Elliptic and Hyperelliptic Curves: A Practical Security Analysis View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2014

AUTHORS

Joppe W. Bos , Craig Costello , Andrea Miele

ABSTRACT

Motivated by the advantages of using elliptic curves for discrete logarithm-based public-key cryptography, there is an active research area investigating the potential of using hyperelliptic curves of genus 2. For both types of curves, the best known algorithms to solve the discrete logarithm problem are generic attacks such as Pollard rho, for which it is well-known that the algorithm can be sped up when the target curve comes equipped with an efficiently computable automorphism. In this paper we incorporate all of the known optimizations (including those relating to the automorphism group) in order to perform a systematic security assessment of two elliptic curves and two hyperelliptic curves of genus 2. We use our software framework to give concrete estimates on the number of core years required to solve the discrete logarithm problem on four curves that target the 128-bit security level: on the standardized NIST CurveP-256, on a popular curve from the Barreto-Naehrig family, and on their respective analogues in genus 2. More... »

PAGES

203-220

References to SciGraph publications

  • 2013. Families of Fast Elliptic Curves from ℚ-curves in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2013
  • 1989-10. Hyperelliptic cryptosystems in JOURNAL OF CRYPTOLOGY
  • 2011. On the Correct Use of the Negation Map in the Pollard rho Method in PUBLIC KEY CRYPTOGRAPHY – PKC 2011
  • 2012. Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2012
  • 2012. Group Law Computations on Jacobians of Hyperelliptic Curves in SELECTED AREAS IN CRYPTOGRAPHY
  • 2006. Pairing-Friendly Elliptic Curves of Prime Order in SELECTED AREAS IN CRYPTOGRAPHY
  • 2011. Faster Explicit Formulas for Computing Pairings over Ordinary Curves in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2011
  • 2013. Fast Cryptography in Genus 2 in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2013
  • 2002-03-28. Faster Attacks on Elliptic Curve Cryptosystems in SELECTED AREAS IN CRYPTOGRAPHY
  • 2000. Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves in ALGORITHMIC NUMBER THEORY
  • 1999-01. Parallel Collision Search with Cryptanalytic Applications in JOURNAL OF CRYPTOLOGY
  • 1999. Speeding up the Discrete Log Computation on Curves with Automorphisms in ADVANCES IN CRYPTOLOGY - ASIACRYPT’99
  • 2001-08-02. Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms in ADVANCES IN CRYPTOLOGY — CRYPTO 2001
  • 2011. Counting Points on Genus 2 Curves with Real Multiplication in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2011
  • 2010. On the Use of the Negation Map in the Pollard Rho Method in ALGORITHMIC NUMBER THEORY
  • 2006. Curve25519: New Diffie-Hellman Speed Records in PUBLIC KEY CRYPTOGRAPHY - PKC 2006
  • 2011-07. Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves in JOURNAL OF CRYPTOLOGY
  • Book

    TITLE

    Public-Key Cryptography – PKC 2014

    ISBN

    978-3-642-54630-3
    978-3-642-54631-0

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-54631-0_12

    DOI

    http://dx.doi.org/10.1007/978-3-642-54631-0_12

    DIMENSIONS

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