{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:21:51Z","timestamp":1764980511396,"version":"3.46.0"},"reference-count":6,"publisher":"Walter de Gruyter GmbH","issue":"4","license":[{"start":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T00:00:00Z","timestamp":1507766400000},"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":[[2017,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    The security of the asymmetric cryptosystem MST\n                    <jats:inline-formula id=\"j_jmc-2016-0065_ineq_9999_w2aab3b7b3b1b6b1aab1c17b1b1Aa\">\n                      <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <m:msub>\n                            <m:mi\/>\n                            <m:mn>1<\/m:mn>\n                          <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_jmc-2016-0065_eq_mi305.png\"\/>\n                        <jats:tex-math>{{}_{1}}<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    relies on the hardness of factoring group elements with respect to a logarithmic signature.\nIn this paper we investigate the factorization problem with respect to logarithmic signatures of abelian groups represented in primary decomposition.\nWe present an efficient factorization algorithm for logarithmic signatures, where descending into factor groups induced by period subgroups is possible.\nEspecially, we show that a logarithmic signature is tame when all its blocks are of prime size.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2016-0065","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T06:01:05Z","timestamp":1507788065000},"page":"205-214","source":"Crossref","is-referenced-by-count":1,"title":["Tame logarithmic signatures of abelian groups"],"prefix":"10.1515","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4288-9963","authenticated-orcid":false,"given":"Dominik","family":"Reichl","sequence":"first","affiliation":[{"name":"Fachbereich Informatik , Universit\u00e4t T\u00fcbingen , Sand 13, 72076 T\u00fcbingen , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,10,12]]},"reference":[{"key":"2025120600200414630_j_jmc-2016-0065_ref_001_w2aab3b7b3b1b6b1ab1b7b1Aa","doi-asserted-by":"crossref","unstructured":"S. R.  Blackburn, C.  Cid and C.  Mullan,\nCryptanalysis of the MST3{{}_{3}} public key cryptosystem,\nJ. Math. Cryptol. 3 (2009), no. 4, 321\u2013338.","DOI":"10.1515\/JMC.2009.020"},{"key":"2025120600200414630_j_jmc-2016-0065_ref_002_w2aab3b7b3b1b6b1ab1b7b2Aa","doi-asserted-by":"crossref","unstructured":"S. S.  Magliveras, D. R.  Stinson and T.  van Trung,\nNew approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups,\nJ. Cryptol. 15 (2002), no. 4, 285\u2013297.\n10.1007\/s00145-001-0018-3","DOI":"10.1007\/s00145-001-0018-3"},{"key":"2025120600200414630_j_jmc-2016-0065_ref_003_w2aab3b7b3b1b6b1ab1b7b3Aa","unstructured":"A.  Nuss,\nOn group based public key cryptography,\nPh.D. thesis, University of T\u00fcbingen, 2011, http:\/\/hdl.handle.net\/10900\/49707."},{"key":"2025120600200414630_j_jmc-2016-0065_ref_004_w2aab3b7b3b1b6b1ab1b7b4Aa","doi-asserted-by":"crossref","unstructured":"L.  R\u00e9dei,\nDie neue Theorie der endlichen abelschen Gruppen und Verallgemeinerung des Hauptsatzes von Haj\u00f3s,\nActa Math. Acad. Sci. Hung. 16 (1965), no. 3\u20134, 329\u2013373.\n10.1007\/BF01904843","DOI":"10.1007\/BF01904843"},{"key":"2025120600200414630_j_jmc-2016-0065_ref_005_w2aab3b7b3b1b6b1ab1b7b5Aa","unstructured":"D.  Reichl,\nGroup factorizations and cryptology,\nPh.D. thesis, University of T\u00fcbingen, 2015,\nhttp:\/\/hdl.handle.net\/10900\/65399"},{"key":"2025120600200414630_j_jmc-2016-0065_ref_006_w2aab3b7b3b1b6b1ab1b7b6Aa","doi-asserted-by":"crossref","unstructured":"P.  Svaba, T.  van Trung and P.  Wolf,\nLogarithmic signatures for abelian groups and their factorization,\nTatra Mt. Math. Publ. 57 (2013), no. 1, 21\u201333.","DOI":"10.2478\/tmmp-2013-0033"}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/jmc.2017.11.issue-4\/jmc-2016-0065\/jmc-2016-0065.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2016-0065\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2016-0065\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:20:13Z","timestamp":1764980413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2016-0065\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,12]]},"references-count":6,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,10,18]]},"published-print":{"date-parts":[[2017,12,1]]}},"alternative-id":["10.1515\/jmc-2016-0065"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2016-0065","relation":{},"ISSN":["1862-2984","1862-2976"],"issn-type":[{"type":"electronic","value":"1862-2984"},{"type":"print","value":"1862-2976"}],"subject":[],"published":{"date-parts":[[2017,10,12]]}}}