Forward-secure signatures guarantee that the signatures generated before the compromise of private key remain secure, and therefore offer an enhanced compromise-resiliency for real-life applications such as digital forensics, audit logs, and financial systems. However, the vast majority of state-of-the-art forward-secure signatures rely on conventional intractability assumptions and therefore are not secure against quantum computers. Hash-based signatures (HBS) (e.g., XMSS) can offer forward-secure post-quantum security. However, they are efficient only for a pre-defined number of messages to be signed and incur high key generation overhead, highly expensive signing, and large signature sizes for an increasing number of messages. It is an open problem to develop quantum-safe forward-secure signatures that are efficient and practical with a signing capability scalable to their security parameters. In this work, we propose a new series of post-quantum signatures that we call FROG (Forward-secuRe pOst-quantum siGnature). Unlike HBS alternatives, FROG can achieve highly computational efficient signatures with sub-linear key/signature sizes and (practically) unbounded signing capability. This is achieved by transforming suitable post-quantum signatures into forward-secure settings via MMM constructions. We investigated the transformation of prominent post-quantum secure signatures such as Dilithium, WOTS, and BLISS with MMM. Our experiments indicate that FROG outperforms XMSS for the vast majority (if not all for a large number of messages) of performance metrics. We also discuss one-time variants of these base signature schemes that can push the performance of FROG to the edge. Overall, FROG shows a better performance than the existing alternatives with forward-security and therefore is an ideal alternative for the standardization efforts for forward-secure post-quantum signatures.
Forward-secure signatures guarantee that the signatures generated before the compromise of private key remain secure, and therefore offer an enhanced compromise-resiliency for real-life applications such as digital forensics, audit logs, and financial systems. However, the vast majority of state-of-the-art forward-secure signatures rely on conventional intractability assumptions and therefore are not secure against quantum computers. Hash-based signatures (HBS) (e.g., XMSS) can offer forward-secure post-quantum security. However, they are efficient only for a pre-defined number of messages to be signed and incur high key generation overhead, highly expensive signing, and large signature sizes for an increasing number of messages. It is an open problem to develop quantum-safe forward-secure signatures that are efficient and practical with a signing capability scalable to their security parameters. In this work, we propose a new series of post-quantum signatures that we call FROG (Forward-secuRe pOst-quantum siGnature). Unlike HBS alternatives, FROG can achieve highly computational efficient signatures with sub-linear key/signature sizes and (practically) unbounded signing capability. This is achieved by transforming suitable post-quantum signatures into forward-secure settings via MMM constructions. We investigated the transformation of prominent post-quantum secure signatures such as Dilithium, WOTS, and BLISS with MMM. Our experiments indicate that FROG outperforms XMSS for the vast majority (if not all for a large number of messages) of performance metrics. We also discuss one-time variants of these base signature schemes that can push the performance of FROG to the edge. Overall, FROG shows a better performance than the existing alternatives with forward-security and therefore is an ideal alternative for the standardization efforts for forward-secure post-quantum signatures.
One emerging threat to Public Key Infrastructures is the possible development of large-scale quantum computers, which would be able to break the public-key cryptosystems used today. Several possibly post-quantum secure cryptographic algorithms have been proposed but so far they have not been used in many practical settings. The purpose of this thesis was to find post-quantum digital signature algorithms that might be suitable for use in Public Key Infrastructures today. To answer the research question, an extensive literature study was conducted where relevant algorithms were surveyed. Algorithms with high-grade implementations in different cryptographic libraries were benchmarked for performance. Hash-based XMSS and SPHINCS, multivariate-based Rainbow and lattice-based BLISS-B were benchmarked and the results showed that BLISS-B offered the best performance, on par with RSA and ECDSA. All the algorithms did however have relatively large signature sizes and/or key sizes. Support for post-quantum digital signature algorithms in Public Key Infrastructure products could easily be achieved since many algorithms are implemented in cryptographic libraries. The algorithms that could be recommended for use today were SPHINCS for high-security applications and possibly BLISS-B for lower security applications requiring higher efficiency. The biggest obstacles to widespread deployment of post-quantum algorithms was deemed to be lack of standardisation and either inefficient operations compared to classical algorithms, uncertain security levels, or both.
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.
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.
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.
The Internet of Things (IoT) is gaining ground as a pervasive presence around us by enabling miniaturized “things” with computation and communication capabilities to collect, process, analyze, and interpret information. Consequently, trustworthy data act as fuel for applications that rely on the data generated by these things, for critical decision-making processes, data debugging, risk assessment, forensic analysis, and performance tuning. Currently, secure and reliable data communication in IoT is based on public-key cryptosystems such as the elliptic curve cryptosystem (ECC). Nevertheless, the reliance on the security of de-facto cryptographic primitives is at risk of being broken by the impending quantum computers. Therefore, the transition from classical primitives to quantum-safe primitives is indispensable to ensure the overall security of data en route. In this article, we investigate applications of one of the postquantum signatures called hash-based signature (HBS) schemes for the security of IoT devices in the quantum era. We give a succinct overview of the evolution of HBS schemes with an emphasis on their construction parameters and associated strengths and weaknesses. Then, we outline the striking features of HBS schemes and their significance for IoT security in the quantum era. We also investigate the optimal selection of HBS in the IoT networks with respect to their performance-constrained requirements, resource-constrained nature, and design optimization objectives. In addition to ongoing standardization efforts, we also highlight current and future research and deployment challenges along with possible solutions. Finally, we outline the essential measures and recommendations that must be adopted by the IoT ecosystem while preparing for the quantum world.
Signature schemes, proposed in 1976 by Diffie and Hellman, have become ubiquitous across modern communications. They allow for the exchange of messages from one sender to multiple recipients, with the guarantees that messages cannot be forged or tampered with and that messages also can be forwarded from one recipient to another without compromising their validity. Signatures are different from, but no less important than encryption, which ensures the privacy of a message. Commonly used signature protocols—signatures based on the Rivest–Adleman–Shamir (RSA) algorithm, the digital signature algorithm (DSA), and the elliptic curve digital signature algorithm (ECDSA)—are only computationally secure, similar to public key encryption methods. In fact, since these rely on the difficulty of finding discrete logarithms or factoring large primes, it is known that they will become completely insecure with the emergence of quantum computers. We may therefore see a shift towards signature protocols that will remain secure even in a post-quantum world. Ideally, such schemes would provide unconditional or information-theoretic security. In this paper, we aim to provide an accessible and comprehensive review of existing unconditionally securesecure signature schemes for signing classical messages, with a focus on unconditionally secure quantum signature schemes.