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Computers

Optimizing Post-Quantum Digital Signatures with Verkle Trees and Quantum Seed-Based Pseudo-Random Generators

Maksim Iavich, Nursulu A. Kapalova

Published Mar 14, 2025• 5 citations
Publisher

Abstract

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.

DOI
10.3390/computers14030103

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The security of public key cryptosystems has become a major concern due to recent developments in the field of quantum computing. Despite efforts to enhance defenses against quantum attacks, current methods are impractical due to safety and efficacy concerns. A recent study explores hash-based digital signature methods and evaluates their effectiveness using Merkle trees. Furthermore, novel approaches based on Verkle trees and vector commitments have been studied to reduce quantum threats. First, we introduce a post-quantum digital signature system that combines vector commitments based on lattices with Verkle trees. This architecture optimizes traditional Merkle tree architecture by preserving resistance to quantum attacks while improving cryptographic proofs. Second, in order to ensure secure initial seed generation without sacrificing operational viability, we create a hybrid random number generation framework that combines quantum random number generation (QRNG) with pseudorandom approaches. We provide a detailed analysis of generating random numbers in our article, which makes it easier to build a post quantum cryptosystem that uses our generator to provide initial random values. Our system is notable for its robust security against quantum threats, speed, and efficiency.
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.
In recent years, work on quantum computers has made substantial progress. Many of the current public key cryptosystems can be broken if humans ever develop a powerful quantum computer. There are currently several commercial products that use these cryptosystems. Though we have developed defenses against quantum attacks, they are too risky and ineffective to be applied in daily life. The study analyzes hash-based digital signature methods. The evaluation of a digital signature using a Merkle tree. The paper investigates unique ideas using vector commitments and a Verkle tree. The authors of this study describe a novel, Verkle tree technology-based method for creating a digital signature system. This is accomplished using the Verkle tree, vector commitments, and vector commitments based on lattices for post-quantum aspects. This work also provides the theories behind post-quantum signature design using Verkle Tree.
Many public key cryptosystems in use today run the risk of being broken as quantum computing develops, affecting the security of popular commercial applications. Although there are possible defenses against quantum assaults, their complexity and inefficiency make them unsuitable for daily usage. This article discusses asymmetric hash-based digital signature algorithms, focusing on the symmetric and balanced structure achieved through the use of k-ary Verkle trees and lattice-based vector commitments. The study investigates the new concepts using vector commitments, a Verkle tree, and k-ary Verkle tree, which enhance efficiency and scalability while maintaining a symmetric structure in cryptographic proofs. Using cutting-edge Verkle tree technology, the authors of this paper provide a novel approach to creating a digital signature system. This is accomplished by using vector commitments, a k-ary Verkle tree, Verkle tree, and lattice-based vector commitments for post-quantum characteristics. The study also presents the ideas for designing post-quantum signatures using a k-ary Verkle tree, emphasizing the symmetry in tree structures and the balance between security and efficiency in asymmetric cryptographic systems.
Modern-day cryptographic schemes are threatened by the rapid development of quantum computers, which are capable of solving discrete-logarithm-based problems in a reasonable amount of time. The paper proposes a novel approach to a PORS post-quantum secure signature. The main idea of the proposal is integrating a PORS signature scheme with a Verkle tree, which greatly reduces the signature size compared to a PORST that uses a Merkle tree, while reducing authentication overhead through constant-size vector commitment proofs at each tree level. The work is highly relevant as it proposes a post-quantum digital signature which has compact proofs and at the same time solves the problems of the original HORS signature scheme (subset-resilience problem). The work contributes to the ongoing standardization efforts in post-quantum cryptography by providing a theoretically scalable and efficient signature scheme that balances security, size, and verification speed.
The rapid development of quantum computing poses challenges to the foundations of traditional cryptography. The threats are significant in terms of both asymmetric cryptography (which exposes schemes like RSA and ECC to efficient attacks) and symmetric cryptography, where key sizes must be increased to mitigate these threats. In this paper, we review the evolution of hash-based digital signatures, from early one-time signatures to modern stateless schemes, with an emphasis on their security properties, efficiency, and practical constraints. Moreover, we propose a simple comparative metric that reflects structural symmetry across key parameters such as key size, signature size, and computational cost, enabling a visual clustering of the schemes. We give particular attention to recent developments such as Verkle trees, which preserve symmetric design principles while improving scalability and proof compactness. The study highlights ongoing tradeoffs between stateful and stateless designs and argues for the continued relevance of symmetric cryptographic constructions in building secure, efficient post-quantum systems.