Cryptology ePrint Archive: Report 2002/006

The best and worst of supersingular abelian varieties in cryptology

Karl Rubin and Alice Silverberg

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 which are optimal for use in cryptography.

Category / Keywords: public key cryptography / abelian varieties, supersingular, elliptic curves, short signatures, identity based encryption

Date: received 5 Jan 2002, last revised 13 Feb 2002

Contact author: silver at math ohio-state edu

Available format(s): PDF | BibTeX Citation

Note: The paper has been updated, with new results and constructions.

Version: 20020214:040003 (All versions of this report)

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