High-Performance Scalar Multiplication Using 8-Dimensional GLV/GLS Decomposition View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2013

AUTHORS

Joppe W. Bos , Craig Costello , Huseyin Hisil , Kristin Lauter

ABSTRACT

This paper explores the potential for using genus 2 curves over quadratic extension fields in cryptography, motivated by the fact that they allow for an 8-dimensional scalar decomposition when using a combination of the GLV/GLS algorithms. Besides lowering the number of doublings required in a scalar multiplication, this approach has the advantage of performing arithmetic operations in a 64-bit ground field, making it an attractive candidate for embedded devices. We found cryptographically secure genus 2 curves which, although susceptible to index calculus attacks, aim for the standardized 112-bit security level. Our implementation results on both high-end architectures (Ivy Bridge) and low-end ARM platforms (Cortex-A8) highlight the practical benefits of this approach. More... »

PAGES

331-348

References to SciGraph publications

  • 2010. Speeding Up Bipartite Modular Multiplication in ARITHMETIC OF FINITE FIELDS
  • 2000. An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2000
  • 2012. Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2012
  • 2002-04-29. Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2002
  • 2011. Faster Explicit Formulas for Computing Pairings over Ordinary Curves in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2011
  • 2002-03. Constructive and destructive facets of Weil descent on elliptic curves in JOURNAL OF CRYPTOLOGY
  • 2013. Fast Cryptography in Genus 2 in ADVANCES IN CRYPTOLOGY – EUROCRYPT 2013
  • 2012. Fast Elliptic Curve Cryptography in OpenSSL in FINANCIAL CRYPTOGRAPHY AND DATA SECURITY
  • 2010. Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field in ALGORITHMIC NUMBER THEORY
  • 2012. NEON Crypto in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2012
  • 2001-08-02. Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms in ADVANCES IN CRYPTOLOGY — CRYPTO 2001
  • 2002-09-24. Generating RSA Moduli with a Predetermined Portion in ADVANCES IN CRYPTOLOGY — ASIACRYPT’98
  • 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

    Cryptographic Hardware and Embedded Systems - CHES 2013

    ISBN

    978-3-642-40348-4
    978-3-642-40349-1

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-40349-1_19

    DOI

    http://dx.doi.org/10.1007/978-3-642-40349-1_19

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1033411073


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