Cryptographically resilient functions

IEEE Transactions on Information Theory

Volumn 43, Issue 5, 1997, Pages 1740-1747

  Zhang, Xian Mo ^b   Zheng, Yuliang ^a,c  

^a IEEE

^b UNIVERSITY OF WOLLONGONG   (Australia)

^c MONASH UNIVERSITY   (Australia)

Author keywords

Correlation immune functions; Cryptography; Nonlinearity; Resilient functions

Indexed keywords

AFFINE SEQUENCE; CORRELATION IMMUNE FUNCTIONS; RESILIENT FUNCTIONS; STREAM CIPHERS;

ALGEBRA; ALGORITHMS; FUNCTIONS; NONLINEAR EQUATIONS; RANDOM NUMBER GENERATION; VECTORS;

CRYPTOGRAPHY;

EID: 0031238366     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.623184     Document Type: Article

References (24)

1. B. Chor, O. Goldreich, J. Håstad, J. Friedman, S. Rudich, and R. Smolensky, "The bit extraction problem or t-resilient functions," in IEEE Symp. on Foundations of Computer Science, 1985, vol. 26, pp. 396-407.
2. C. H. Bennett, G. Brassard, and J. M. Robert, "Privacy amplification by public discussion," SIAM J. Comput., vol. 17, pp. 210-229, 1988.
3. T. Siegenthaler, "Correlation-immunity of nonlinear combining functions for cryptographic applications," IEEE Trans. Inform. Theory, vol. IT-30, pp. 776-779, Sept. 1984.
4. R. A. Rueppel, "Analysis and design of stream ciphers," in Communications and Control Engineering Series, A. Fettweis, J. L. Massey, and M. Thoma, Eds. Berlin/New York/Tokyo: Springer-Verlag, 1986.
5. D. R. Stinson and J. L. Massey, "An infinite class of counterexamples to a conjecture concerning non-linear resilient functions," J. Cryptol., vol. 8, no. 3, pp. 167-173, 1995.
6. M. Matsui, "Linear cryptanalysis method for DES cipher," in Advances in Cryptology-EUROCRYPT'93 (Lecture Notes in Computer Science, vol. 765). Berlin/Heidelberg/New York: Springer-Verlag, 1994, pp. 386-397.
7. C. Ding, G. Xiao, and W. Shan, The Stability Theory of Stream Ciphers (Lecture Notes in Computer Science, vol. 561). Berlin/Heidelberg/New York: Springer-Verlag, 1991.
8. J. Seberry, X. M. Zhang, and Y. Zheng, "Nonlinearity and propagation characteristics of balanced Boolean functions," Inform. Comput., vol. 119, no. 1, pp. 1-13, 1995.
9. X. M. Zhang and Y. Zheng, "GAC - The criterion for global avalanche characteristics of cryptographic functions," J. Universal Comput. Sci, vol. 1, no. 5, pp. 316-333, 1995. [Online] Available WWW:http://hgiicm.tu-graz.ac.at/.
10. _, "Characterizing the structures of cryptographic functions satisfying the propagation criterion for almost all vectors," Des., Codes and Cryptogr., vol. 7, nos. 1/2, pp. 111-134, 1996, special issue dedicated to Gus Simmons.
11. K. Nyberg, "On the construction of highly nonlinear permutations," in Advances in Cryptology-EUROCRYPT'92 (Lecture Notes in Computer Science, vol. 658). Berlin/Heidelberg/New York: Springer-Verlag, 1993, pp. 92-98.
12. J. Bierbrauer, K. Gopalakrishnan, and D. R. Stinson, "Bounds on resilient functions and orthogonal arrays," in Advances in Cryptology-CRYPTO'94 (Lecture Notes in Computer Science, vol. 839). Berlin/Heidelberg/New York: Springer-Verlag, 1994, pp. 247-256.
13. R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and Its Applications. Cambridge, U.K.: Cambridge Univ. Press, 1983.
14. J. Seberry, X. M. Zhang, and Y. Zheng, "Relationships among nonlinearity criteria," in Advances in Cryptology-EUROCRYPT'94 (Lecture Notes in Computer Science, vol. 950). Berlin/Heidelberg/New York: Springer-Verlag, 1995, pp. 376-388.
15. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam/New York/Oxford: North-Holland, 1978.
16. D. R. Stinson, "Resilient functions and large sets of orthogonal arrays," Congressus Numerantium, vol. 92, pp. 105-110, 1993.
17. X. Guo-Zhen and J. L. Massey, "A spectral characterization of correlation-immune combining functions," IEEE Trans. Inform. Theory, vol. 34, pp. 569-571, May 1988.
18. J. Friedman, "On the bit extraction problem," in Proc. 33rd IEEE Symp. on Foundations of Computer Science, 1992, pp. 314-319.
19. K. Gopalakrishnan, D. G. Huffman, and D. R. Stinson, "A note on a conjecture concerning symmetric resilient functions," Inform. Process. Lett., vol. 47, pp. 139-143, 1993.
20. K. Gopalakrishnan and D. R. Stinson, "Three characterizations of nonbinary correlation-immune and resilient functions," Des., Codes and Cryptogr., vol. 5, pp. 241-251, 1995.
21. P. Camion, C. Carlet, P. Charpin, and N. Sendrier, "On correlation-immune functions," in Advances in Cryptology-CRYPTO'91, (Lecture Notes in Computer Science, vol. 576). Berlin/Heidelberg/New York: Springer-Verlag, 1991, pp. 87-100.
22. J. Seberry, X. M. Zhang, and Y. Zheng, "On constructions and nonlinearity of correlation immune functions," in Advances in Cryptology-EUROCRYPT'93 (Lecture Notes in Computer Science, vol. 765). Berlin/Heidelberg/New York: Springer-Verlag, 1994, pp. 181-199.
23. K. Nyberg, "Differentially uniform mappings for cryptography," in Advances in Cryptology-EUROCRYPT'93 (Lecture Notes in Computer Science, vol. 765). Berlin/Heidelberg/New York: Springer-Verlag, 1994, pp. 55-65.
24. T. Beth and C. Ding, "On permutations against differential cryptanalysis," in Advances in Cryptology-EUROCRYPT'93 (Lecture Notes in Computer Science, vol. 765). Berlin/Heidelberg/New York: Springer-Verlag, 1994, pp. 65-76.