{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,20]],"date-time":"2025-12-20T22:05:45Z","timestamp":1766268345120,"version":"3.46.0"},"reference-count":13,"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":[[2022,1,7]]},"abstract":"Abstract<\/jats:title>\n \n We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over\n \n \n \n \n \n \n Z<\/m:mi>\n <\/m:mrow>\n \n p<\/m:mi>\n <\/m:mrow>\n <\/m:msub>\n <\/m:math>\n {{\\mathbb{Z}}}_{p}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . One of the (semi)groups is additive, and the other one is multiplicative. This allows us to take advantage of both operations on matrices to diffuse information. We note that in our protocol, no power of any matrix or of any element of\n \n \n \n \n \n \n Z<\/m:mi>\n <\/m:mrow>\n \n p<\/m:mi>\n <\/m:mrow>\n <\/m:msub>\n <\/m:math>\n {{\\mathbb{Z}}}_{p}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is ever exposed, so standard classical attacks on Diffie\u2013Hellman-like protocols are not applicable.\n <\/jats:p>","DOI":"10.1515\/jmc-2020-0053","type":"journal-article","created":{"date-parts":[[2022,1,7]],"date-time":"2022-01-07T09:12:51Z","timestamp":1641546771000},"page":"64-72","source":"Crossref","is-referenced-by-count":8,"title":["MAKE: A matrix action key exchange"],"prefix":"10.1515","volume":"16","author":[{"given":"Nael","family":"Rahman","sequence":"first","affiliation":[{"name":"Department of Mathematics, The City College of New York , New York , NY 10031 , USA"}]},{"given":"Vladimir","family":"Shpilrain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The City College of New York , New York , NY 10031 , USA"}]}],"member":"374","published-online":{"date-parts":[[2022,1,7]]},"reference":[{"key":"2025120600292421394_j_jmc-2020-0053_ref_001","doi-asserted-by":"crossref","unstructured":"Diffie W, Hellman ME. New directions in cryptography. IEEE Trans Inform Theory. 1976;IT-22:644\u201354.","DOI":"10.1109\/TIT.1976.1055638"},{"key":"2025120600292421394_j_jmc-2020-0053_ref_002","unstructured":"Menezes A, van Oorschot P, Vanstone S. Handbook of applied cryptography. Boca Raton, FL: CRC-Press; 1996."},{"key":"2025120600292421394_j_jmc-2020-0053_ref_003","doi-asserted-by":"crossref","unstructured":"Habeeb M, Kahrobaei D, Koupparis C, Shpilrain V. Public key exchange using semidirect product of (semi)groups. In: ACNS 2013, Lecture notes on computer science. Vol. 7954. Springer; 2013. p. 475\u201386.","DOI":"10.1007\/978-3-642-38980-1_30"},{"key":"2025120600292421394_j_jmc-2020-0053_ref_004","doi-asserted-by":"crossref","unstructured":"Stickel E. 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. IEEE Computer Society; 2005. p. 426\u201330.","DOI":"10.1109\/ICITA.2005.33"},{"key":"2025120600292421394_j_jmc-2020-0053_ref_005","doi-asserted-by":"crossref","unstructured":"Shpilrain V. Cryptanalysis of Stickel\u2019s key exchange scheme. In: Computer science in Russia 2008, Lecture notes on computer science. Vol. 5010. Springer; 2008. p. 283\u20138.","DOI":"10.1007\/978-3-540-79709-8_29"},{"key":"2025120600292421394_j_jmc-2020-0053_ref_006","doi-asserted-by":"crossref","unstructured":"Myasnikov AG, Roman\u2019kov V. A linear decomposition attack. Groups Complexity Cryptol. 2015;7:81\u201394.","DOI":"10.1515\/gcc-2015-0007"},{"key":"2025120600292421394_j_jmc-2020-0053_ref_007","unstructured":"Roman\u2019kov V. Linear decomposition attack on public key exchange protocols using semidirect products of (semi)groups. Preprint. http:\/\/arxiv.org\/abs\/1501.01152."},{"key":"2025120600292421394_j_jmc-2020-0053_ref_008","doi-asserted-by":"crossref","unstructured":"Grigoriev D, Shpilrain V. Tropical cryptography II: extensions by homomorphisms. Comm Algebra. 2019;47:4224\u20139.","DOI":"10.1080\/00927872.2019.1581213"},{"key":"2025120600292421394_j_jmc-2020-0053_ref_009","doi-asserted-by":"crossref","unstructured":"Kahrobaei D, Shpilrain V. Using semidirect product of (semi)groups in public key cryptography. In: CiE 2016, Lecture Notes on Computer Science. Vol. 9709. Springer; 2016. p. 132\u201341.","DOI":"10.1007\/978-3-319-40189-8_14"},{"key":"2025120600292421394_j_jmc-2020-0053_ref_010","unstructured":"Brown D, Koblitz N, LeGrow J. Cryptanalysis of \u201cMAKE.\u201d Preprint. https:\/\/eprint.iacr.org\/2021\/465."},{"key":"2025120600292421394_j_jmc-2020-0053_ref_011","unstructured":"Battarbee C, Kahrobaei D, Tailor D, Shahandashti SF. On the efficiency of a general attack against the MOBS cryptosystem. Preprint. https:\/\/arxiv.org\/abs\/2111.05806."},{"key":"2025120600292421394_j_jmc-2020-0053_ref_012","unstructured":"Rahman N, Shpilrain V. MOBS (Matrices Over Bit Strings) public key exchange. Preprint. https:\/\/eprint.iacr.org\/2021\/560."},{"key":"2025120600292421394_j_jmc-2020-0053_ref_013","unstructured":"Python code: MAKE, MAKE Challenge, http:\/\/shpilrain.ccny.cuny.edu\/make.py.txt, http:\/\/shpilrain.ccny.cuny.edu\/MAKE_Challenge.py.txt."}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2020-0053\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2020-0053\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:29:40Z","timestamp":1764980980000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2020-0053\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,1]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,2,10]]},"published-print":{"date-parts":[[2022,2,10]]}},"alternative-id":["10.1515\/jmc-2020-0053"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2020-0053","relation":{},"ISSN":["1862-2984"],"issn-type":[{"type":"electronic","value":"1862-2984"}],"subject":[],"published":{"date-parts":[[2022,1,1]]}}}