Skip to main content

Arithmetic Circuits for Discrete Logarithms

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2976))

Abstract

We introduce a new model of “generic discrete log algorithms” based on arithmetic circuits. It is conceptually simpler than previous ones, is actually applicable to the natural representations of the popular groups, and we can derive upper and lower bounds that differ only by a constant factor, namely 10.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Babai, L., Szemerédi, E.: On the complexity of matrix group problems I. In: Proceedings of the 25th Annual IEEE Symposium on Foundations of Computer Science, Singer Island FL, pp. 229–240. IEEE Computer Society Press, Los Alamitos (1984); ISBN 0-8186-0591-X. ISSN 0272-5428

    Google Scholar 

  2. Boneh, D., Lipton, R.J.: Algorithms for Black-Box Fields and their Application to Cryptography. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 283–297. Springer, Heidelberg (1996) ISSN 0302-9743

    Google Scholar 

  3. Maurer, U., Wolf, S.: Lower Bounds on Generic Algorithms in Groups. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 72–84. Springer, Heidelberg (1998), ISSN 0302-9743, http://link.springer.de/link/service/series/0558/bibs/1403/14030072.htm

    Chapter  Google Scholar 

  4. Maurer, U.M., Wolf, S.: The relationship between breaking the Diffie-Hellman protocol and computing discrete logarithms. SIAM Journal on Computing 28(5), 1689–1721 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  5. Nechaev, V.I.: К вопросу о сложности детерминировaнного aлгоритмa для дискретного логарифма. Российская Академия Наук. Математические Заметки 55(2), 91–101, 189 (1994) ISSN 0025-567X; Complexity of a determinate algorithm for the discrete logarithm. Mathematical Notes 55(2), 165–172 (1994)

    Google Scholar 

  6. Schnorr, C.P.: Security of DL-encryption and signatures against generic attacks-a survey. In: Public-Key Cryptography and Computational Number Theory Conference 2000, pp. 257–282 (2001), http://www.mi.informatik.uni-frankfurt.de/research/papers.html

  7. Schnorr, C.P., Jakobsson, M.: Security Of Discrete Log Cryptosystems in the Random Oracle and the Generic Model. Technical report, Universität Frankfurt/Main and Bell Laboratories, Murray Hill, New Jersey (2000), The Mathematics of Public-Key Cryptography, The Fields Institute, Toronto, http://www.mi.informatik.uni-frankfurt.de/research/papers.html

  8. Shoup, V.: Lower Bounds for Discrete Logarithms and Related Problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997) ISSN 0302-9743

    Google Scholar 

  9. Strassen, V.: Berechnung und Programm. I. Acta Informatica 1, 320–335 (1972)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

von zur Gathen, J. (2004). Arithmetic Circuits for Discrete Logarithms. In: Farach-Colton, M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24698-5_58

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24698-5_58

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21258-4

  • Online ISBN: 978-3-540-24698-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics