{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:28:55Z","timestamp":1766269735343,"version":"3.46.0"},"reference-count":9,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,2,10]]},"abstract":"Abstract<\/jats:title>\n \n Rahman and Shpilrain proposed a Diffie\u2013Hellman style key exchange based on a semidirect product of\n \n \n \n \n n<\/m:mi>\n \u00d7<\/m:mo>\n n<\/m:mi>\n <\/m:math>\n n\\times n<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -matrices over a finite field. We show that, using public information, an adversary can recover the agreed upon secret key by solving a system of\n \n \n \n \n \n \n n<\/m:mi>\n <\/m:mrow>\n \n 2<\/m:mn>\n <\/m:mrow>\n <\/m:msup>\n <\/m:math>\n {n}^{2}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n linear equations.\n <\/jats:p>","DOI":"10.1515\/jmc-2021-0016","type":"journal-article","created":{"date-parts":[[2022,2,10]],"date-time":"2022-02-10T03:56:35Z","timestamp":1644465395000},"page":"98-102","source":"Crossref","is-referenced-by-count":8,"title":["Cryptanalysis of \u201cMAKE\u201d"],"prefix":"10.1515","volume":"16","author":[{"given":"Daniel R. L.","family":"Brown","sequence":"first","affiliation":[{"name":"BlackBerry , Mississauga , Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neal","family":"Koblitz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Washington, Box 354350 , Seattle , WA 98195 , United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jason T.","family":"LeGrow","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Auckland , Auckland , New Zealand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,2,10]]},"reference":[{"doi-asserted-by":"crossref","unstructured":"Diffie W\n, \nHellman M\n. New directions in cryptography. IEEE Trans Inform Theory. 1976;IT-22:644\u201354.","key":"2025120600292398168_j_jmc-2021-0016_ref_001","DOI":"10.1109\/TIT.1976.1055638"},{"unstructured":"Menezes AJ\n, \nWu Y-H\n. The discrete logarithm problem in GL(n,q). Ars Combinatoria. 1997;47:23\u201332.","key":"2025120600292398168_j_jmc-2021-0016_ref_002"},{"doi-asserted-by":"crossref","unstructured":"Stickel E\n. A new method for exchanging secret keys. In: Proceedings of the Third International Conference on Information Technology and Applications (ICITA 05), Contemporary Mathematics; vol. 2; 2005. p. 426\u201330.","key":"2025120600292398168_j_jmc-2021-0016_ref_003","DOI":"10.1109\/ICITA.2005.33"},{"doi-asserted-by":"crossref","unstructured":"Shpilrain V\n. Cryptanalysis of Stickelas key exchange scheme. Computer Science in Russia 2008. LNCS. 2008;5010:283\u20138.","key":"2025120600292398168_j_jmc-2021-0016_ref_004","DOI":"10.1007\/978-3-540-79709-8_29"},{"doi-asserted-by":"crossref","unstructured":"Habeeb M\n, \nKahrobaei D\n, \nKoupparis C\n, \nShpilrain V\n. Public key exchange using semidirect product of (semi)groups. ACNS 2013. LNCS. 2013;7954:475\u201386.","key":"2025120600292398168_j_jmc-2021-0016_ref_005","DOI":"10.1007\/978-3-642-38980-1_30"},{"doi-asserted-by":"crossref","unstructured":"Myasnikov AG\n, \nRoman\u2019kov V\n. A linear decomposition attack. Groups Complexity Cryptol. 2015;7:81\u201394.","key":"2025120600292398168_j_jmc-2021-0016_ref_006","DOI":"10.1515\/gcc-2015-0007"},{"unstructured":"Roman\u2019kov V\n. Linear decomposition attack on public key exchange protocols using semidirect products of (semi)groups. http:\/\/arxiv.org\/abs\/1501.01152.","key":"2025120600292398168_j_jmc-2021-0016_ref_007"},{"unstructured":"Rahman N\n, \nShpilrain V\n. MAKE: a Matrix Action Key Exchange. https:\/\/eprint.iacr.org\/2021\/116.pdf.","key":"2025120600292398168_j_jmc-2021-0016_ref_008"},{"unstructured":"Monico C\n, \nMahalanobis A\n. A remark on MAKE - a Matrix Action Key Exchange, https:\/\/arxiv.org\/pdf\/2012.00283.pdf.","key":"2025120600292398168_j_jmc-2021-0016_ref_009"}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2021-0016\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2021-0016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:29:34Z","timestamp":1764980974000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2021-0016\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,1]]},"references-count":9,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,2,10]]},"published-print":{"date-parts":[[2022,2,10]]}},"alternative-id":["10.1515\/jmc-2021-0016"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2021-0016","relation":{},"ISSN":["1862-2984"],"issn-type":[{"type":"electronic","value":"1862-2984"}],"subject":[],"published":{"date-parts":[[2022,1,1]]}}}