On Efficient Pairings on Elliptic Curves over Extension Fields

  • Xusheng Zhang
  • Kunpeng Wang
  • Dongdai Lin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7708)


In implementation of elliptic curve cryptography, three kinds of finite fields have been widely studied, i.e. prime field, binary field and optimal extension field. In pairing-based cryptography, however, pairing-friendly curves are usually chosen among ordinary curves over prime fields and supersingular curves over extension fields with small characteristics. In this paper, we study pairings on elliptic curves over extension fields from the point of view of accelerating the Miller’s algorithm to present further advantage of pairing-friendly curves over extension fields, not relying on the much faster field arithmetic. We propose new pairings on elliptic curves over extension fields can make better use of the multi-pairing technique for the efficient implementation. By using some implementation skills, our new pairings could be implemented much more efficiently than the optimal ate pairing and the optimal twisted ate pairing on elliptic curves over extension fields. At last, we use the similar method to give more efficient pairings on Estibals’s supersingular curves over composite extension fields in parallel implementation.


pairing elliptic curve over extension field multi-pairing technique 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Xusheng Zhang
    • 1
    • 2
  • Kunpeng Wang
    • 3
  • Dongdai Lin
    • 3
  1. 1.Institute of SoftwareChinese Academy of SciencesBeijingChina
  2. 2.Graduate University of Chinese Academy of SciencesBeijingChina
  3. 3.SKLOIS, Institute of Information EngineeringChinese Academy of SciencesBeijingChina

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