Date: 13 Sep 2002

Supersingular Abelian Varieties in Cryptology

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.

Rubin was partially supported by NSF grant DMS-9800881.
Silverberg was partially supported by Xerox PARC and by NSF grant DMS-9988869. Some of this work was conducted while she was a visiting researcher at Xerox PARC.