<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Cryptographic aspects of real hyperelliptic curves

Department of Computer Science University of Calgary 2500 University Drive NW Calgary, Alberta Canada T2N 1N4

Renate Scheidler Department of Mathematics and Statistics University of Calgary 2500 University Drive NW Calgary, Alberta Canada T2N 1N4

Andreas Stein Institut f¨ur Mathematik Carl-von-Ossietzky Universit¨at Oldenburg D-26111 Oldenburg GERMANY

Tatra Mountains Mathematical Publications

{"article-title":"Cryptographic aspects of real hyperelliptic curves"}

In this paper, we give an overview of cryptographic applications using real hyperelliptic curves. We review previously proposed cryptographic protocols and...

Cryptographic aspects of real hyperelliptic curves

Published Online: Nov 13, 2012

Page range: 31 - 65

DOI: https://doi.org/10.2478/v10127-010-0030-9

Keywords
hyperelliptic curve, Jacobian, infrastructure, public-key cryptography, discrete logarithm.

This content is open access.

Cryptographic aspects of real hyperelliptic curves

Published Online: Nov 13, 2012

Page range: 31 - 65

DOI: https://doi.org/10.2478/v10127-010-0030-9

Keywordshyperelliptic curve, Jacobian, infrastructure, public-key cryptography, discrete logarithm.

This content is open access.

Keywords
hyperelliptic curve, Jacobian, infrastructure, public-key cryptography, discrete logarithm.