The order of elliptic curves over finite fields of characteristic two using the Schoof algorithm

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Abstract

The elliptic curve cryptosystem is a popular cryptosystem. Its safety depends on the difficulty of the elliptic curve discrete logarithm problem (ECDLP). From the viewpoint of ECDLP, it is very interesting to determine the order of elliptic curves. We tabulate the order of elliptic curves on the finite field of characteristic two using the Schoof algorithm, which is an efficient algorithm to decide orders. The Schoof algorithm is carried out by O(log(8)q). Because the calculation of y(q2) occupies most of the time used to execute the Schoof algorithm, it is necessary to reduce the amount of y(q2) calculations.

Journal

  • Journal of the Faculty of Environmental Science and Technology,Okayama University

    Journal of the Faculty of Environmental Science and Technology,Okayama University 12, 7-18, 2007-03

    岡山大学環境理工学部

Codes

  • NII Article ID (NAID)
    120002313838
  • NII NACSIS-CAT ID (NCID)
    AN10529213
  • Text Lang
    ENG
  • Article Type
    departmental bulletin paper
  • Journal Type
    大学紀要
  • ISSN
    13419099
  • NDL Article ID
    8795635
  • NDL Source Classification
    ZV1(一般学術誌--一般学術誌・大学紀要)
  • NDL Call No.
    Z22-B196
  • Data Source
    NDL  IR 
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