{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T21:29:28Z","timestamp":1773696568163,"version":"3.50.1"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2012,5,26]],"date-time":"2012-05-26T00:00:00Z","timestamp":1337990400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n                  <jats:p>\n                    We consider finding discrete logarithms in\na group\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_2ffc695e7692dbf9cd77c45c918d6ba7.png\"\/>\n                    of prime order\n                    <jats:italic>p<\/jats:italic>\n                    when the help of an algorithm\n                    <jats:italic>D<\/jats:italic>\n                    that distinguishes\ncertain subsets of\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_2ffc695e7692dbf9cd77c45c918d6ba7.png\"\/>\n                    from each other is available. If\nthe complexity of\n                    <jats:italic>D<\/jats:italic>\n                    is a polynomial,\nsay\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_9bf5793c53c4216535740008ad1601f2.png\"\/>\n                    , then we can find discrete logarithms faster than\nsquare-root algorithms. We consider two variations on this idea and\ngive algorithms solving the discrete logarithm problem in\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_2ffc695e7692dbf9cd77c45c918d6ba7.png\"\/>\n                    with\ncomplexity\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_0bf951f591059e70f716a5f0730d9879.png\"\/>\n                    and\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_3b826b4f74c27c4ff17dab5329de5c4b.png\"\/>\n                    when\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_6524ccb89dd15efee39ea5caccaa9c57.png\"\/>\n                    has factors of suitable size.\nWhen multiple\ndistinguishers are available and\n                    <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"jmc-2012-0002_6524ccb89dd15efee39ea5caccaa9c57.png\"\/>\n                    is sufficiently smooth,\nlogarithms can be found in polynomial\ntime. We discuss natural classes of algorithms\n                    <jats:italic>D<\/jats:italic>\n                    that distinguish\nthe required subsets, and prove that for\n                    <jats:italic>some<\/jats:italic>\n                    of these classes\nno algorithm for distinguishing can be efficient. The subsets\ndistinguished are also relevant in the study of error correcting\ncodes, and we give an application of our work to bounds for\nerror-correcting codes.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2012-0002","type":"journal-article","created":{"date-parts":[[2012,3,22]],"date-time":"2012-03-22T04:25:17Z","timestamp":1332390317000},"page":"1-20","source":"Crossref","is-referenced-by-count":0,"title":["Finding discrete logarithms with a set orbit distinguisher"],"prefix":"10.1515","volume":"6","author":[{"given":"Robert P.","family":"Gallant","sequence":"first","affiliation":[{"name":"Memorial University (Grenfell Campus), Canada"}]}],"member":"374","published-online":{"date-parts":[[2012,5,26]]},"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2012-0002\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2012-0002\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T20:25:23Z","timestamp":1773692723000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2012-0002\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,5,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2012,5,26]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1515\/jmc-2012-0002"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2012-0002","relation":{},"ISSN":["1862-2984","1862-2976"],"issn-type":[{"value":"1862-2984","type":"electronic"},{"value":"1862-2976","type":"print"}],"subject":[],"published":{"date-parts":[[2012,5,26]]}}}