Cryptology ePrint Archive: Report 2010/125

Cryptographic Aspects of Real Hyperelliptic Curves

M. J. Jacobson, Jr., R. Scheidler, AND A. Stein

Abstract: In this paper, we give an overview of cryptographic applications using real hyperelliptic curves. We review previously proposed cryptographic protocols, and discuss the infrastructure of a real hyperelliptic curve, the mathematical structure underlying all these protocols. We then describe recent improvements to infrastructure arithmetic, including explicit formulas for divisor arithmetic in genus 2; and advances in solving the infrastructure discrete logarithm problem, whose presumed intractability is the basis of security for the related cryptographic protocols.

Category / Keywords: public-key cryptography / hyperelliptic curve cryptosystems, public-key cryptography

Publication Info: Tatra Mountains Mathematical Publication

Date: received 5 Mar 2010

Contact author: jacobs at cpsc ucalgary ca

Available format(s): PDF | BibTeX Citation

Version: 20100306:042031 (All versions of this report)

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