Linear complexity of the discrete logarithm

Designs, Codes, and Cryptography

Volumn 28, Issue 2, 2003, Pages 135-146

  Konyagin, Sergei ^a   Lange, Tanja ^b   Shparlinski, Igor ^c  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

^c MACQUARIE UNIVERSITY   (Australia)

Author keywords

discrete logarithm; linear complexity; linear recurrence sequences

Indexed keywords

EID: 84867927721     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022584306676     Document Type: Article

References (24)

1. J. Buchmann and D. Weber, Discrete logarithms: Recent progress, In Proc. International Conference on Coding Theory, Cryptography and Related Areas, Guanajuato, 1998, Springer-Verlag, Berlin (2000) pp. 42-56.
2. D. Coppersmith I. E. Shparlinski 2000 On polynomial approximation of the discrete logarithm and the Diffie- Hellman mapping J. Cryptology 13 339 360
3. T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, Elsevier, Amsterdam (1998).
4. C. Ding 1997 Linear complexity of generalized cyclotomic binary sequences of order 2 Finite Fields and Their Appl. 3 159 174
5. C. Ding T. Helleseth 1998 On cyclotomic generator of order r Inform. Proc. Letters 66 21 25
6. C. Ding T. Helleseth K. Y. Lam 2000 Duadic sequences of prime length Discr. Math. 218 33 49
7. C. Ding T. Helleseth W. Shan 1998 On the linear complexity of Legendre sequences IEEE Trans. Inform. Theory 44 1276 1278
8. T. Lange and A. Winterhof, Interpolation of the discrete logarithm by Boolean functions, In Proc. Intern. Workshop on Coding and Cryptography, INRIA, Paris (2001) pp. 335-343.
9. T. Lange A. Winterhof 2002 Incomplete character sums and their application to the interpolation of the discrete logarithm by Boolean functions Acta Arith. 101 223 229
10. R. Lovorn Bender and C. Pomerance, Rigorous discrete logarithm computations in finite fields via smooth polynomials, Computational Perspectives on Number Theory, Amer. Math. Soc., Providence, RI (1998) pp. 221-232.
11. K. S. McCurley, The discrete logarithm problem, In Proc. Symp. in Appl. Math., Amer. Math. Soc., Providence, RI, Vol. 42 (1990) pp. 49-74.
12. W. Meidl A. Winterhof 2001 Lower bounds on the linear complexity of the discrete logarithm in finite fields IEEE Trans. Inform. Theory 47 2807 2811
13. A. J. Menezes, P. C. van Oorschot and S. A. Vanstone, Handbook of Applied Cryptography. CRC Press, Boca Raton, FL (1996).
14. G. L. Mullen D. White 1986 A polynomial representation for logarithms in GF(q) Acta Arith. 47 255 261
15. H. Niederreiter, Some computable complexity measures for binary sequences, In Proc. Intern. Conf. on Sequences and their Applications (SETA'98), Singapore, Springer-Verlag, London (1999) pp. 67-78.
16. H. Niederreiter A. Winterhof 2002 Incomplete exponential sums and their applications to the polynomial approximation of the discrete logarithm Finite Fields and Their Appl. 8 184 192
17. A. M. Odlyzko, Discrete logarithms: The past and the future, Designs, Codes and Cryptography, Springer-Verlag, Berlin, Vol. 19 (2000) pp. 129-145.
18. C. Pomerance, Fast, rigorous factorization and discrete logarithm algorithms, Discrete Algorithms and Complexity, Academic Press, San Diego, CA (1987) pp. 119-143.
19. R. A. Rueppel, Stream ciphers, Contemporary Cryptology: The Science of Information Integrity, IEEE Press, NY (1992) pp. 65-134.
20. O. Schirokauer, D. Weber and T. Denny, Discrete logarithms: The effectiveness of the index calculus method, Lect. Notes in Comp. Sci., Springer-Verlag, Berlin, Vol. 1122 (1996) pp. 337-362.
21. I. E. Shparlinski, Finite Fields: Theory and Computation, Kluwer Acad. Publ., Dordrecht (1999).
22. I. E. Shparlinski, Number Theoretic Methods in Cryptography: Complexity Lower Bounds, Birkhäuser (1999).
23. D. R. Stinson, Cryptography: Theory and Practice, CRC Press, Boca Raton, FL (1995).
24. A. Winterhof 2002 Polynomial interpolation of the discrete logarithm Designs, Codes and Cryptography 25 63 72