Efficient Scalar Multiplication for Ate Based Pairing over KSS Curve of Embedding Degree 18 View Full Text


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Chapter Info

DATE

2017

AUTHORS

Al-Amin Khandaker , Yasuyuki Nogami , Hwajeong Seo , Sylvain Duquesne

ABSTRACT

Efficiency of the next generation pairing based security protocols rely not only on the faster pairing calculation but also on efficient scalar multiplication on higher degree rational points. In this paper we proposed a scalar multiplication technique in the context of Ate based pairing with Kachisa-Schaefer-Scott (KSS) pairing friendly curves with embedding degree \(k = 18\) at the 192-bit security level. From the systematically obtained characteristics p, order r and Frobenious trace t of KSS curve, which is given by certain integer z also known as mother parameter, we exploit the relation \(\#E({\mathbb {F}}_{p}) = p+1-t\) mod r by applying Frobenius mapping with rational point to enhance the scalar multiplication. In addition we proposed z-adic representation of scalar s. In combination of Frobenious mapping with multi-scalar multiplication technique we efficiently calculate scalar multiplication by s. Our proposed method can achieve 3 times or more than 3 times faster scalar multiplication compared to binary scalar multiplication, sliding-window and non-adjacent form method. More... »

PAGES

221-232

References to SciGraph publications

  • 2010-04. A Taxonomy of Pairing-Friendly Elliptic Curves in JOURNAL OF CRYPTOLOGY
  • 2004. Short Group Signatures in ADVANCES IN CRYPTOLOGY – CRYPTO 2004
  • 2011. On the Efficient Implementation of Pairing-Based Protocols in CRYPTOGRAPHY AND CODING
  • 2008. Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field in PAIRING-BASED CRYPTOGRAPHY – PAIRING 2008
  • 2013. Implementing Pairings at the 192-Bit Security Level in PAIRING-BASED CRYPTOGRAPHY – PAIRING 2012
  • 2010. Constructing Tower Extensions of Finite Fields for Implementation of Pairing-Based Cryptography in ARITHMETIC OF FINITE FIELDS
  • 2001-06. Efficient Arithmetic in Finite Field Extensions with Application in Elliptic Curve Cryptography in JOURNAL OF CRYPTOLOGY
  • 2003. Constructing Elliptic Curves with Prescribed Embedding Degrees in SECURITY IN COMMUNICATION NETWORKS
  • 2014. Pseudo 8–Sparse Multiplication for Efficient Ate–Based Pairing on Barreto–Naehrig Curve in PAIRING-BASED CRYPTOGRAPHY – PAIRING 2013
  • 2005. Collusion Resistant Broadcast Encryption with Short Ciphertexts and Private Keys in ADVANCES IN CRYPTOLOGY – CRYPTO 2005
  • 2002-09-13. Efficient Algorithms for Pairing-Based Cryptosystems in ADVANCES IN CRYPTOLOGY — CRYPTO 2002
  • 2008. Integer Variable χ–Based Ate Pairing in PAIRING-BASED CRYPTOGRAPHY – PAIRING 2008
  • 2007. Optimised Versions of the Ate and Twisted Ate Pairings in CRYPTOGRAPHY AND CODING
  • 1998. Optimal extension fields for fast arithmetic in public-key algorithms in ADVANCES IN CRYPTOLOGY — CRYPTO '98
  • Book

    TITLE

    Information Security Applications

    ISBN

    978-3-319-56548-4
    978-3-319-56549-1

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-56549-1_19

    DOI

    http://dx.doi.org/10.1007/978-3-319-56549-1_19

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1084693448


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