Propagation characteristics and correlation-immunity of highly nonlinear Boolean functions

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

Volumn 1807, Issue , 2000, Pages 507-522

  Canteaut, Anne ^a   Carlet, Claude ^b   Charpin, Pascale ^a   Fontaine, Caroline ^c  

^a INRIA   (France)

^b UNIVERSITÉ DE CAEN   (France)

^c UNIV LILLE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHY;

CORRELATION IMMUNITY; HIGH NONLINEARITY; LINEAR SUBSPACE; NONLINEAR FUNCTIONS; PROPAGATION CHARACTERISTICS; PROPAGATION CRITERION; PROPAGATION PROPERTIES; WALSH SPECTRUM;

BOOLEAN FUNCTIONS;

EID: 77954757533     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45539-6_36     Document Type: Conference Paper

References (32)

1. E.R. Berlekamp and L.R. Welch. Weight distributions of the cosets of the (32, 6) Reed-Muller code. IEEE Trans. Inform. Theory, 18(1): 203-207, 1972.
2. E. Biham, A. Biryukov, and A. Shamir. Cryptanalysis of Skipjack reduced to 31 rounds using impossible differentials. In Advances in Cryptology - EURO-CRYPT’99, number 1592 in Lecture Notes in Computer Science, pages 12-23. Springer-Verlag, 1999.
3. E. Biham and A. Shamir. Differential cryptanalysis of DES-like cryptosystems. Journal of Cryptology, 4(1): 3-72, 1991.
4. A. Canteaut, C. Carlet, P. Charpin, and C. Fontaine. On cryptographic properties of the cosets of R(1; m). Submitted.
5. C. Carlet. Partially-bent functions. In Advances in Cryptology - CRYPTO’92, number 740 in Lecture Notes in Computer Science, pages 280-291. Springer-Verlag, 1992.
6. C. Carlet. Two new classes of bent functions. In Advances in Cryptology - EU-ROCRYPT’93, number 765 in Lecture Notes in Computer Science, pages 77-101. Springer-Verlag, 1994.
7. C. Carlet. On the propagation criterion of degree l and order k. In Advances in Cryptology - EUROCRYPT’98, number 1403 in Lecture Notes in Computer Science, pages 462-474. Springer-Verlag, 1998.
8. L. E. Dickson. History of the Theory of Numbers, volume 2. Chelsea Publishing Compagny, 1919.
9. J.F. Dillon. Elementary Hadamard Difference sets. PhD thesis, University of Maryland, 1974.
10. E. Filiol and C. Fontaine. Highly nonlinear balanced Boolean functions with a good correlation-immunity. In Advances in Cryptology - EUROCRYPT’98, number 1403 in Lecture Notes in Computer Science, pages 475-488. Springer-Verlag, 1998.
11. C. Fontaine. On some cosets of the First-Order Reed-Muller code with high minimum weight. IEEE Trans. Inform. Theory, 45(4): 1237-1243, 1999.
12. T. Johansson and F. Jönsson. Fast correlation attacks based on turbo code techniques. In Advances in Cryptology - CRYPTO’99, number 1666 in Lecture Notes in Computer Science, pages 181-197. Springer-Verlag, 1999.
13. T. Johansson and F. Jönsson. Improved fast correlation attack on stream ciphers via convolutional codes. In Advances in Cryptology - EUROCRYPT’99, number 1592 in Lecture Notes in Computer Science, pages 347-362. Springer-Verlag, 1999.
14. F.J. MacWilliams and N.J.A. Sloane. The theory of error-correcting codes. North-Holland, 1977.
15. M. Matsui. Linear cryptanalysis method for DES cipher. In Advances in Cryptology - EUROCRYPT’93, number 765 in Lecture Notes in Computer Science. Springer-Verlag, 1994.
16. R.J. McEliece. Weight congruence for p-ary cyclic codes. Discrete Mathematics, 3: 177-192, 1972.
17. W. Meier and O. Staffelbach. Fast correlation attack on certain stream ciphers. Jounal of Cryptology, pages 159-176, 1989.
18. W. Meier and O. Staffelbach. Nonlinearity criteria for cryptographic functions. In Advances in Cryptology - EUROCRYPT’89, number 434 in Lecture Notes in Computer Science, pages 549-562. Springer-Verlag, 1990.
19. K. Nyberg. Differentially uniform mappings for cryptography. In Advances in Cryptology - EUROCRYPT’93, number 765 in Lecture Notes in Computer Science, pages 55-64. Springer-Verlag, 1993.
20. N.J. Patterson and D.H. Wiedemann. The covering radius of the [215; 16] Reed-Muller code is at least 16276. IEEE Trans. Inform. Theory, IT-36(2): 443, 1983.
21. N.J. Patterson and D.H. Wiedemann. Correction to [20]. IEEE Trans. Inform. Theory, IT-36(2): 443, 1990.
22. B. Preneel, W. Van Leekwijck, L. Van Linden, R. Govaerts, and J. Vandewalle. Propagation characteristics of Boolean functions. In Advances in Cryptology - EUROCRYPT’90, number 437 in Lecture Notes in Computer Science, pages 155-165, Springer-Verlag, 1990. Springer-Verlag.
23. O.S. Rothaus. On bent functions. J. Combin. Theory Ser. A, 20: 300-305, 1976.
24. 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 (this volume).
25. C.E. Shannon. Communication theory of secrecy systems. Bell system technical journal, 28: 656-715, 1949.
26. T. Siegenthaler. Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Trans. Inform. Theory, IT-30(5): 776-780, 1984.
27. T. Siegenthaler. Decrypting a class of stream ciphers using ciphertext only. IEEE Trans. Computers, C-34(1): 81-84, 1985.
28. A.F. Webster and S.E. Tavares. On the design of S-boxes. In Advances in Cryptology - CRYPTO’85, number 219 in Lecture Notes in Computer Science, pages 523-534. Springer-Verlag, 1985.
29. G. Xiao and J.L. Massey. A spectral characterization of correlation-immune combining functions. IEEE Trans. Inform. Theory, IT-34(3): 569-571, 1988.
30. X.-M. Zhang and Y. Zheng. GAC - the criterion for global avalanche characterics of cryptographic functions. Journal of Universal Computer Science, 1(5): 320-337, 1995.
31. X.-M. Zhang and Y. Zheng. Characterizing the structures of cryptographic functions satisfying the propagation criterion for almost all vectors. Designs, Codes and Cryptography, 7(1): 11-134, 1996.
32. Y. Zheng and X.-M. Zhang. Plateaued functions. In Information and Communication Security, ICICS’99, number 1726 in Lecture Notes in Computer Science, pages 284-300. Springer-Verlag, 1999.