Abstract Post-quantum (or quantum-resistant) cryptography refers to a set of cryptographic algorithms that are thought to remain secure even in the world of quantum computers. These algorithms are usually considered to be inefficient because of their big keys, or their running time. However, if quantum computers became a reality, security professionals will not have any other choice, but to use these algorithms. Lamport signature is a hash based one-time digital signature algorithm that is thought to be quantum-resistant. In this paper we will describe some simulation results related to the efficiency of the Lamport signature.
Abstract Post-quantum (or quantum-resistant) cryptography refers to a set of cryptographic algorithms that are thought to remain secure even in the world of quantum computers. These algorithms are usually considered to be inefficient because of their big keys, or their running time. However, if quantum computers became a reality, security professionals will not have any other choice, but to use these algorithms. Lamport signature is a hash based one-time digital signature algorithm that is thought to be quantum-resistant. In this paper we will describe some simulation results related to the efficiency of the Lamport signature.
With the advancement of quantum computing, conventional digital signature algorithms such as RSA and El-Gamal are increasingly vulnerable to quantum attacks. This presents a significant challenge for ensuring the security and integrity of electronic signatures. As a result, there is a need to develop post-quantum signature algorithms that can withstand attacks from quantum computers while maintaining computational efficiency. This study proposes a novel modification of the Merkle post-quantum signature scheme, integrating an optimized version of Lamport’s one-time signature algorithm. The core contribution of this work is the design and implementation of a new algorithm that significantly reduces signature verification time without compromising cryptographic strength. A software implementation of the modified scheme was developed using Python and the PyQt 6 library, allowing for practical testing and analysis. The performance of the modified algorithm was compared against the standard Lamport algorithm using execution time measurements and statistical analysis. The experimental results demonstrate that the modified algorithm significantly improves signature verification speed, reducing the time required by up to 44.81% compared to the standard algorithm. The study presents a more efficient post-quantum Merkle signature scheme with a modified Lamport algorithm that enhances signature verification speed while maintaining strong cryptographic security. The results suggest that the proposed scheme is particularly well-suited for environments where fast authentication of multiple digital signatures is required. Experimental results confirm the advantage of the proposed approach, offering a more efficient solution for secure, high-speed digital authentication in post-quantum environments
The rapid advancement of quantum computing poses a serious threat to classical digital signature algorithms such as RSA and ECDSA, which rely on mathematical problems vulnerable to quantum attacks. Hash-based digital signatures offer a strong post-quantum alternative due to their reliance on cryptographic hash functions and their resistance to both classical and quantum adversaries. This study evaluates the feasibility of hash-based signatures in lightweight and resource-constrained environments by implementing three representative schemes: Lamport One-Time Signatures (OTS), Winternitz One-Time Signatures (WOTS), and Merkle-WOTS. The analysis focuses on key performance factors relevant to constrained devices, including key size, signature size, signing time, and verification speed. Experimental results show that while Lamport OTS provides conceptual simplicity and WOTS offers improved efficiency, the Merkle-WOTS scheme delivers the most practical balance. It supports multiple signatures under a compact public key while maintaining moderate signature sizes and competitive performance. These findings indicate that Merkle-WOTS is a strong candidate for post-quantum authentication in IoT and other lightweight embedded systems.
In the era of active information technologies and device development, the emergence of portable and general-purpose quantum computers is only a matter of time. And although the benefit of their many times greater efficiency, compared to ordinary bit computers, will be obvious, at the same time, they will bring many vulnerabilities to modern algorithms of cryptography and cybersecurity. To prevent this from happening, society has already started researching post-quantum protocols to replace modern ones. Digital signature protocols were no exception. Thus, one of the approaches was constructing post-quantum digital signature protocols based on hash functions. The first representatives were schemes of one-time signatures based on hash functions, which were protected from the capabilities of quantum computers but had the obvious disadvantage of one-time use. The most famous is the so-called Lamport one-time signature. However, this disadvantage of one-time use has been solved by proposing different schemes of multi-time digital signatures based on the creation and use of many one-time signatures. Thus, chain-based and tree-based schemes of multi-time signatures were proposed. This work is devoted to the implementation and comparison of various multi-time signature schemes. During the research, theoretical estimates of memory usage and time required for the operations of various schemes were given. Further implementation of these schemes and final measurements showed the correspondence of theoretical estimates with empirical results and clearly demonstrated the advantages and disadvantages of different schemes. Thus, tree-based schemes showed the best performance, especially those where the tree is built sequentially. However, in certain cases, it makes sense to use a tree with full-depth construction. Due to the relative novelty and small amount of research in this field, multi-time digital signatures have much room for further research, for example, considering N-ary trees and comparing them with binary ones.
Quantum computing represents one of the most disruptive technological advancements of the 21st century, with profound implications for modern cryptographic systems. Traditional digital signature algorithms—such as RSA, DSA, and Elliptic Curve Cryptography (ECC)—derive their security from mathematical problems like integer factorization and discrete logarithms, which are computationally infeasible for classical computers. However, the advent of quantum algorithms, particularly Shor’s and Grover’s algorithms, poses a direct threat to these cryptographic assumptions by drastically reducing the time required to solve such problems. This development renders existing Digital Signature infrastructures potentially obsolete once large-scale quantum computers become operational. To counter this threat, researchers have proposed a range of post-quantum cryptographic (PQC) algorithms, including lattice-based, hash-based, and multivariate polynomial-based signature schemes, which are designed to resist quantum attacks. This paper critically examines the extent of quantum vulnerability in current Digital Signature systems and evaluates the comparative performance, efficiency, and security trade-offs of post-quantum alternatives. The study aims to provide a structured understanding of the ongoing transition toward quantum-resistant digital authentication and to propose a roadmap for secure implementation in future cryptographic environments.
The recent advancement in quantum computing poses a concern over the security of current public key cryptography systems.Since then, hash-based signature schemes have been created to replace vulnerable schemes, although they have limitations such as requiring a large key and/or signature size or only working a limited number of times.This paper discusses a solution to these two problems through key replacement to allow a single initial agreement to be used an arbitrary number of times with a reasonable key size.The experiments were done by extending the Lamport signature scheme with this key replacement, leading to a signature scheme that is slower than DSA and ECDSA, but faster than RSA for sufficiently large security levels.As a result, while applying this technique does not lead to very fast performance, it still has the advantage of postquantum security, and it is not excessively slow.
One of the most crucial measures to maintain data security is the use of cryptography schemes and digital signatures built upon cryptographic algorithms. The resistance of cryptographic algorithms against conventional attacks is guaranteed by the computational difficulties and the immense amount of computation required to them. In the last decade, with the advances in quantum computing technology and the realization of quantum computers, which have higher computational power compared to conventional computers and can execute special kinds of algorithms (i.e., quantum algorithms), the security of many existing cryptographic algorithms has been questioned. The reason is that by using quantum computers and executing specific quantum algorithms through them, the computational difficulties of conventional cryptographic algorithms can be reduced, which makes it possible to overcome and break them in a relatively short period of time. Therefore, researchers began efforts to find new quantum-resistant cryptographic algorithms that would be impossible to break, even using quantum computers, in a short time. Such algorithms are called post-quantum cryptographic algorithms. In this article, we provide a comprehensive review of the challenges and vulnerabilities of different kinds of conventional cryptographic algorithms against quantum computers. Afterward, we review the latest cryptographic algorithms and standards that have been proposed to confront the threats posed by quantum computers. We present the classification of post-quantum cryptographic algorithms and digital signatures based on their technical specifications, provide examples of each category, and outline the strengths and weaknesses of each category.