{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T16:43:07Z","timestamp":1772556187575,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T00:00:00Z","timestamp":1772496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of Russia","award":["FEWM-2023-0015 (TUSUR)"],"award-info":[{"award-number":["FEWM-2023-0015 (TUSUR)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCP"],"abstract":"<jats:p>Continuous authentication is a promising method for protecting computer systems in the event of compromise of primary authentication factors, such as passwords or tokens. Systems employing continuous authentication that rely on biometrics may not be restricted to a single biometric characteristic; rather, they can simultaneously utilize multiple characteristics and subsequently arrive at a conclusive decision based on their collective analysis outcomes. One of the significant challenges researchers encounter when investigating effective fusion in decision-making is the lack of data. At present, data generation primarily involves the creation of feature vectors or attack simulation. This paper introduces a method for directly generating distances derived from a Siamese neural network, utilizing the probability density function of an existing distribution. Through statistical analysis, we successfully generated 5000 samples that correspond to the initial distribution, which were then employed to discover the threshold values at which FAR and FRR were less than 1%. The methods developed can be further applied to identify the most efficient strategies for integrating the results of continuous authentication in systems that incorporate multiple biometric characteristics.<\/jats:p>","DOI":"10.3390\/jcp6020045","type":"journal-article","created":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T12:48:56Z","timestamp":1772542136000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Generation of Distances Between Feature Vectors Derived from a Siamese Neural Network for Continuous Authentication"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7398-9716","authenticated-orcid":false,"given":"Sergey","family":"Davydenko","sequence":"first","affiliation":[{"name":"Faculty of Security, Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5305-3312","authenticated-orcid":false,"given":"Pavel","family":"Laptev","sequence":"additional","affiliation":[{"name":"Faculty of Security, Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8000-2716","authenticated-orcid":false,"given":"Evgeny","family":"Kostyuchenko","sequence":"additional","affiliation":[{"name":"Faculty of Security, Tomsk State University of Control Systems and Radioelectronics, 40 Lenina Prospect, Tomsk 634050, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,3]]},"reference":[{"key":"ref_1","first-page":"246","article-title":"A review of authentication methods","volume":"5","author":"Lal","year":"2016","journal-title":"Int. J. Sci. Technol. Res."},{"key":"ref_2","unstructured":"Afanasev, A.A., Vedeneev, L.T., and Vorontsov, A.A. (2012). Autentifikatsiya: Teoriya i Praktika Obespecheniya Bezopasnogo Dostupa k Informatsionnym Resursam [Authentication: Theory and Practice of Secure Access to Information Resources], Goryachaya liniya\u2013Telekom. (In Russian)."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cankaya, E. (2011). Authentication. Encyclopedia of Cryptography and Security, Springer.","DOI":"10.1007\/978-1-4419-5906-5_772"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Baig, A.F., and Eskeland, S. (2021). Security, privacy, and usability in continuous authentication: A survey. Sensors, 21.","DOI":"10.3390\/s21175967"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.21293\/1818-0442-2017-20-3-11-24","article-title":"Modern trends in development of methods and means for information protection","volume":"20","author":"Shelupanov","year":"2017","journal-title":"Proc. Tomsk. State Univ. Control. Syst. Radioelectron."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Davydenko, S., and Kostyuchenko, E. (2024). Continuous Authentication with Eye Movement Biometrics. International Conference on Intelligent Information Technologies for Industry, Springer Nature.","DOI":"10.1007\/978-3-031-77688-5_35"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Segundo, M.P., Sarkar, S., Goldgof, D., Silva, L., and Bellon, O. (2013, January 23\u201328). Continuous 3D face authentication using RGB-D cameras. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, Portland, OR, USA.","DOI":"10.1109\/CVPRW.2013.17"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Hanmandlu, M., and Vasikarla, S. (2012). Online biometric authentication using facial thermograms. 2012 IEEE Applied Imagery Pattern Recognition Workshop (AIPR), IEEE.","DOI":"10.1109\/AIPR.2012.6528223"},{"key":"ref_9","unstructured":"Wu, Z., Cheng, Y., Zhang, S., Ji, X., and Xu, W. (March, January 26). Uniid: Spoofing face authentication system by universal identity. Proceedings of the Network and Distributed System Security Symposium (NDSS), San Diego, CA, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1109\/TIFS.2010.2075927","article-title":"Soft biometric traits for continuous user authentication","volume":"5","author":"Niinuma","year":"2010","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Romanov, A.S., Kurtukova, A.V., Sobolev, A.A., Shelupanov, A.A., and Fedotova, A.M. (2020). Determining the age of the author of the text based on deep neural network models. Information, 11.","DOI":"10.3390\/info11120589"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhang, H., and Yin, L. (2025). Robust Camera-Based Eye-Tracking Method Allowing Head Movements and Its Application in User Experience Research. J. Eye Mov. Res., 18.","DOI":"10.3390\/jemr18060071"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Traore, I., Woungang, I., Obaidat, M.S., Nakkabi, Y., and Lai, I. (2012). Combining mouse and keystroke dynamics biometrics for risk-based authentication in web environments. 2012 Fourth International Conference on Digital Home, IEEE.","DOI":"10.1109\/ICDH.2012.59"},{"key":"ref_14","unstructured":"Romanov, A.S., Shelupanov, A.A., and Bondarchuk, S.S. (2010). Obobshchennaya metodika identifikatsii avtora neizvestnogo teksta [Generalized authorship identification technique]. Dokl. TUSUR\u2013Proc. TUSUR Univ., 108\u2013112. (In Russian)."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Fedotova, A., Romanov, A., Kurtukova, A., and Shelupanov, A. (2021). Authorship attribution of social media and literary Russian-language texts using machine learning methods and feature se-lection. Futur. Internet, 14.","DOI":"10.3390\/fi14010004"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Jarullah, T.G., Mohammad, A.S., Al-Kaltakchi, M.T.S., and Al-Ani, J.A. (2025). Intelligent Face Recognition: Comprehensive Feature Extraction Methods for Holistic Face Analysis and Modalities. Signals, 6.","DOI":"10.3390\/signals6030049"},{"key":"ref_17","unstructured":"Sabanov, A.G., Shelupanov, A.A., and Mescheryakov, R.V. (2012). Trebovaniya k sistemam autentifikatsii po urovnyam strogosti [Requirements for authentication systems by levels of strictness]. Polzunovskiy Vestn., 61\u201367. (In Russian)."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"596","DOI":"10.18287\/2412-6179-CO-621","article-title":"Automatic text-independent speaker verification using convolutional deep belief network","volume":"44","author":"Rakhmanenko","year":"2020","journal-title":"Comput. Opt."},{"key":"ref_19","unstructured":"Centeno, M.P., Guan, Y., and van Moorsel, A. (2018, January 15). Mobile based continuous authentication using deep features. Proceedings of the 2nd International Workshop on Embedded and Mobile Deep Learning, Munich, Germany."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"179057","DOI":"10.1109\/ACCESS.2025.3615290","article-title":"Shadow Eye: A Security System Featuring Few-Shot Face Recognition With Siamese Networks and Triplet Loss","volume":"13","author":"Afrah","year":"2025","journal-title":"IEEE Access"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Giot, R., and Rocha, A. (2019). Siamese networks for static keystroke dynamics authentication. 2019 IEEE International Workshop on Information Forensics and Security (WIFS), IEEE.","DOI":"10.1109\/WIFS47025.2019.9035100"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Lis, K., Niewiadomska-Szynkiewicz, E., and Dziewulska, K. (2023). Siamese neural network for keystroke dynamics-based authentication on partial passwords. Sensors, 23.","DOI":"10.3390\/s23156685"},{"key":"ref_23","unstructured":"Solano, J., Rivera, E., Tengana, L., L\u00f3pez, C., Fl\u00f3rez, J., and Ochoa, M. (2026, February 25). A Siamese Neural Network for Behavioral Biometrics Authentication. Available online: https:\/\/openreview.net\/references\/pdf?id=eBXtf16EHc."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Eberz, S., Lovisotto, G., Rasmussen, K.B., Lenders, V., and Martinovic, I. (2019, January 11\u201315). 28 blinks later: Tackling practical challenges of eye movement biometrics. Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, London, UK.","DOI":"10.1145\/3319535.3354233"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.patrec.2015.11.020","article-title":"A score level fusion method for eye movement biometrics","volume":"82","author":"George","year":"2016","journal-title":"Pattern Recognit. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Jia, S., Koh, D.H., Seccia, A., Antonenko, P., Lamb, R., Keil, A., Schneps, M., and Pomplun, M. (2018). Biometric recognition through eye movements using a recurrent neural network. 2018 IEEE International Conference on Big Knowledge (ICBK), IEEE.","DOI":"10.1109\/ICBK.2018.00016"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2904018","article-title":"Looks like eve: Exposing insider threats using eye movement biometrics","volume":"19","author":"Eberz","year":"2016","journal-title":"ACM Trans. Priv. Secur. (TOPS)"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TIFS.2012.2223677","article-title":"User authentication through mouse dynamics","volume":"8","author":"Shen","year":"2012","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Quraishi, S.J., and Bedi, S.S. (2022). Secure system of continuous user authentication using mouse dynamics. 2022 3rd International Conference on Intelligent Engineering and Management (ICIEM), IEEE.","DOI":"10.1109\/ICIEM54221.2022.9853050"},{"key":"ref_30","first-page":"5","article-title":"On using mouse movements as a biometric","volume":"Volume 1","author":"Hashia","year":"2005","journal-title":"Proceeding in the International Conference on Computer Science and its Applications"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.inffus.2018.12.003","article-title":"A comprehensive overview of biometric fusion","volume":"52","author":"Singh","year":"2019","journal-title":"Inf. Fusion"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1016\/S0031-3203(02)00349-7","article-title":"A hybrid fingerprint matcher","volume":"36","author":"Ross","year":"2003","journal-title":"Pattern Recognit."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2115","DOI":"10.1016\/S0167-8655(03)00079-5","article-title":"Information fusion in biometrics","volume":"24","author":"Ross","year":"2003","journal-title":"Pattern Recognit. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2270","DOI":"10.1016\/j.patcog.2005.01.012","article-title":"Score normalization in multimodal biometric systems","volume":"38","author":"Jain","year":"2005","journal-title":"Pattern Recognit."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.patcog.2005.06.011","article-title":"Database, protocols and tools for evaluating score-level fusion algorithms in biometric authentication","volume":"39","author":"Poh","year":"2006","journal-title":"Pattern Recognit."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1789","DOI":"10.1016\/j.patcog.2009.11.018","article-title":"Performance evaluation of score level fusion in multimodal biometric systems","volume":"43","author":"He","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.inffus.2016.02.003","article-title":"Score level fusion of classifiers in off-line signature verification","volume":"32","year":"2016","journal-title":"Inf. Fusion"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Poh, N., Kittler, J., and Bourlai, T. (2007). Improving biometric device interoperability by likelihood ratio-based quality dependent score normalization. 2007 First IEEE International Conference on Biometrics: Theory, Applications, and Systems, IEEE.","DOI":"10.1109\/BTAS.2007.4401964"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1109\/TPAMI.2007.70796","article-title":"Likelihood ratio-based biometric score fusion","volume":"30","author":"Nandakumar","year":"2008","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1142\/S0129065707001196","article-title":"Integrating image quality in 2\u03bd-SVM biometric match score fusion","volume":"17","author":"Vatsa","year":"2007","journal-title":"Int. J. Neural Syst."},{"key":"ref_41","first-page":"9345969","article-title":"Multimodal personal verification using likelihood ratio for the match score fusion","volume":"2017","author":"Tran","year":"2017","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Wang, S., Yuan, J., and Chen, S. (2020, January 10\u201312). Quality-based score level fusion for continuous authentication with motion sensor and face. Proceedings of the 2020 4th International Conference on Cryptography, Security and Privacy, Nanjing, China.","DOI":"10.1145\/3377644.3377647"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Vatsa, M., Singh, R., Ross, A., and Noore, A. (2010). Quality-based fusion for multichannel iris recognition. 2010 20th International Conference on Pattern Recognition, IEEE.","DOI":"10.1109\/ICPR.2010.327"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Smith-Creasey, M., and Rajarajan, M. (2019). A novel scheme to address the fusion uncertainty in multi-modal continuous authentication schemes on mobile devices. 2019 International Conference on Biometrics (ICB), IEEE.","DOI":"10.1109\/ICB45273.2019.8987390"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Srivastava, S., and Sudhish, P.S. (2016). Continuous multi-biometric user authentication fusion of face recognition and keystoke dynamics. 2016 IEEE Region 10 Humanitarian Technology Conference (R10-HTC), IEEE.","DOI":"10.1109\/R10-HTC.2016.7906823"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Hamouda, E., Alaerjan, A.S., Mostafa, A.M., and Tarek, M. (2025). A Score-Fusion Method Based on the Sine Cosine Algorithm for Enhanced Multimodal Biometric Authentication. Sensors, 26.","DOI":"10.3390\/s26010208"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Abaza, A., and Ross, A. (2009). Quality based rank-level fusion in multibiometric systems. 2009 IEEE 3rd International Conference on Biometrics: Theory, Ap-Plications, and Systems, IEEE.","DOI":"10.1109\/BTAS.2009.5339081"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Zhang, D., Qian, X., Shi, C., Zhang, Y., Qian, Y., and Zhou, S. (2025). Iron Ore Image Recognition Through Multi-View Evolutionary Deep Fusion Method. Futur. Internet, 17.","DOI":"10.3390\/fi17120553"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"103614","DOI":"10.1016\/j.bspc.2022.103614","article-title":"Data augmentation for cross-subject EEG features using Siamese neural network","volume":"75","author":"Fu","year":"2022","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_50","unstructured":"Mirza, M., and Osindero, S. (2014). Conditional generative adversarial nets. arXiv."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2648","DOI":"10.1109\/TIFS.2016.2594132","article-title":"Reconstruction attacks against mobile-based continuous authentication systems in the cloud","volume":"11","author":"Chang","year":"2016","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_52","unstructured":"Mondal, S. (2016). Continuous User Authentication and Identification: Combination of Security & Forensics. [Ph.D. Thesis, Norwegian University of Science and Technology]."},{"key":"ref_53","unstructured":"Ballard, L., Monrose, F., and Lopresti, D.P. (August, January 31). Biometric Authentication Revisited: Understanding the Impact of Wolves in Sheep\u2019s Clothing. Proceedings of the 15th USENIX Security Symposium, Vancouver, BC, Canada. Available online: https:\/\/www.usenix.org\/legacy\/events\/sec06\/tech\/full_papers\/ballard\/ballard.pdf."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/s10462-024-10847-7","article-title":"Federated learning for biometric recognition: A survey","volume":"57","author":"Guo","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Petricioli, L., Humski, L., and Vrani\u0107, M. (2025). Preserving Clusters in Synthetic Data Sets Based on Correlations and Distributions. Electronics, 14.","DOI":"10.3390\/electronics14112230"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Forte, A.G., Wang, W., Veltri, L., and Ferrari, G. (2019). A Next-Generation Core Network Architecture for Mobile Networks. Futur. Internet, 11.","DOI":"10.3390\/fi11070152"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Dong, S., Yang, Z., Li, W., and Zou, K. (2021). Dynamic Detection and Recognition of Objects Based on Sequential RGB Images. Futur. Internet, 13.","DOI":"10.3390\/fi13070176"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Sluganovic, I., Roeschlin, M., Rasmussen, K.B., and Martinovic, I. (2016, January 24\u201328). Using reflexive eye movements for fast challenge-response authentication. Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria.","DOI":"10.1145\/2976749.2978311"}],"container-title":["Journal of Cybersecurity and Privacy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2624-800X\/6\/2\/45\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T14:19:26Z","timestamp":1772547566000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2624-800X\/6\/2\/45"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,3]]},"references-count":58,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["jcp6020045"],"URL":"https:\/\/doi.org\/10.3390\/jcp6020045","relation":{},"ISSN":["2624-800X"],"issn-type":[{"value":"2624-800X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,3]]}}}