{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T15:30:22Z","timestamp":1781710222770,"version":"3.54.5"},"reference-count":16,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T00:00:00Z","timestamp":1701820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shota Rustaveli National Science Foundation of Georgia (SRNSF)","award":["STEM\u201322-1076"],"award-info":[{"award-number":["STEM\u201322-1076"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Research on quantum computers has advanced significantly in recent years. If humanity ever creates an effective quantum computer, many of the present public key cryptosystems can be compromised. These cryptosystems are currently found in many commercial products. We have devised solutions that seem to protect us from quantum attacks, but they are unsafe and inefficient for use in everyday life. In the paper, hash-based digital signature techniques are analyzed. A Merkle-tree-based digital signature is assessed. Using a Verkle tree and vector commitments, the paper explores novel ideas. The authors of this article present a unique technology for developing a post-quantum digital signature system using state-of-the-art Verkle tree technology. A Verkle tree, vector commitments, and vector commitments based on lattices for post-quantum features are used for this purpose. The concepts of post-quantum signature design utilizing a Verkle tree are also provided in the paper.<\/jats:p>","DOI":"10.3390\/sym15122165","type":"journal-article","created":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T03:48:41Z","timestamp":1701834521000},"page":"2165","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Post-Quantum Digital Signature Using Verkle Trees and Lattices"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3109-7971","authenticated-orcid":false,"given":"Maksim","family":"Iavich","sequence":"first","affiliation":[{"name":"Department of Computer Science, Caucasus University, Tbilisi 0102, Georgia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tamari","family":"Kuchukhidze","sequence":"additional","affiliation":[{"name":"Department of Computer Science, International Black Sea University, Tbilisi 0131, Georgia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6577-1904","authenticated-orcid":false,"given":"Razvan","family":"Bocu","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Chen, L., Chen, L., Jordan, S., Liu, Y.K., Moody, D., Peralta, R., Perlner, R.A., and Smith-Tone, D. (2016). Report on Post-Quantum Cryptography, US Department of Commerce, National Institute of Standards and Technology.","DOI":"10.6028\/NIST.IR.8105"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J., Buchmann, J., and Dahmen, E. (2009). Post-Quantum Cryptography, Springer.","DOI":"10.1007\/978-3-540-88702-7"},{"key":"ref_3","unstructured":"Bhaskar, B., and Sendrier, N. (2008). Post-Quantum Cryptography, Proceedings of the Second International Workshop, PQCrypto 2008, Cincinnati, OH, USA, 17\u201319 October 2008, Springer. Proceedings 2."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Yin, X., He, J., Guo, Y., Han, D., Li, K.-C., and Castiglione, A. (2020). An Efficient Two-Factor Authentication Scheme Based on the Merkle Tree. Sensors, 20.","DOI":"10.3390\/s20205735"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chen, Y.-C., Chou, Y.-P., and Chou, Y.-C. (2019). An Image Authentication Scheme Using Merkle Tree Mechanisms. Future Internet, 11.","DOI":"10.3390\/fi11070149"},{"key":"ref_6","unstructured":"Lamport, L. (2023, December 05). Constructing Digital Signatures from a One Way Function. Available online: https:\/\/www.microsoft.com\/en-us\/research\/publication\/constructing-digital-signatures-one-way-function\/."},{"key":"ref_7","unstructured":"Iavich, M., Bocu, R., Arakelian, A., and Iashvili, G. (2023, December 05). Post-Quantum Digital Signatures with Attenuated Pulse Generator. Volume 2698. 2020. Available online: https:\/\/www.researchgate.net\/profile\/Maksim-Iavich\/publication\/346971219_Post-Quantum_Digital_Signatures_with_Attenuated_Pulse_Generator\/links\/5fd63e2845851553a0b26923\/Post-Quantum-Digital-Signatures-with-Attenuated-Pulse-Generator.pdf."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Koo, D., Shin, Y., Yun, J., and Hur, J. (2018). Improving Security and Reliability in Merkle Tree-Based Online Data Authentication with Leakage Resilience. Appl. 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Advances in Computer Science for Engineering and Education III 3, Springer International Publishing."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/12\/2165\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:33:54Z","timestamp":1760132034000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/12\/2165"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,6]]},"references-count":16,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["sym15122165"],"URL":"https:\/\/doi.org\/10.3390\/sym15122165","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,6]]}}}