{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T22:56:41Z","timestamp":1777157801219,"version":"3.51.4"},"reference-count":234,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,5]],"date-time":"2018-01-05T00:00:00Z","timestamp":1515110400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>Today, digitalization decisively penetrates all the sides of the modern society. One of the key enablers to maintain this process secure is authentication. It covers many different areas of a hyper-connected world, including online payments, communications, access right management, etc. This work sheds light on the evolution of authentication systems towards Multi-Factor Authentication (MFA) starting from Single-Factor Authentication (SFA) and through Two-Factor Authentication (2FA). Particularly, MFA is expected to be utilized for human-to-everything interactions by enabling fast, user-friendly, and reliable authentication when accessing a service. This paper surveys the already available and emerging sensors (factor providers) that allow for authenticating a user with the system directly or by involving the cloud. The corresponding challenges from the user as well as the service provider perspective are also reviewed. The MFA system based on reversed Lagrange polynomial within Shamir\u2019s Secret Sharing (SSS) scheme is further proposed to enable more flexible authentication. This solution covers the cases of authenticating the user even if some of the factors are mismatched or absent. Our framework allows for qualifying the missing factors by authenticating the user without disclosing sensitive biometric data to the verification entity. Finally, a vision of the future trends in MFA is discussed.<\/jats:p>","DOI":"10.3390\/cryptography2010001","type":"journal-article","created":{"date-parts":[[2018,1,8]],"date-time":"2018-01-08T04:21:21Z","timestamp":1515385281000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":339,"title":["Multi-Factor Authentication: A Survey"],"prefix":"10.3390","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3412-1639","authenticated-orcid":false,"given":"Aleksandr","family":"Ometov","sequence":"first","affiliation":[{"name":"Laboratory of Electronics and Communications Engineering, Tampere University of Technology, FI-33720 Tampere, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0924-6221","authenticated-orcid":false,"given":"Sergey","family":"Bezzateev","sequence":"additional","affiliation":[{"name":"Department of Security of Cyberphysical Systems, ITMO University, St. Petersburg RU-197101, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7994-3700","authenticated-orcid":false,"given":"Niko","family":"M\u00e4kitalo","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Helsinki, FI-00014 Helsinki, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8223-3665","authenticated-orcid":false,"given":"Sergey","family":"Andreev","sequence":"additional","affiliation":[{"name":"Laboratory of Electronics and Communications Engineering, Tampere University of Technology, FI-33720 Tampere, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8540-9918","authenticated-orcid":false,"given":"Tommi","family":"Mikkonen","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Helsinki, FI-00014 Helsinki, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3976-297X","authenticated-orcid":false,"given":"Yevgeni","family":"Koucheryavy","sequence":"additional","affiliation":[{"name":"Laboratory of Electronics and Communications Engineering, Tampere University of Technology, FI-33720 Tampere, Finland"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,5]]},"reference":[{"key":"ref_1","unstructured":"(2018, January 04). 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