The best and worst of supersingular abelian varieties in cryptography

Alice Silverberg
Ohio State University

For certain cryptographic applications, including Boneh-Franklin's
Identity Based Encryption (Crypto 2001) and Boneh-Lynn-Shacham's
Short Signature Scheme (Asiacrypt 2001), it is important to have
simple abelian varieties with security parameters that are
neither too small nor too large. Simple supersingular abelian
varieties are natural candidates for these applications. In joint
work with K. Rubin we improve on the upper bounds of Galbraith
(Asiacrypt 2001) for the security parameters of simple
supersingular abelian varieties, and construct several families
of curves whose Jacobians achieve these upper bounds.

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