An infinite class of quadratic APN functions which are not equivalent to power mappings

IEEE International Symposium on Information Theory - Proceedings

Volumn , Issue , 2006, Pages 2637-2641

  Budaghyan, Lilya ^a,b   Carlet, Claude ^c,d   Felke, Patrick ^e   Leander, Gregor ^e  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

^b UNIVERSITY OF TRENTO   (Italy)

^c INRIA   (France)

^d UNIVERSITÉ PARIS 8   (France)

^e RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Affine equivalence; Almost bent; Almost perfect nonlinear; CCZ equivalence; Differential uniformity; Nonlinearity; S box; Vectorial boolean function

Indexed keywords

KASAMI FUNCTIONS; NONLINEAR QUADRATIC POLYNOMIALS;

CONFORMAL MAPPING; POLYNOMIALS; QUADRATIC PROGRAMMING;

DISTRIBUTION FUNCTIONS;

EID: 39049086333     PISSN: 21578101     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2006.262131     Document Type: Conference Paper

References (34)

1. T. Bending, D. Fon-Der-Flaass. Crooked functions, bent functions and distance-regular graphs. Electron. J. Comb.. 5(R34), 14, 1998.
2. n. Proceedings of International Symposium on Information Theory ISIT 2005.
3. T. Beth and C. Ding. On almost perfect nonlinear permutations. Advances in Cryptology-EUROCRYPT'93, Lecture Notes in Computer Science. 765, Springer-Verlag, New York, pp. 65-76, 1993.
4. E. Biham and A. Shamir. Differential Cryptanalysis of DES-like Cryptosystems. Journal of Cryptology. vol. 4, No.1, pp. 3-72, 1991.
5. L. Budaghyan, C. Carlet, A. Pott. New Constructions of Almost Perfect Nonlinear and Almost Bent Functions. Proceedings of the Workshop on Coding and Cryptography 2005. P. Charpin and 0. Ytrehus eds, pp. 306-315, 2005.
6. A. Canteaut, P. Charpin and H. Dobbertin. A new characterization of almost bent functions. Fast Software Encryption 99, Lecture Notes in Computer Science 1636, L. Knudsen edt, pp. 186-200. Springer-Verlag, 1999.
7. A. Canteaut, P. Charpin and H. Dobbertin. Binary m-sequences with three-valued crosscorrelation: A proof of Welch's conjecture. IEEE Trans. Inform. Theory. 46 (1), pp. 4-8, 2000.
8. 2m, and crosscorrelation of maximum-length sequences. SIAM Journal on Discrete Mathematics, 13(1), pp. 105-138, 2000.
9. C. Carlet. Boolean Functions for Cryptography and Error Correcting Codes. Chapter of the monography Boolean Methods and Models. Y. Crama and P. Hammer eds, Cambridge University Press, to appear (winter 2005-2006).
10. C. Carlet. Vectorial Boolean Functions for Cryptography. Chapter of the monography Boolean Methods and Models. Y. Crama and P. Hammer eds, Cambridge University Press, to appear (winter 2005-2006).
11. C. Carlet, P. Charpin and V. Zinoviev. Codes, bent functions and permutations suitable for DES-like cryptosystems. Designs, Codes and Cryptography. 15(2), pp. 125-156, 1998.
12. C. Carlet and C. Ding. Highly Nonlinear Mappings. Special Issue "Complexity Issues in Coding and Cryptography", dedicated to Prof. Harald Niederreiter on the occasion of his 60th birthday, Journal of Complexity 20, pp. 205-244, 2004.
13. F. Chabaud and S. Vaudenay. Links between differential and linear cryptanalysis, Advances in Cryptology -EUROCRYPT'94, Lecture Notes in Computer Science. Springer-Verlag, New York, 950, pp. 356-365, 1995.
14. N. Courtois and J. Pieprzyk. Cryptanalysis of block ciphers with overdefined systems of equations. Advances in cryptology-ASIACRYPT 2002, Lecture Notes in Computer Science 2501, pp. 267-287, Springer, 2003.
15. J. Daemen and V. Rijmen. AES proposal: Rijndael. http://csrc.nist.gov/ encryption/aes/rijndael/Rijndael.pdf, 1999.
16. n). Appl. Algebra Eng. Commun. Comput. 9 (2), pp. 139-152, 1998.
17. n): the Niho case. Inform, and Comput.. 151, pp. 57-72, 1999.
18. n): the Welch case. IEEE Trans. Inform. Theory. 45, pp. 1271-1275, 1999.
19. n): a new case for n divisible by 5. D. Jungnickel and H. Niederreiter eds. Proceedings of Finite Fields and Applications FQ5. Augsburg, Germany, Springer, pp. 113-121, 2000.
20. H. Dobbertin, Uniformly representable permutation polynomials, T. Helleseth, P.V. Kumar and K. Yang eds. in the Proceedings of "Sequences and their applications-SETA '01 ", Springer Verlag, London, 2002, 1-22.
21. Y. Edel, G. Kyureghyan and A. Pott. A new APN function which is not equivalent to a power mapping. Preprint, 2005, http://arxiv.org/abs/math.CO/ 0506420
22. R. Gold. Maximal recursive sequences with 3-valued recursive crosscorrelation functions. IEEE Trans. Inform. Theory. 14, pp. 154-156, 1968.
23. T.Helleseth and D. Sandberg. Some power mappings with low differential uniformity. Applic Alg. Eng., Commun. Comput.. vol.8, pp. 363-370, 1997.
24. H. Hollmann and Q. Xiang. A proof of the Welch and Niho conjectures on crosscorrelations of binary m-sequences. Finite Fields and Their Applications 7. pp. 253-286, 2001.
25. 2 in char. 2 and some applications to cyclic codes. Proceedings of AAECC-10, Lecture Notes in Computer Science, vol. 673, Berlin, Springer-Verlag, pp. 180-194, 1993.
26. T. Kasami. The weight enumerators for several classes of subcodes of the second order binary Reed-Muller codes. Inform, and Control. 18, pp. 369-394, 1971.
27. G. Lachaud and J. Wolfmann. The Weights of the Orthogonals of the Extended Quadratic Binary Goppa Codes. IEEE Trans. Inform. Theory. vol. 36, pp. 686-692, 1990.
28. M. Matsui. Linear cryptanalysis method for DES cipher. Advances in Cryptology-EUROCRYPT'93, Lecture Notes in Computer Science. Springer-Verlag, pp. 386-397, 1994.
29. K. Nyberg. On the construction of highly nonlinear permutations. Advances in Cryptography, EUROCRYPT'92, Lecture Notes in Computer Science. Springer-Verlag, 658, pp. 92-98, 1993.
30. K. Nyberg. Differentially uniform mappings for cryptography, Advances in Cryptography, EUROCRYPT'93, Lecture Notes in Computer Science. Springer-Verlag, New York, 765, pp. 55-64, 1994.
31. K. Nyberg. S-boxes and Round Functions with Controllable Linearity and Differential Uniformity. Proceedings of Fast Software Encryption 1994, Lecture Notes in Computer Science 1008, pp. 111-130, 1995.
32. A. Pott. Nonlinear functions in Abelian groups and relative difference sets. Discrete Applied Math. 138, pp. 177-193, 2004.
33. V. Sidelnikov. On mutual correlation of sequences, Soviet Math. Dokl. 12(1971), pp. 197-201.
34. H. M. Trachtenberg. On the cross-correlation functions of maximal linear recurring sequences. PhD Thesis, University of Southern California, 1970.