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<journal>
  <journal_metadata lang="en">
    <full_title>Bulletin of the Australian Mathematical
    Society</full_title>
    <abbrev_title>Bull. Austral. Math. Soc.</abbrev_title>
    <issn media_type="online">0004-9727</issn>
    <coden>ALNBAB</coden>
  </journal_metadata>
  <journal_issue>
    <publication_date media_type="online">
      <year>2005</year>
    </publication_date>
    <journal_volume>
      <volume>72</volume>
    </journal_volume>
    <issue>2</issue>
    <doi_data>
      <doi>10.wxyz/CV72P2</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P2/</resource>
    </doi_data>
  </journal_issue>
  <journal_article publication_type="full_text">
    <titles>
      <title>Finding the group structure of elliptic curves over
      finite fields</title>
    </titles>
    <contributors>
      <person_name sequence="first" contributor_role="author">John
      B. Friedlander</person_name>
      <person_name sequence="additional" contributor_role="author">
      Carl Pomerance</person_name>
      <person_name sequence="additional" contributor_role="author">
      Igor E. Shparlinski</person_name>
    </contributors>
    <publication_date media_type="online">
      <given_date>14 February 2006</given_date>
      <year>2006</year>
      <month>2</month>
      <day>14</day>
    </publication_date>
    <pages>
      <first_page>251</first_page>
      <last_page>263</last_page>
    </pages>
    <publisher_item>
      <item_number>722-5116-FrPoSh-2005</item_number>
    </publisher_item>
    <doi_data>
      <doi>10.wxyz/C2005V72P2p251</doi>
      <resource>
      http://www.austms.org.au/Publ/Bulletin/V72P2/722-5116-FrPoSh/</resource>
    </doi_data>
    <extra_info>
      <abstract>We show that an algorithm of V.~Miller to compute
      the group structure of an elliptic curve over a prime finite
      field runs in probabilistic polynomial time for almost all
      curves over the field. Important to our proof are estimates
      for some divisor sums.</abstract>
      <subject_class>11Y16</subject_class>
      <review type="MathReviews">MR2183406</review>
      <review type="Zentralblatt">02246387</review>
      <acknowledgement>During the preparation of this paper, the
      first author was supported in part by NSERC grant A5123 and
      by a Killam Research Fellowship. The second author was
      supported in part by NSF grant DMS-0401422 and the third
      author was supported in part by ARC grant
      DP0211459.</acknowledgement>
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