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Mathematics
Volume 14
Issue 12
10.3390/math14122058
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

VPS: A Verkle-Based Polynomial Signature Scheme with Post-Quantum Security

by
Maria Nutu
1,*,
Razvan Bocu
1 and
Maksim Iavich
2
1
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania
2
Department of Computer Science, Caucasus University, 0102 Tbilisi, Georgia
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(12), 2058; https://doi.org/10.3390/math14122058 (registering DOI)
Submission received: 21 April 2026 / Revised: 29 May 2026 / Accepted: 3 June 2026 / Published: 9 June 2026
(This article belongs to the Section E1: Mathematics and Computer Science)
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Abstract

With the development of large-scale quantum computers, classical cryptographic algorithms such as RSA or ECC can easily be broken by Shor’s algorithm. Consequently, the cryptography community is shifting its focus toward Post-Quantum Cryptography (PQC), developing primitives that are secure against both classical and quantum attacks. In this paper, we propose a novel Verkle-Polynomial Signature (VPS) scheme by combining the lattice-based polynomial commitment scheme of Cini et al. with Verkle trees and a lattice-based One-Time Signature (OTS) engine to achieve post-quantum security. We demonstrate that while sacrificing the operational efficiency and structural maturity of traditional hash-based signatures, our framework provides robust post-quantum security guarantees inherited from standard lattice assumptions.
Keywords: Verkle trees; Post-Quantum Cryptography (PQC); One-Time Signature (OTS); lattice-based polynomial commitment Verkle trees; Post-Quantum Cryptography (PQC); One-Time Signature (OTS); lattice-based polynomial commitment
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MDPI and ACS Style

Nutu, M.; Bocu, R.; Iavich, M. VPS: A Verkle-Based Polynomial Signature Scheme with Post-Quantum Security. Mathematics 2026, 14, 2058. https://doi.org/10.3390/math14122058

AMA Style

Nutu M, Bocu R, Iavich M. VPS: A Verkle-Based Polynomial Signature Scheme with Post-Quantum Security. Mathematics. 2026; 14(12):2058. https://doi.org/10.3390/math14122058

Chicago/Turabian Style

Nutu, Maria, Razvan Bocu, and Maksim Iavich. 2026. "VPS: A Verkle-Based Polynomial Signature Scheme with Post-Quantum Security" Mathematics 14, no. 12: 2058. https://doi.org/10.3390/math14122058

APA Style

Nutu, M., Bocu, R., & Iavich, M. (2026). VPS: A Verkle-Based Polynomial Signature Scheme with Post-Quantum Security. Mathematics, 14(12), 2058. https://doi.org/10.3390/math14122058

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