{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:31:02Z","timestamp":1764981062366,"version":"3.46.0"},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"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":[[2023,2,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Plactic key agreement is a new type of cryptographic key agreement that uses Knuth\u2019s multiplication of semistandard tableaux from combinatorial algebra. The security of plactic key agreement relies on the difficulty of some computational problems, particularly the division of semistandard tableaux. Tableau division can be used to find the private key from its public key or to find the shared secret from the two exchanged public keys. Monico found a fast division algorithm, which could be a polynomial time in the length of the tableaux. Monico\u2019s algorithm solved a challenge that had been previously estimated to cost 2\n                    <jats:sup>128<\/jats:sup>\n                    steps to break, which is an infeasibly large number for any foreseeable computing power on earth. Monico\u2019s algorithm solves this challenge in only a few minutes. Therefore, Monico\u2019s attack likely makes the plactic key agreement insecure. If it were not for Monico\u2019s attack, plactic key agreement with 1,000-byte public keys might perhaps have provided 128-bit security, with a runtime of a millisecond. But Monico\u2019s attack breaks these public keys\u2019 sizes in minutes.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2022-0010","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T10:37:15Z","timestamp":1676457435000},"source":"Crossref","is-referenced-by-count":1,"title":["Plactic key agreement (insecure?)"],"prefix":"10.1515","volume":"17","author":[{"given":"Daniel R. L.","family":"Brown","sequence":"first","affiliation":[{"name":"BlackBerry Ltd , Missisauga , Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,2,15]]},"reference":[{"key":"2025120600280457252_j_jmc-2022-0010_ref_001","doi-asserted-by":"crossref","unstructured":"Knuth DE. Permutations, matrices, and generalized Young tableaux. Pacific J Math. 1970;34(3):709\u201327.","DOI":"10.2140\/pjm.1970.34.709"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_002","doi-asserted-by":"crossref","unstructured":"Merkle RC. Secure communications over insecure channels. Commun ACM. 1978 Apr;21(4):294\u20139.","DOI":"10.1145\/359460.359473"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_003","doi-asserted-by":"crossref","unstructured":"Diffie W, Hellman ME. New directions in cryptography. IEEE Trans Inform Theory. 1976 Nov;22(6):644\u201354.","DOI":"10.1109\/TIT.1976.1055638"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_004","unstructured":"Rabi M, Sherman AT. Associative one-way functions: a new paradigm for secret-key agreement and digital signatures. University of Maryland; 1993. CS-TR-3183\/UMIACS-TR-93-124. https:\/\/citeseerx.ist.psu.edu\/viewdoc\/download?doi=10.1.1.118.6837&rep=rep1&type=pdf."},{"key":"2025120600280457252_j_jmc-2022-0010_ref_005","unstructured":"Brown DRL. Key agreement: security\/division; 2021. Cryptology ePrint Archive, Paper 2021\/1112. https:\/\/eprint.iacr.org\/2021\/1112."},{"key":"2025120600280457252_j_jmc-2022-0010_ref_006","doi-asserted-by":"crossref","unstructured":"Johnson M, Kambites M. Tropical representations and identities of plactic monoids. Trans Amer Math Soc. 2021;374:4423\u201347.","DOI":"10.1090\/tran\/8355"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_007","unstructured":"Lascoux A, Schutzenberger MP. Le monoide plaxique. In: Proc. Colloqu. Naples, Noncommutative structures in algebra and geometric combinatorics (Naples, 1978). vol. 109 of Quad. Ricerca Sci. CNR. 1981. p. 129\u201356."},{"key":"2025120600280457252_j_jmc-2022-0010_ref_008","doi-asserted-by":"crossref","unstructured":"Robinson Gd. On the representations of the symmetric group. Amer J Math. 1938;60:745\u201360.","DOI":"10.2307\/2371609"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_009","doi-asserted-by":"crossref","unstructured":"Schensted C. Longest increasing and decreasing subsequences. Canad J Math. 1961;13:179\u201391.","DOI":"10.4153\/CJM-1961-015-3"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_010","doi-asserted-by":"crossref","unstructured":"Greene C, Nijenhuis A, Wilf HS. A probabilistic proof of a formula for the number of Young tableaux of a given shape. Adv Math. 1979;31:104\u20139.","DOI":"10.1016\/0001-8708(79)90023-9"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_011","doi-asserted-by":"crossref","unstructured":"Novelli JC, Pak IM, Stoyanovskii AV. A direct bijective proof of the hook-length formula. Discrete Math Theoret Comput Sci. 1997;1:53\u201367.","DOI":"10.46298\/dmtcs.239"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_012","doi-asserted-by":"crossref","unstructured":"Sagan BE. The symmetric group: representations, combinatorial algorithms, and symmetric functions. 2nd ed. No. 203 in Graduate Texts in Mathematics. Springer; 2001.","DOI":"10.1007\/978-1-4757-6804-6"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_013","unstructured":"Brown DRL. Layering diverse cryptography to lower risks of future and secret attacks: post-quantum estimates; 2021. Cryptology ePrint Archive, Paper 2021\/608. https:\/\/eprint.iacr.org\/2021\/608."},{"key":"2025120600280457252_j_jmc-2022-0010_ref_014","doi-asserted-by":"crossref","unstructured":"Kostka C. Uber den Zusammenhang zwischen einigen Formen von symmetrischen Funktionen. Crelleas J. 1882;93:89\u2013123.","DOI":"10.1515\/crll.1882.93.89"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_015","doi-asserted-by":"crossref","unstructured":"Jacobi CG. De functionibus alternantibus. Crelleas J. 1841;22:360\u201371.","DOI":"10.1515\/crll.1841.22.360"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_016","unstructured":"Schur I. Uber eine Klasse von Matrizen, die sich einer gegebenen Matrix zuordnen lassen. Doctoral Dissertation. Universitat Berlin; 1901."},{"key":"2025120600280457252_j_jmc-2022-0010_ref_017","doi-asserted-by":"crossref","unstructured":"Young A. On quantitative substitutional analysis. Proc London Math Soc Ser 1. 1900;33(1):97\u2013145.","DOI":"10.1112\/plms\/s1-33.1.97"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_018","doi-asserted-by":"crossref","unstructured":"Cain AJ, Gray RD, Malheiro A. Finite Grobner-Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids. J Algebra. 2014;423:37\u201353. http:\/\/dx.doi.org\/10.1016\/j.jalgebra.2014.09.037.","DOI":"10.1016\/j.jalgebra.2014.09.037"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_019","doi-asserted-by":"crossref","unstructured":"Cain AJ, Malheiro A. Identities in plactic, hypoplactic, sylvester, baxter, and related monoids. Electronic J Combinatorics. 2018 Aug;25(3).","DOI":"10.37236\/6873"},{"key":"2025120600280457252_j_jmc-2022-0010_ref_020","unstructured":"Berenstein A, Chernyak L. Geometric key establishment. In: Canadian Mathematical Society Conference. 2004. p. 1\u201319."},{"key":"2025120600280457252_j_jmc-2022-0010_ref_021","unstructured":"Soro KF, Akeke ED, Kouakou KM. An application of young tableaux to cryptography. Palestine J Math. 2020;9(2):639\u201357."}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2022-0010\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2022-0010\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:28:27Z","timestamp":1764980907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2022-0010\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,1]]},"references-count":21,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,6,5]]},"published-print":{"date-parts":[[2023,6,5]]}},"alternative-id":["10.1515\/jmc-2022-0010"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2022-0010","relation":{},"ISSN":["1862-2984"],"issn-type":[{"type":"electronic","value":"1862-2984"}],"subject":[],"published":{"date-parts":[[2023,1,1]]},"article-number":"20220010"}}