Fast Cryptography in Genus 2 View Full Text


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Chapter Info

DATE

2013

AUTHORS

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

ABSTRACT

In this paper we highlight the benefits of using genus 2 curves in public-key cryptography. Compared to the standardized genus 1 curves, or elliptic curves, arithmetic on genus 2 curves is typically more involved but allows us to work with moduli of half the size. We give a taxonomy of the best known techniques to realize genus 2 based cryptography, which includes fast formulas on the Kummer surface and efficient 4-dimensional GLV decompositions. By studying different modular arithmetic approaches on these curves, we present a range of genus 2 implementations. On a single core of an Intel Core i7-3520M (Ivy Bridge), our implementation on the Kummer surface breaks the 120 thousand cycle barrier which sets a new software speed record at the 128-bit security level for constant-time scalar multiplications compared to all previous genus 1 and genus 2 implementations. More... »

PAGES

194-210

References to SciGraph publications

  • 2006. Efficiently Computable Endomorphisms for Hyperelliptic Curves in ALGORITHMIC NUMBER THEORY
  • 2010. Speeding Up Bipartite Modular Multiplication in ARITHMETIC OF FINITE FIELDS
  • 2011. High-Speed High-Security Signatures in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS – CHES 2011
  • 2012. Four-Dimensional Gallant-Lambert-Vanstone Scalar Multiplication in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2012
  • 2008. Twisted Edwards Curves Revisited in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2008
  • 2012. Group Law Computations on Jacobians of Hyperelliptic Curves in SELECTED AREAS IN CRYPTOGRAPHY
  • 2001. Software Implementation of the NIST Elliptic Curves Over Prime Fields in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2002-09-24. Generating RSA Moduli with a Predetermined Portion in ADVANCES IN CRYPTOLOGY — ASIACRYPT’98
  • 2002-03-28. Faster Attacks on Elliptic Curve Cryptosystems in SELECTED AREAS IN CRYPTOGRAPHY
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  • 2000. An Algorithm for Solving the Discrete Log Problem on Hyperelliptic Curves in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2000
  • 2012. Fast Elliptic Curve Cryptography in OpenSSL in FINANCIAL CRYPTOGRAPHY AND DATA SECURITY
  • 2004. Counting Points for Hyperelliptic Curves of Type y2=x5+ax over Finite Prime Fields in SELECTED AREAS IN CRYPTOGRAPHY
  • 2011. Counting Points on Genus 2 Curves with Real Multiplication in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2011
  • 2002-04-29. Speeding Up Point Multiplication on Hyperelliptic Curves with Efficiently-Computable Endomorphisms in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2002
  • 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
  • 1999-01. A Fast Diffie—Hellman Protocol in Genus 2 in JOURNAL OF CRYPTOLOGY
  • 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

    Advances in Cryptology – EUROCRYPT 2013

    ISBN

    978-3-642-38347-2
    978-3-642-38348-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-38348-9_12

    DOI

    http://dx.doi.org/10.1007/978-3-642-38348-9_12

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1031094507


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