• DocumentCode
    1365655
  • Title

    Optimal Pairings

  • Author

    Vercauteren, Frederik

  • Author_Institution
    Flanders Dept. of Electr. Eng., Univ. of Leuven, Leuven-Heverlee, Belgium
  • Volume
    56
  • Issue
    1
  • fYear
    2010
  • Firstpage
    455
  • Lastpage
    461
  • Abstract
    In this paper, we introduce the concept of an optimal pairing, which by definition can be computed using only log 2 r/¿(k) basic Miller iterations, with r the order of the groups involved and k the embedding degree. We describe an algorithm to construct optimal ate pairings on all parametrized families of pairing friendly elliptic curves. Finally, we conjecture that any nondegenerate pairing on an elliptic curve without efficiently computable endomorphisms different from powers of Frobenius requires at least log 2 r/¿(k) basic Miller iterations.
  • Keywords
    iterative methods; public key cryptography; Frobenius power; Miller iterations; ate pairings; elliptic curves; embedding degree; nondegenerate pairing; optimal pairings; parametrized families; Elliptic curve cryptography; Elliptic curves; Embedded computing; Jacobian matrices; Ate pairing; Tate pairing; elliptic curves; pairing-based cryptography;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2009.2034881
  • Filename
    5361495
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1365655