Annual International Cryptology Conference

CRYPTO 2003: Advances in Cryptology - CRYPTO 2003 pp 349-365

Torus-Based Cryptography

  • Karl Rubin
  • Alice Silverberg
Conference paper

DOI: 10.1007/978-3-540-45146-4_21

Volume 2729 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Rubin K., Silverberg A. (2003) Torus-Based Cryptography. In: Boneh D. (eds) Advances in Cryptology - CRYPTO 2003. CRYPTO 2003. Lecture Notes in Computer Science, vol 2729. Springer, Berlin, Heidelberg


We introduce the concept of torus-based cryptography, give a new public key system called CEILIDH, and compare it to other discrete log based systems including Lucas-based systems and XTR. Like those systems, we obtain small key sizes. While Lucas-based systems and XTR are essentially restricted to exponentiation, we are able to perform multiplication as well. We also disprove the open conjectures from [2], and give a new algebro-geometric interpretation of the approach in that paper and of LUC and XTR.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Karl Rubin
    • 1
  • Alice Silverberg
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA