{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T17:14:47Z","timestamp":1784135687272,"version":"3.55.0"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T00:00:00Z","timestamp":1694563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the rapid development of quantum theory, the discrete logarithm problem and significant integer factorization problem have polynomial solution algorithms under quantum computing, and their security is seriously threatened. Therefore, a three-party password-authenticated key agreement scheme based on module learning with errors problem was proposed, and its security was proved in the BPR model. Compared with other password-authenticated key agreement protocols, the proposed protocol has higher efficiency and a shorter key length, which can resist quantum attacks. Therefore, the protocol is efficient and secure and suitable for large-scale network communication.<\/jats:p>","DOI":"10.3390\/sym15091750","type":"journal-article","created":{"date-parts":[[2023,9,13]],"date-time":"2023-09-13T05:08:21Z","timestamp":1694581701000},"page":"1750","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Three-Party Password Authentication and Key Exchange Protocol Based on MLWE"],"prefix":"10.3390","volume":"15","author":[{"given":"Songhui","family":"Guo","sequence":"first","affiliation":[{"name":"Third Academic, PLA Information Engineering University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunfan","family":"Song","sequence":"additional","affiliation":[{"name":"Third Academic, PLA Information Engineering University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Song","family":"Guo","sequence":"additional","affiliation":[{"name":"Third Academic, PLA Information Engineering University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yeming","family":"Yang","sequence":"additional","affiliation":[{"name":"Third Academic, PLA Information Engineering University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuaichao","family":"Song","sequence":"additional","affiliation":[{"name":"Third Academic, PLA Information Engineering University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,13]]},"reference":[{"key":"ref_1","unstructured":"Shor, P.W. 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