With the rapid development of quantum technologies, quantum-safe cryptography has found significant attention. Hash-based signature schemes have been in particular of interest because of (i) the importance of digital signature as the main source of trust on the Internet, (ii) the fact that the security of these signatures relies on existence of one-way functions, which is the minimal assumption for signature schemes, and (iii) they can be efficiently implemented. Basic hash-based signatures are for a single message, but have been extended for signing multiple messages. In this paper we design a Multi-message Signature Scheme (MSS) based on an existing One-Time Signature (OTS) that we refer to as KSN-OTS. KSN uses SWIFFT, an additive homomorphic lattice-based hash function family with provable one-wayness property, as the one-way-function and achieves a short signature. We prove security of our proposed signature scheme in a new strengthened security model (multi-target multi-function) of MSS, determine the system parameters for 512 bit classical (256 bit quantum) security, and compare parameter sizes of our scheme against XMSS, a widely studied hash based MSS that has been a candidate for NIST standardization of post-quantum signature scheme. We give an efficient implementation of our scheme using Intel SIMD (Single Instruction Multiple Data) instruction set. For this, we first implement SWIFFT computation using a SIMD parallelization of Number Theoretic Transform (NTT) of elements of the ring Zp[X]/(Xn+1), that can support different levels of parallelization. We compare efficiency of this implementation with a comparable (security level) implementation of XMSS and show its superior performance on a number of efficiency parameters.
With the rapid development of quantum technologies, quantum-safe cryptography has found significant attention. Hash-based signature schemes have been in particular of interest because of (i) the importance of digital signature as the main source of trust on the Internet, (ii) the fact that the security of these signatures relies on existence of one-way functions, which is the minimal assumption for signature schemes, and (iii) they can be efficiently implemented. Basic hash-based signatures are for a single message, but have been extended for signing multiple messages. In this paper we design a Multi-message Signature Scheme (MSS) based on an existing One-Time Signature (OTS) that we refer to as KSN-OTS. KSN uses SWIFFT, an additive homomorphic lattice-based hash function family with provable one-wayness property, as the one-way-function and achieves a short signature. We prove security of our proposed signature scheme in a new strengthened security model (multi-target multi-function) of MSS, determine the system parameters for 512 bit classical (256 bit quantum) security, and compare parameter sizes of our scheme against XMSS, a widely studied hash based MSS that has been a candidate for NIST standardization of post-quantum signature scheme. We give an efficient implementation of our scheme using Intel SIMD (Single Instruction Multiple Data) instruction set. For this, we first implement SWIFFT computation using a SIMD parallelization of Number Theoretic Transform (NTT) of elements of the ring Zp[X]/(Xn+1), that can support different levels of parallelization. We compare efficiency of this implementation with a comparable (security level) implementation of XMSS and show its superior performance on a number of efficiency parameters.
Recently, NIST released the quantum cryptography standard, which includes three new encryption algorithms capable of effectively resisting attacks from quantum computers. Experts predict that quantum computers with the ability to break current encryption methods may emerge within the next decade. In particular, the advent of Shor’s algorithm [1] has rendered public-key encryption systems based on factoring and discrete logarithm problems vulnerable. Therefore, the release of the PQC (Post-Quantum Cryptography) standard is especially timely and significant. NIST encourages system administrators to begin integrating these standards into their systems immediately to ensure future security.Among these three new encryption algorithms, SLH-DSA (derived from SPHINCS+ [2]) is a stateless hash-based digital signature scheme. This innovative scheme is designed to provide robust security while maintaining efficiency. In the SLH-DSA signature scheme, the One-Time Signature (OTS) serves as its fundamental building block. This means that improving the OTS directly enhances the overall performance of the SLH-DSA scheme.Hash-based signature schemes are generally constructed using OTS schemes. The underlying OTS scheme plays a crucial role in determining the key size and signature size of hash-based signature schemes. We propose a novel signature scheme that allows partial key reuse while maintaining a minimum quantum security level of 128 bits. Compared to the popular Winternitz OTS scheme [3] [4] [5], our proposed signature scheme demonstrates superior performance in terms of key and signature sizes for the same number of signatures, while still preserving post-quantum security.
This paper proposes a new post-quantum signature scheme, Syrga2, based on hash functions. As known, existing post-quantum algorithms are classified based on their structures. The proposed Syrga2 scheme belongs to the class of multi-use signatures with state retention. A distinctive feature of state-retaining signatures is achieving a compromise between performance and signature size. This scheme enables the creation of a secure signature for r messages using a single pair of secret and public keys. The strength of signature algorithms based on hash functions depends on the properties of the hash function used in their structure. Additionally, for such algorithms, it is possible to specify the security level precisely. In the proposed scheme, the HBC-256 algorithm developed at the Institute of Information and Computational Technologies (IICT) is used as the hash function. The security of the HBC-256 algorithm has been thoroughly studied in other works by the authors. In contrast to the Syrga1 scheme presented in previous works by the authors, the Syrga2 scheme provides for the definition of different security levels determined by the parameter τ. This paper experimentally demonstrates the impossibility of breaking the proposed scheme using a chosen-plaintext attack. Additionally, the scheme’s performance is evaluated for signature creation, signing, and message verification.
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.
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.
Distributed systems are widely used in modern environments such as cloud platforms, Internet of Things (IoT) networks, smart grids, and blockchain-based systems. These platforms often require digital signatures to maintain trust between devices or users. When many signatures are shared at once, the size of the communication grows, and processing takes more time. This becomes a problem in applications where quick message verification is important. Classical digital signature schemes, such as Rivest-Shamir-Adleman (RSA) and Elliptic Curve Digital Signature Algorithm (ECDSA), are not safe against quantum attacks. Post-quantum cryptography offers better protection, but it often increases communication size and computation cost. This paper introduces a quantum-resistant model that supports signature aggregation and constant-time verification. The method is based on lattice-based techniques, using structures similar to CRYSTALS-Dilithium. By combining several signatures into a single aggregated form, the model reduces the time needed for verification and the overall communication overhead. The design is suitable for real-time applications, offering strong accuracy and faster message handling. Simulation results show that the proposed method performs better than recent approaches in multiple areas. The model achieves a low authentication time, high verification accuracy, reduced message size, and improved throughput. These benefits help meet the needs of distributed systems where speed, accuracy, and security must work together. The architecture is designed to be flexible for use in real-world deployments. Future directions include support for multi-party signing, adaptive quantum-safe policies, and integration with quantum co-processors. This research supports the development of secure and efficient communication frameworks that remain effective even in the presence of future quantum threats.
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.