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Title:
Cryptographic Aspects of Real Hyperelliptic Curves
Authors: M. J. Jacobson Jr., R. Scheidler, 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.
ePrint: https://eprint.iacr.org/2010/125
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