{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T15:42:47Z","timestamp":1776181367119,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union-Next Generation EU","award":["CUP H93C22000620001"],"award-info":[{"award-number":["CUP H93C22000620001"]}]},{"name":"Project \u201cEuropean Digital Innovation Hub for Secure Digital Transformation EDIH4DT\u201d-Next Generation EU","award":["CUP B97H22004920001"],"award-info":[{"award-number":["CUP B97H22004920001"]}]},{"name":"Italian Presidenza del Consiglio dei Ministri, Patti Territoriali per l\u2019alta formazione delle imprese"},{"id":[{"id":"https:\/\/ror.org\/02rc7fh29","id-type":"ROR","asserted-by":"publisher"}]},{"name":"\u201cPatto: Sistema Universitario Pugliese \u2013 Open Apulian University\u201d","award":["CUP F61B23000370006"],"award-info":[{"award-number":["CUP F61B23000370006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>Classical approaches to cryptography exhibit several limitations when applied to scenarios involving more than two users. The One-Time User Key (OTUK) meta-cryptographic model addresses these limitations by enabling multi-user encryption that is flexible, applicable to any cryptographic algorithm, and designed for systematic deployment without compromising system security. Each user possesses an individual key from which One-Time keys are derived; these keys feed a secret-sharing function (\u03c9) that establishes the multi-user encrypted channel. In this paper, we present a polynomial-based implementation of the \u03c9 function under a (1,n) threshold model. The generated polynomial has roots at points corresponding to valid user keys and is mapped to the real encryption key. We provide a formal threat model, pseudocode for the complete protocol, and a detailed computational analysis across the numerical domains N, Z, and R. Furthermore, we present experimental benchmarks measuring encryption\/decryption speed, scalability up to 30 users, parameter sensitivity, and a comparative evaluation against Shamir\u2019s Secret Sharing scheme. A systematic security analysis examines partial-information attacks, derivative-root distance margins, and brute-force resistance, demonstrating that the effective security margin remains above 245 bits for configurations of up to 30 users with 256-bit keys. The proposed method offers a concrete, efficient, and secure foundation for multi-user encrypted communication in domains such as IoT, public administration, and e-health.<\/jats:p>","DOI":"10.3390\/cryptography10020026","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T14:24:58Z","timestamp":1776176698000},"page":"26","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Multiple User Cryptography Approach Using a One-Time User Key Model and a (1, n) Threshold Polynomial Secret Sharing"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6713-7788","authenticated-orcid":false,"given":"Alessandro","family":"Caniglia","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Bari Aldo Moro, 72125 Bari, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8887-800X","authenticated-orcid":false,"given":"Felice","family":"Franchini","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Bari Aldo Moro, 72125 Bari, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3955-0478","authenticated-orcid":false,"given":"Stefano","family":"Galantucci","sequence":"additional","affiliation":[{"name":"Department of Agricultural Sciences, Food, Natural Resources and Engineering (DAFNE), University of Foggia, 71122 Foggia, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7305-2210","authenticated-orcid":false,"given":"Giuseppe","family":"Pirlo","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Bari Aldo Moro, 72125 Bari, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1666-8323","authenticated-orcid":false,"given":"Gianfranco","family":"Semeraro","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Bari Aldo Moro, 72125 Bari, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"148521","DOI":"10.1109\/ACCESS.2021.3124637","article-title":"One Time User Key: A User-Based Secret Sharing XOR-ed Model for Multiple User Cryptography in Distributed Systems","volume":"9","author":"Galantucci","year":"2021","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Winarno, A., and Sari, R.F. (2022). A Novel Secure End-to-End IoT Communication Scheme Using Lightweight Cryptography Based on Block Cipher. Appl. Sci., 12.","DOI":"10.3390\/app12178817"},{"key":"ref_3","unstructured":"Council of the European Union (2026, February 23). Council Resolution on Encryption Security Through Encryption and Security Despite Encryption. Available online: https:\/\/data.consilium.europa.eu\/doc\/document\/ST-13084-2020-REV-1\/en\/pdf."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Aversano, L., Bernardi, M.L., Cimitile, M., Montano, D., Pecori, R., and Veltri, L. (2023, January 11\u201313). Anomaly Detection of Medical IoT Traffic Using Machine Learning. Proceedings of the DATA, Rome, Italy.","DOI":"10.5220\/0012132000003541"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1007\/s42979-024-02830-4","article-title":"Explainable anomaly detection of synthetic medical iot traffic using machine learning","volume":"5","author":"Aversano","year":"2024","journal-title":"SN Comput. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1145\/359168.359176","article-title":"How to share a secret","volume":"22","author":"Shamir","year":"1979","journal-title":"Commun. ACM"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Blakley, G.R. (1979). Safeguarding cryptographic keys. 1979 International Workshop on Managing Requirements Knowledge (MARK), IEEE Computer Society.","DOI":"10.1109\/MARK.1979.8817296"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/0167-4048(94)90097-3","article-title":"The breadth of Shamir\u2019s secret-sharing scheme","volume":"13","author":"Dawson","year":"1994","journal-title":"Comput. Secur."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1142\/S0129054104002510","article-title":"Several generalizations of Shamir\u2019s secret sharing scheme","volume":"15","author":"Lai","year":"2004","journal-title":"Int. J. Found. Comput. Sci."},{"key":"ref_10","first-page":"840","article-title":"A new (t, n) multi-secret sharing scheme based on Shamir\u2019s secret sharing","volume":"167","author":"Pang","year":"2005","journal-title":"Appl. Math. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5134534","DOI":"10.1155\/2019\/5134534","article-title":"Linear secret sharing scheme with reduced number of polynomials","volume":"2019","author":"Phiri","year":"2019","journal-title":"Secur. Commun. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TIT.1985.1057074","article-title":"A public key cryptosystem and a signature scheme based on discrete logarithms","volume":"31","author":"ElGamal","year":"1985","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1109\/TIT.1983.1056651","article-title":"A modular approach to key safeguarding","volume":"29","author":"Asmuth","year":"1983","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Herzberg, A., Jarecki, S., Krawczyk, H., and Yung, M. (1995). Proactive secret sharing or: How to cope with perpetual leakage. Proceedings of the Annual International Cryptology Conference, Springer.","DOI":"10.1007\/3-540-44750-4_27"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Meng, K., Miao, F., Ning, Y., Huang, W., Xiong, Y., and Chang, C.C. (2021). A proactive secret sharing scheme based on Chinese remainder theorem. Frontiers Comput. Sci., 15.","DOI":"10.1007\/s11704-019-9123-z"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ning, Y., Miao, F., Huang, W., Meng, K., Xiong, Y., and Wang, X. (2018, January 8\u201312). Constructing ideal secret sharing schemes based on chinese remainder theorem. Proceedings of the International Conference on the Theory and Application of Cryptology and Information Security, Melbourne, VIC, Australia.","DOI":"10.1007\/978-3-030-03332-3_12"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Komargodski, I., Naor, M., and Yogev, E. (2016). How to share a secret, infinitely. Proceedings of the Theory of Cryptography Conference, Springer.","DOI":"10.1007\/978-3-662-53644-5_19"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4179","DOI":"10.1109\/TIT.2017.2779121","article-title":"How to Share a Secret, Infinitely","volume":"64","author":"Komargodski","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/TIT.2020.3028194","article-title":"Distributed multi-user secret sharing","volume":"67","author":"Soleymani","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_20","unstructured":"Okamura, R., and Koga, H. (2020). New Constructions of an Evolving 2-Threshold Scheme Based on Binary or D-ary Prefix Codes. Proceedings of the 2020 International Symposium on Information Theory and Its Applications (ISITA), IEEE."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.tcs.2021.01.019","article-title":"Secret sharing schemes for infinite sets of participants: A new design technique","volume":"859","year":"2021","journal-title":"Theor. Comput. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3718","DOI":"10.1109\/TIT.2024.3379278","article-title":"Evolving secret sharing schemes based on polynomial evaluations and algebraic geometry codes","volume":"70","author":"Xing","year":"2024","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1186\/s42400-024-00344-3","article-title":"Adaptively secure, splittable, and robust threshold unsigncryption","volume":"8","author":"Tong","year":"2025","journal-title":"Cybersecurity"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Boudgoust, K., and Scholl, P. (2023). Simple threshold (fully homomorphic) encryption from LWE with polynomial modulus. Proceedings of the International Conference on the Theory and Application of Cryptology and Information Security, Springer.","DOI":"10.1007\/978-981-99-8721-4_12"},{"key":"ref_25","first-page":"51166","article-title":"Communication-efficient secure computation of encrypted inputs using (k, n) threshold secret sharing","volume":"11","author":"Iwamura","year":"2023","journal-title":"IEEE Access"},{"key":"ref_26","unstructured":"(2019). IEEE Standard for Floating-Point Arithmetic (Standard No. IEEE Std 754-2019 (Revision of IEEE 754-2008))."},{"key":"ref_27","unstructured":"Burden, R., Faires, J., and Burden, A. (2015). Numerical Analysis, Cengage Learning."}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/10\/2\/26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T14:43:45Z","timestamp":1776177825000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/10\/2\/26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,14]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["cryptography10020026"],"URL":"https:\/\/doi.org\/10.3390\/cryptography10020026","relation":{},"ISSN":["2410-387X"],"issn-type":[{"value":"2410-387X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,14]]}}}