• DocumentCode
    2645220
  • Title

    Rho Method with Period k on Non -- symmetric Ordinary Pairings of Embedding Degree k -- Especially for Barreto -- Naehrig Curves

  • Author

    Nogami, Yasuyuki ; Takai, Yusuke ; Matsushima, Tomoko ; Uehara, Satoshi

  • Author_Institution
    Okayama Univ., Okayama, Japan
  • fYear
    2011
  • fDate
    June 30 2011-July 2 2011
  • Firstpage
    618
  • Lastpage
    621
  • Abstract
    Pollard´s ρ method is well known as an efficient method for solving elliptic curve discrete logarithm problem (ECDLP). This paper applies it to non-super singular pairing-friendly curves, especially to Barreto-Naehrig curves, together with Frobenius endomorphism. Then, it is shown that the list of rational points can be reduced with norms of their x and y coordinates without loss of theoretic uniqueness.
  • Keywords
    computational geometry; Barreto-Naehrig curves; Frobenius endomorphism; elliptic curve discrete logarithm problem; nonsuper singular pairing-friendly curves; nonsymmetric ordinary pairings; rho method; Acceleration; Additives; Cryptography; Electronic mail; Elliptic curves; Equations; Mathematical model; Pollard´s ? method; non–symmetric pairing group;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Innovative Mobile and Internet Services in Ubiquitous Computing (IMIS), 2011 Fifth International Conference on
  • Conference_Location
    Seoul
  • Print_ISBN
    978-1-61284-733-7
  • Electronic_ISBN
    978-0-7695-4372-7
  • Type

    conf

  • DOI
    10.1109/IMIS.2011.62
  • Filename
    5976285
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2645220