{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T15:17:04Z","timestamp":1759331824001,"version":"3.37.3"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T00:00:00Z","timestamp":1636848000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T00:00:00Z","timestamp":1636848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"The research was supported with a grant rom the Russian Science Foundation","award":["19-71-10017"],"award-info":[{"award-number":["19-71-10017"]}]},{"name":"Doctor in physics and mathematics."}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s10623-021-00969-2","type":"journal-article","created":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T18:02:28Z","timestamp":1636912948000},"page":"139-153","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An improvement of the Diffie\u2013Hellman noncommutative protocol"],"prefix":"10.1007","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8713-7170","authenticated-orcid":false,"given":"Vitaly","family":"Roman\u2019kov","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,14]]},"reference":[{"key":"969_CR1","doi-asserted-by":"crossref","unstructured":"Anshel I., Anshel M., Goldfeld D.: An algebraic method for public-key cryptography. Math. Res. Lett. 6(3), 287\u2013291 (1999).","DOI":"10.4310\/MRL.1999.v6.n3.a3"},{"key":"969_CR2","doi-asserted-by":"crossref","unstructured":"Anshel I., Anshel M., Goldfeld D.: Non-abelian key agreement protocols, Discrete Appl. Math. 130 (1), 312 (2003). The 2000 Com 2MaC Workshop on Cryptography (Pohang).","DOI":"10.1016\/S0166-218X(02)00585-1"},{"key":"969_CR3","unstructured":"Ben-Zvi A., Kalka A., Tsaban B.: Cryptanalysis via algebraic span. Preprint https:\/\/eprint.iacr.org\/2014\/041."},{"key":"969_CR4","first-page":"255","volume-title":"Advances in Cryptology\u2014CRYPTO 2018\u201438th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19\u201323, 2018, Proceedings, Part I","author":"A Ben-Zvi","year":"2018","unstructured":"Ben-Zvi A., Kalka A., Tsaban B.: Cryptanalysis via algebraic span. In: Shacham H., Boldyreva A. (eds.) Advances in Cryptology\u2014CRYPTO 2018\u201438th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 19\u201323, 2018, Proceedings, Part I, vol. 10991, pp. 255\u2013274. Springer, Cham (2018)."},{"key":"969_CR5","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1090\/S0894-0347-00-00361-1","volume":"14","author":"S Bigelow","year":"2001","unstructured":"Bigelow S.: Braid groups are linear. J. Am. Math. Soc. 14, 471\u2013486 (2001).","journal-title":"J. Am. Math. Soc."},{"key":"969_CR6","doi-asserted-by":"crossref","unstructured":"Cha J., Ko K., Lee S., Han J., Cheon J.: An Efficient Implementations of Braid Groups. In: Proc. of Asiacrypt 2001, Lecture Notes in Computer Science, Vol. 2248, Springer-Verlag, pp. 144-156 (2001).","DOI":"10.1007\/3-540-45682-1_9"},{"key":"969_CR7","series-title":"Lecture Notes in Comp. Sci.","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1007\/978-3-540-45146-4_13","volume-title":"Advances in Cryptology\u2014CRYPTO 2003","author":"JH Cheon","year":"2003","unstructured":"Cheon J.H., Jun B.: A polynomial time algorithm for the braid Diffie\u2013Hellman conjugacy problem. In: Boneh D. (ed.) Advances in Cryptology\u2014CRYPTO 2003, vol. 2729, pp. 212\u201325. Lecture Notes in Comp. Sci. Springer, Heidelberg (2003)."},{"key":"969_CR8","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W Diffie","year":"1976","unstructured":"Diffie W., Hellman M.E.: New directions in cryptography. IEEE Trans. Inf. Theory 22, 644\u2013654 (1976).","journal-title":"IEEE Trans. Inf. Theory"},{"key":"969_CR9","doi-asserted-by":"crossref","unstructured":"Hall P.: Verbal and marginal subgroups, Journal f$$\\ddot{\\rm u}$$r die reine und angewandte Mathematik 182, 156\u2013157 (1940).","DOI":"10.1515\/crll.1940.182.156"},{"key":"969_CR10","doi-asserted-by":"crossref","unstructured":"Hofheinz D., Steinwandt R.: A practical attack on some braid group based cryptography primitives. In: Proc. of PKC 2003, Lexture Notes in Computer Science, vol. 2567, Springer, pp. 187\u2013198 (2003).","DOI":"10.1007\/3-540-36288-6_14"},{"key":"969_CR11","unstructured":"Kalka A., Teicher M.: Iterated LD-problem in non-associative key establishment. arXiv:1312.6791 (2013)."},{"key":"969_CR12","first-page":"85","volume-title":"Non-associative Public-Key Cryptography, Algebra and Computer Science, Contemp. Math.","author":"A Kalka","year":"2016","unstructured":"Kalka A.: Non-associative Public-Key Cryptography, Algebra and Computer Science, Contemp. Math., vol. 677, pp. 85\u2013112. Amer. Math. Soc, Providence (2016)."},{"issue":"2","key":"969_CR13","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1515\/gcc-2013-0009","volume":"5","author":"A Kalka","year":"2013","unstructured":"Kalka A., Teicher M.: Non-associative key establishment for left distributive systems. Groups Complex. Cryptol. 5(2), 169\u2013191 (2013).","journal-title":"Groups Complex. Cryptol."},{"key":"969_CR14","first-page":"112","volume-title":"Algebra and Computer Science, Contemp. Math.","author":"A Kalka","year":"2016","unstructured":"Kalka A., Teicher M.: Non-associative key establishment protocols and their implementation. In: Algebra and Computer Science, Contemp. Math., vol. 677, pp. 112\u2013128. Amer. Math. Soc, Providence (2016)."},{"key":"969_CR15","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1007\/3-540-44598-6_10","volume-title":"Advances in Cryptology\u2014CRYPTO 2000, Lecture Notes in Comp. Sci.","author":"KH Ko","year":"2000","unstructured":"Ko K.H., Lee S.J., Cheon J.H., Han J.W., Kang J.V., Park C.: New public-key cryptosystem using braid groups. In: Bellare M. (ed.) Advances in Cryptology\u2014CRYPTO 2000, Lecture Notes in Comp. Sci., vol. 1880, pp. 166\u2013183. Springer, Berlin, Heidelberg (2000)."},{"key":"969_CR16","doi-asserted-by":"publisher","first-page":"131","DOI":"10.2307\/3062152","volume":"155","author":"D Krammer","year":"2002","unstructured":"Krammer D.: Braid groups are linear. Ann. Math. 155, 131\u2013156 (2002).","journal-title":"Ann. Math."},{"key":"969_CR17","doi-asserted-by":"crossref","unstructured":"Lee E., Park J.: Cryptanalysis of the public-key encryption based on braid groups. In: Advances in Cryptology\u2014EUROCRYPT 2003. International Conference on the Theory and Applications of Cryptographic Techniques, Warsaw, Poland, May 4-8, 2003 Proceedings, pp. 477\u2013490 (2003).","DOI":"10.1007\/3-540-39200-9_30"},{"key":"969_CR18","unstructured":"Merz S.-P., Petit C.: Factoring Products of Braids via Garside Normal Form. Cryptology ePrint Archive: Report 2018\/1142. https:\/\/eprint.iacr.org\/2018\/1142"},{"key":"969_CR19","doi-asserted-by":"crossref","unstructured":"Myasnikov A., Roman\u2019kov V.: A linear decomposition attack. Groups Complex. Cryptol. 7(1), 81\u201394 (2015).","DOI":"10.1515\/gcc-2015-0007"},{"key":"969_CR20","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/978-1-4684-0128-8","volume-title":"A Course in the Group Theory","author":"DJS Robinson","year":"1982","unstructured":"Robinson D.J.S.: A Course in the Group Theory, p. 481. Springer, New York, Heidelberg, Berlin (1982)."},{"key":"969_CR21","doi-asserted-by":"crossref","unstructured":"Roman\u2019kov V.A.: Cryptanalysis of some schemes applying automorphisms (in Russian). Prikladnaya Discretnaya Matematika 3, 35\u201351 (2013).","DOI":"10.17223\/20710410\/21\/5"},{"key":"969_CR22","unstructured":"Roman\u2019kov V.A.: Algebraic Cryptography (in Russian), p. 136. Omsk State University, Omsk (2013)."},{"key":"969_CR23","doi-asserted-by":"crossref","unstructured":"Roman\u2019kov V.: A nonlinear decomposition attack. Groups Complex. Cryptol. 8(2), 197\u2013207 (2016).","DOI":"10.1515\/gcc-2016-0017"},{"key":"969_CR24","unstructured":"Roman\u2019kov V.A.: Essays in Algebra and Cryptology: Algebraic Cryptanalysis, p. 207. Omsk State University, Omsk (2018)."},{"key":"969_CR25","doi-asserted-by":"crossref","unstructured":"Roman\u2019kov V.: Two general schemes of algebraic cryptography. Groups Complex. Cryptol. 10(2), 83\u201398 (2018).","DOI":"10.1515\/gcc-2018-0009"},{"key":"969_CR26","doi-asserted-by":"crossref","unstructured":"Roman\u2019kov V.: An improved version of the AAG cryptographic protocol. Groups Complex. Cryptol. 11(1), 35\u201342 (2019).","DOI":"10.1515\/gcc-2019-2003"},{"issue":"3","key":"969_CR27","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s00145-013-9170-9","volume":"28","author":"B Tsaban","year":"2015","unstructured":"Tsaban B.: Polynomial-time solutions of computational problems in noncommutative-algebraic cryptography. J. Cryptol. 28(3), 601\u2013622 (2015).","journal-title":"J. Cryptol."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00969-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-021-00969-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00969-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,6]],"date-time":"2022-01-06T07:18:45Z","timestamp":1641453525000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-021-00969-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,14]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["969"],"URL":"https:\/\/doi.org\/10.1007\/s10623-021-00969-2","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2021,11,14]]},"assertion":[{"value":"31 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 October 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}