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
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.
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 paper offers a novel digital signature scheme that integrates ElGamal cryptographic principles with the Short Integer Solution (SIS) problem, specifically designed to ensure post-quantum security. As quantum computers advance and present significant risks to traditional cryptographic systems, this scheme offers an interesting alternative for securing digital signatures against potential quantum threats. The scheme uses only basic secure principles. The offered approach offers key generation, where parameters and random matrices are selected, and signature generation, which involves creating signatures based on hashed messages and matrix computations. Verification ensures the authenticity and integrity of signatures. We provide experimental evaluations detailing key generation, signature creation, and verification times across different matrix dimensions and message sizes. Key generation takes between 2.5–10.2 seconds, while signature generation ranges from 0.20 to 9.30 milliseconds and verification from 0.18 to 8.90 milliseconds, depending on message size and matrix dimension. The scheme maintains a consistent signature size of 1.7 KB, independent of message length due to a hash-and-sign strategy. These results demonstrate that the scheme balances post-quantum security with practical performance, especially in high-security contexts. A comparison with traditional ElGamal encryption reveals the trade-offs between security and efficiency. While the SIS-based scheme delivers enhanced protection against quantum threats, it also entails increased computational complexity and larger signature sizes compared to conventional schemes. Overall, our proposed digital signature scheme stands as an excellent option for safe communications in a post-quantum world, representing a crucial step in protecting the authenticity and integrity of digital exchanges against changing technological risks. We believe that as quantum computing continues to develop, research into robust cryptographic alternatives will become increasingly important for safeguarding sensitive information across various sectors.
Digital signatures are essential for the security of computer networks such as the Internet. For example, digital signatures are widely used to ensure the authenticity and integrity of updates for operating systems and other software applications. The security of the few practically used signature schemes is threatened by quantum computers. When large quantum computers are built, all currently used signature schemes will become insecure. It is therefore of extreme importance to develop alternative signature schemes that remain secure in the presence of quantum computers and which are able to compete with currently used signature schemes. A very promising candidate for a signature scheme that withstands quantum computer attacks is the Merkle signature scheme invented by Merkle in 1979. However, even combined with the improvements by Szydlo and Coronado, the Merkle signature scheme has certain efficiency drawbacks that keep it from being truly practical. First of all, it has highly unbalanced signature generation times. In the worst case, signature generation takes significantly longer than on average. Secondly, the Merkle--Szydlo--Coronado signature scheme produces very large signatures. It is also unclear if Merkle's signature scheme is suitable for application on resource constrained devices. The generalized Merkle signature scheme (GMSS) presented in this thesis solves the problems mentioned above. It drastically reduces the worst case signature generation time of the Merkle--Szydlo--Coronado signature scheme. The worst case signature generation time of GMSS corresponds to the average case signature generation time of the Merkle--Szydlo--Coronado signature scheme. Further, the worst case signature generation time of GMSS is extremely close to its average case signature generation time and thus, GMSS provides balanced timings for the signature generation. GMSS exploits the improved signature generation times to provide a noticeable reduction of the signature sizes while maintaining timings that are highly competitive to currently used signature schemes. A proof-of-concept implementation shows that GMSS can also be used on resource constrained devices and excellently compares to currently used signature schemes. This thesis also introduces a new construction method for Merkle signatures. This construction is provably secure under weaker security assumptions and yields a signature scheme with a significantly higher security level compared to the original construction.
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 quantum computing continues to advance, the security of conventional cryptographic systems faces significant risks, prompting rapid developments in post-quantum cryptography (PQC). This paper presents a series of targeted improvements to the Falcon digital signature scheme in post-quantum cryptography. The analysis of Falcon’s framework, several areas can be identified where optimizations could enhance performance. This lowers the computing overhead while maintaining the algorithm’s resilience to quantum attacks by using GPU offloading, parameter recalibration, and other optimization strategies. Experimental evaluation shows an approximate 11% reduction in execution time without compromising the security guaranteed by the original method. These enhancements make it more practical for resource-constrained environments.