{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T03:05:33Z","timestamp":1763348733748,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T00:00:00Z","timestamp":1741910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["AP23488112"],"award-info":[{"award-number":["AP23488112"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computers"],"abstract":"<jats:p>Nowadays, quantum computing is developing at an unprecedented speed. This will pose a serious threat to the security of widely used public-key cryptosystems in the near future. Scientists are actively looking for ways to protect against quantum attacks; however, existing solutions still face different limitations in terms of efficiency and practicality. This paper explores hash-based digital signature schemes, post-quantum vector commitments and Verkle tree-based approaches for protecting against quantum attacks. The paper proposes an improved approach to generating digital signatures based on Verkle trees using lattice based vector commitments. In order to further reduce the memory space, the paper offers the methodology of integrating a post-quantum secure pseudo-random number generator into the scheme. Finally, the paper proposes an efficient post-quantum digital signature scheme based on Verkle trees, which minimizes memory requirements and reduces the signature size. Our proposed framework has strong resistance to quantum attacks, as well as high speed and efficiency. This study is an important contribution to the elaboration of post-quantum cryptosystems, which lays the foundation for developing secure and practical digital signature systems in the face of emerging quantum threats.<\/jats:p>","DOI":"10.3390\/computers14030103","type":"journal-article","created":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T13:07:51Z","timestamp":1741957671000},"page":"103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimizing Post-Quantum Digital Signatures with Verkle Trees and Quantum Seed-Based Pseudo-Random Generators"],"prefix":"10.3390","volume":"14","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9743-9981","authenticated-orcid":false,"given":"Nursulu","family":"Kapalova","sequence":"additional","affiliation":[{"name":"Laboratory of Information Security at the Institute of Information and Computational Technologies, Ministry of Science and Higher Education of the Republic of Kazakhstan, Almaty 050010, Kazakhstan"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124891","DOI":"10.1016\/j.eswa.2024.124891","article-title":"Image privacy protection scheme based on high-quality reconstruction DCT compression and nonlinear dynamics","volume":"257","author":"Lin","year":"2024","journal-title":"Expert Syst. 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