana J.A. A classification of the cosets of the Reed-Muller code R(1, 6). Mathematics of Computation IT-57 195 (July 1991) 403-414
11. S. Maitra and E. Pasalic. Further constructions of resilient Boolean functions with very high nonlinearity. Preprint, 2000.
12. W. Meier and O. Staffelbach. Fast correlation attack on stream ciphers. In Advances in Cryptology - EUROCRYPT'88, volume 330, pages
13. P. Sarkar and S. Maitra. Construction of nonlinear Boolean functions with important cryptographic properties. In Advances in Cryptology - EUROCRYPT 2000, number 1807 in Lecture Notes in Computer Science, pages 485-506. Springer Verlag, 2000.
14. Sarkar P., and Maitra S. Nonlinearity bounds and constructions of resilient Boolean functions. Advances in Cryptology - CRYPTO 2000, number 1880 in LNCS (2000), Springer Verlag 515-532
15. Siegenthaler T. Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Transactions on Information Theory IT-30 5 (September 1984) 776-780
16. Siegenthaler T. Decrypting a class of stream ciphers using ciphertext only. IEEE Transactions on Computers C-34 1 (January 1985) 81-85
17. Y. V. Tarannikov. On resilient Boolean functions with maximum possible nonlinearity. Cryptology ePrint Archive, eprint.iacr.org, No. 2000/005.
18. Y. V. Tarannikov. New constructions of resilient Boolean functions with maximal nonlinearity. Preprint, 2000.
19. Zheng Y., and Zhang X.M. Improving upper bound on nonlinearity of high order correlation immune functions. SAC 2000, Lecture Notes in Computer Science (2000), Springer Verlag