Supersingular Abelian Varieties in Cryptology

  • Karl Rubin
  • Alice Silverberg
Conference paper

DOI: 10.1007/3-540-45708-9_22

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2442)
Cite this paper as:
Rubin K., Silverberg A. (2002) Supersingular Abelian Varieties in Cryptology. In: Yung M. (eds) Advances in Cryptology — CRYPTO 2002. CRYPTO 2002. Lecture Notes in Computer Science, vol 2442. Springer, Berlin, Heidelberg

Abstract

For certain security applications, including identity based encryption and short signature schemes, it is useful to have abelian varieties with security parameters that are neither too small nor too large. Supersingular abelian varieties are natural candidates for these applications. This paper determines exactly which values can occur as the security parameters of supersingular abelian varieties (in terms of the dimension of the abelian variety and the size of the finite field), and gives constructions of supersingular abelian varieties that are optimal for use in cryptography.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

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

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