{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T17:39:24Z","timestamp":1770226764063,"version":"3.49.0"},"reference-count":16,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,24]],"date-time":"2021-07-24T00:00:00Z","timestamp":1627084800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61972050"],"award-info":[{"award-number":["61972050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Open Foundation of State Key Laboratory of Networking and Switching Technology (Beijing 300 University of Posts and Telecommunications)","award":["SKLNST-2020-2-16"],"award-info":[{"award-number":["SKLNST-2020-2-16"]}]},{"name":"the SNUT Doctorial Research Foundation","award":["SLGQD13-24"],"award-info":[{"award-number":["SLGQD13-24"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Commitment schemes are important tools in cryptography and used as building blocks in many cryptographic protocols. We propose two commitment schemes by using Rubik\u2019s groups. Our proposals do not lay the security on the taken-for-granted hardness of the word problem over Rubik\u2019s groups. Instead, our first proposal is based on a symmetric encryption algorithm that is secure based on the hardness of the conjugacy search problem over Rubik\u2019s groups, while our second proposal is based on the hardness of a newly derived problem\u2014the functional towering conjugacy search problem over Rubik\u2019s groups. The former is proved secure in the sense of both computational hiding and binding, while the latter is proved even secure in the sense of perfect hiding and computational binding. Furthermore, the proposed schemes have a remarkable performance advantage: a linear commitment\/opening speed. We also evaluate the efficiency of the commitment schemes and show that they are considerably fast.<\/jats:p>","DOI":"10.3390\/info12080294","type":"journal-article","created":{"date-parts":[[2021,7,25]],"date-time":"2021-07-25T22:06:21Z","timestamp":1627250781000},"page":"294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New Commitment Schemes Based on Conjugacy Problems over Rubik\u2019s Groups"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3333-5539","authenticated-orcid":false,"given":"Ping","family":"Pan","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Shaanxi University of Technology (SNUT), 1 East Ring Road, Hanzhong 723000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junzhi","family":"Ye","sequence":"additional","affiliation":[{"name":"College of Natural Resources and Environment, Northwest A&F University (NWAFU), No. 3 Taicheng Road, Yangling, Xianyang 712100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0626-5478","authenticated-orcid":false,"given":"Yun","family":"Pan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Media Convergence and Communication, Communication University of China (CUC), 1 Dingfuzhuang East Street, Beijing 100024, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lize","family":"Gu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications (BUPT), 10 West Tucheng Road, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8418-1897","authenticated-orcid":false,"given":"Licheng","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications (BUPT), 10 West Tucheng Road, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pedersen, T.P. (1992). Non-interactive and information theoretic secure verifiable secret sharing. Proceedings on Advances in Cryptology\u2013CRYPTO, LNCS 576, Springer.","DOI":"10.1007\/3-540-46766-1_9"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1137\/S0097539791220688","article-title":"On the composition of zero-knowledge proof systems","volume":"25","author":"Goldreich","year":"1996","journal-title":"SIAM J. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Schoenmakers, B. (1999). A simple publicly verifiable secret sharing scheme and its application to electronic voting. Annual International Cryptology Conference, Springer.","DOI":"10.1007\/3-540-48405-1_10"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Dreier, J., Dumas, J.G., Jonker, H., and Lafourcade, P. (2013, January 16). Verifiability in e-Auction Protocols & Brandt\u2019s Protocol Revisited. 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International Conference on the Theory and Application of Cryptology and Information Security, Springer.","DOI":"10.1007\/3-540-45682-1_9"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/12\/8\/294\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:34:20Z","timestamp":1760164460000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/12\/8\/294"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,24]]},"references-count":16,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["info12080294"],"URL":"https:\/\/doi.org\/10.3390\/info12080294","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,24]]}}}