{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:31:01Z","timestamp":1764981061787,"version":"3.46.0"},"reference-count":12,"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":[[2023,2,20]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this article, we analyze two digital signature schemes, proposed in Moldovyan et al., that use finite noncommutative associative algebras as underlying platforms. We prove that these schemes do not possess the claimed property of being quantum safe. We also show that in many cases these schemes are, in fact, vulnerable to \u201cclassical\u201d algebraic cryptanalysis.<\/jats:p>","DOI":"10.1515\/jmc-2022-0023","type":"journal-article","created":{"date-parts":[[2023,2,20]],"date-time":"2023-02-20T08:06:40Z","timestamp":1676880400000},"source":"Crossref","is-referenced-by-count":4,"title":["Algebraic and quantum attacks on two digital signature schemes"],"prefix":"10.1515","volume":"17","author":[{"given":"Vitaly","family":"Roman\u2019kov","sequence":"first","affiliation":[{"name":"Sobolev Institute of Mathematics of Russian Academy of Sciences (Omsk Branch) , Omsk , Russia"}]},{"given":"Alexander","family":"Ushakov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Stevens Institute of Technology , Hoboken NJ 07030 , New Jersey , United States"}]},{"given":"Vladimir","family":"Shpilrain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The City College of New York , NY 10031 , New York , United States"}]}],"member":"374","published-online":{"date-parts":[[2023,2,20]]},"reference":[{"key":"2025120600280453249_j_jmc-2022-0023_ref_001","doi-asserted-by":"crossref","unstructured":"Moldovyan D, Moldovyan A, Sklavos N. Post-quantum signature schemes for efficient hardware implementation. In: Proceedings of the 10th IFIP International Conference on New Technologies, Mobility and Security (NTMS 2019), IEEE; 2019. p. 1\u20135.","DOI":"10.1109\/NTMS.2019.8763858"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_002","unstructured":"Kitaev A. Quantum measurements and the Abelian stabilizer problem. Preprint. 1995. http:\/\/arxiv.org\/abs\/quant-ph\/9511026."},{"key":"2025120600280453249_j_jmc-2022-0023_ref_003","doi-asserted-by":"crossref","unstructured":"Vyalyi M, Kitaev A, Shen A. Classical and quantum computation. American Mathematical Society; 2002.","DOI":"10.1090\/gsm\/047"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_004","unstructured":"Moldovyan A, Moldovyan N. Post-quantum signature algorithms based on the hidden discrete logarithm problem. Comput Sci J Moldova. 2018;26:301\u201313."},{"key":"2025120600280453249_j_jmc-2022-0023_ref_005","doi-asserted-by":"crossref","unstructured":"Moldovyan D, Moldovyan A, Moldovyan N. Digital signature scheme with doubled verification equation. Comput Sci J Moldova. 2020;28:80\u2013103.","DOI":"10.1016\/j.micpro.2020.103487"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_006","doi-asserted-by":"crossref","unstructured":"Moldovyan D, Moldovyan N. A new hard problem over non-commutative finite groups for cryptographic protocols. In: Computer network security. Berlin Heidelberg: Springer; 2010. p. 183\u201394.","DOI":"10.1007\/978-3-642-14706-7_14"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_007","doi-asserted-by":"crossref","unstructured":"Kuzmin AS, Markov VT, Mikhalev AA, Mikhalev AV, Nechaev AA. Cryptographic algorithms on groups and algebras. J Math Sci. 2017;223:629\u201341.","DOI":"10.1007\/s10958-017-3371-y"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_008","doi-asserted-by":"crossref","unstructured":"Goldwasser S, Micali S, Rivest R. A digital signature scheme secure against adaptive chosen-message attacks. SIAM J Comput. 1988;17:281\u2013308.","DOI":"10.1137\/0217017"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_009","unstructured":"Menezes A, van Oorschot P, Vanstone S. Handbook of applied cryptography. Boca Raton, Florida: CRC Press, 1996."},{"key":"2025120600280453249_j_jmc-2022-0023_ref_010","doi-asserted-by":"crossref","unstructured":"Shor P. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J Comput. 1997;26(5):1484\u2013509.","DOI":"10.1137\/S0097539795293172"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_011","doi-asserted-by":"crossref","unstructured":"Roman\u2019kov V. Cryptanalysis of a combinatorial public key cryptosystem. Groups Complexity Cryptol. 2017;9(2):125\u201335.","DOI":"10.1515\/gcc-2017-0013"},{"key":"2025120600280453249_j_jmc-2022-0023_ref_012","unstructured":"Roman\u2019kov V. Essays in algebra and cryptology: algebraic cryptanalysis. Omsk: Omsk State University; 2018."}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2022-0023\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2022-0023\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:28:26Z","timestamp":1764980906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2022-0023\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,1]]},"references-count":12,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,6,5]]},"published-print":{"date-parts":[[2023,6,5]]}},"alternative-id":["10.1515\/jmc-2022-0023"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2022-0023","relation":{},"ISSN":["1862-2984"],"issn-type":[{"type":"electronic","value":"1862-2984"}],"subject":[],"published":{"date-parts":[[2023,1,1]]},"article-number":"20220023"}}