Chapter

Advances in Cryptology — CRYPTO 2002

Volume 2442 of the series Lecture Notes in Computer Science pp 336-353

Date:

Supersingular Abelian Varieties in Cryptology

  • Karl RubinAffiliated withDepartment of Mathematics, Stanford University
  • , Alice SilverbergAffiliated withDepartment of Mathematics, Ohio State University

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.