Decomposing bent functions

IEEE Transactions on Information Theory

Volumn 49, Issue 8, 2003, Pages 2004-2019

  Canteaut, Anne ^a   Charpin, Pascale ^a  

^a INRIA   (France)

Author keywords

Bent functions; Boolean functions; Derivatives of Boolean functions; Reed Muller codes; Restrictions of Boolean functions

Indexed keywords

ALGEBRA; CODES (SYMBOLS); FOURIER TRANSFORMS; FUNCTION EVALUATION; POLYNOMIALS; VECTORS;

BENT FUNCTIONS; DERIVATIVES OF BOOLEAN FUNCTION; REED MULLER CODES; RESTRICTIONS OF BOOLEAN FUNCTION;

BOOLEAN FUNCTIONS;

EID: 0042265646     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2003.814476     Document Type: Article

References (25)

1. A. Canteaut, C. Carlet, P. Charpin, and C. Fontaine, "On cryptographic properties of the cosets of R(1, m)," IEEE Trans. Inform. Theory, vol. 47, pp. 1494-1513, May 2001.
2. X.-D. Hou, "Cubic bent functions," Discr. Math., no. 189, pp. 149-161, 1998.
3. W. Meier and O. Staffelbach, "Nonlinearity criteria for cryptographic functions," in Advances in Cryptology-EUROCRYPT'89 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1990, vol. 434, pp. 549-562.
4. C. Carlet, "Two new classes of bent functions," in Advances in Cryptology-EUROCRYPT'93 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1994, vol. 765, pp. 77-101.
5. H. Dobbertin, "Construction of bent functions and balanced Boolean functions with high nonlinearity," in Fast Software Encryption (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1994, vol. 1008, pp. 61-74.
6. J. Dillon, "Elementary Hadamard difference sets," Ph.D. dissertation, Univ. Maryland, College Park, 1974.
7. O. Rothaus, "On bent functions," J. Combin. Theory Ser. A, vol. 20, pp. 300-305, 1976.
8. X.-D. Hou, "New constructions of bent functions," J. Combin. Inform. System Sci., vol. 25, no. 1-4, pp. 173-189, 2000.
9. A. Canteaut, C. Carlet, P. Charpin, and C. Fontaine, "Propagation characteristics and correlation-immunity of highly nonlinear Boolean functions," in Advances in Cryptology-EUROCRYPT 2000 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 2000, vol. 1807, pp. 507-522.
10. C. Carlet, "Partially-bent functions," Des. Codes Cryptogr., no. 3, pp. 135-145, 1993.
11. M. Daum, H. Dobbertin, and G. Leander, "An algorithm for checking normality of Boolean functions," in Proc. Int. Workshop on Coding and Cryptography-WCC 2003, Versailles, France, Mar. 2003, pp. 133-142.
12. A. Canteaut, M. Daum, H. Dobbertin, and G. Leander, "Normal and non normal bent functions," in Proc. Int. Workshop on Coding and Cryptography-WCC 2003, Versailles, France, Mar. 2003, pp. 91-100.
13. F. MacWilliams and N. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
14. G. Lachaud and J. Wolfmann, "The weights of the orthogonal of the extended quadratic binary Goppa codes," IEEE Trans. Inform. Theory, vol. 36, pp. 686-692, May 1990.
15. R. L. McFarland, "A family of noncyclic difference sets," J. Combin. Theory Ser. A, vol. 15, pp. 1-10, 1973.
16. K. Nyberg, "Differentially uniform mappings for cryptography," in Advances in Cryptology-EUROCRYPT'93 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1993, vol. 765, pp. 55-64.
17. C. Carlet, P. Charpin, and V. Zinoviev, "Codes, bent functions and permutations suitable for DES-like cryptosystems," Des. Codes Cryptogr., vol. 15, no. 2, pp. 125-156, 1998.
18. F. Chabaud and S. Vaudenay, "Links between differential and linear cryptanalysis," in Advances in Cryptology-EUROCRYPT'94 (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, 1995, vol. 950, pp. 356-365.
19. T. Bending and D. F. der Flass, "Crooked functions, bent functions, and distance regular graphs," Electron. J. Combin., vol. 5, no. 1, 1998, r34.
20. E. van Dam and D. F. der Flass, "Codes, graphs, and schemes from nonlinear functions," Tilburg University, Tilburg, The Netherlands, Res. Memo. FEW 790, May 2000.
21. P. Charpin, A. Tietäväinen, and V. Zinoviev, "On binary cyclic codes with minimum distance d = 3," Probl. Inform. Transm., vol. 33, no. 4, pp. 287-296, 1997.
22. A. Canteaut, "Differential cryptanalysis of Feistel ciphers and differentially uniform mappings," in Proc. Selected Areas on Cryptography, SAC'97, Ottawa, ON, Canada, 1997, pp. 172-184.
23. R. Gold, "Maximal recursive sequences with 3-valued recursive crosscorrelation functions," IEEE Trans. Inform. Theory, vol. IT-14, pp. 154-156, Jan. 1968.
24. n): A new class for n divisible by 5," preprint, 1999.
25. m) and crosscorrelation of maximum-length sequences," SIAM J. Discr. Math., vol. 13, no. 1, pp. 105-138, 2000.