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Computation

Syrga2: Post-Quantum Hash-Based Signature Scheme

Kunbolat T. Algazy, Kairat Sakan, Saule Nyssanbayeva, Oleg Lizunov

Published Jun 15, 2024• 6 citations
Publisher

Abstract

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.

DOI
10.3390/computation12060125

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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 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.
We are surrounded by many smart applications that make human life efficient. The general concept of IoT applications involves communication between devices. To make our smart environment secure, authentication is the most important requirement to be achieved to avoid unwanted attacks. Cryptographic schemes used currently in such IoT devices are public-key cryptographic primitives that are vulnerable to future quantum attacks. Quantum approaches derived by Shor and Grover will break the public-key primitives with square root and cube root speedups. Hence, there is a need to develop a successful and efficient signature scheme to authenticate such devices. Post-quantum cryptographic approaches are based on hard mathematical problems which are difficult to break by future attacks. Amongst all these post-quantum signature approaches, hash-based post-quantum signatures incorporate existing hash algorithms to achieve the required security level. This paper summarises stateful hash-based post-quantum signature schemes that can be implemented on constrained devices for IoT applications.
We are surrounded by many smart applications that make human life efficient. The general concept of IoT applications involves communication between devices. To make our smart environment secure, authentication is the most important requirement to be achieved to avoid unwanted attacks. Cryptographic schemes used currently in such IoT devices are public-key cryptographic primitives that are vulnerable to future quantum attacks. Quantum approaches derived by Shor and Grover will break the public-key primitives with square root and cube root speedups. Hence, there is a need to develop a successful and efficient signature scheme to authenticate such devices. Post-quantum cryptographic approaches are based on hard mathematical problems which are difficult to break by future attacks. Amongst all these post-quantum signature approaches, hash-based post-quantum signatures incorporate existing hash algorithms to achieve the required security level. This paper summarises stateful hash-based post-quantum signature schemes that can be implemented on constrained devices for IoT applications.
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.
Basic security requirements such as confidentiality, user authentication and data integrity, are assured by using public-key cryptography (PKC). In particular, public-key signature schemes provide non-repudiation, integrity of transmitted messages and authentication. The presence of a large scale quantum computer would be a real threat to break the most widely used public-key cryptographic algorithms in practice, RSA, DSA, ECDSA signature schemes and Diffie-Hellman key exchange. Thus, all security protocols and applications where these public-key cryptographic algorithms are used are vulnerable to quantum-computer attacks. There are five directions of cryptographic primitives secure against a quantum computer: multivariate quadratic equation-based, hash-based, lattice-based, code-based and supersingular isogeny-based cryptography. These primitives could serve as replacements for current public-key cryptographic algorithms to prepare for post-quantum era. It is important to prioritize the fields to be replaced by post-quantum cryptography (PQC) since it is hard to replace the currently deployed PKC with PQC at the same time. The fields directly connected to human life such as vehicular communications should be the primary targets of PQC applications. This survey is dedicated to providing guidelines for adapting the most suitable post-quantum candidates to the requirements of various devices and suggesting efficient and physically secure implementations that can be built into existing embedded applications as easily as traditional PKC. It focuses on the five types of post-quantum signature schemes and investigates their theoretical backgrounds, structures, state-of-the-art constructions and implementation aspects on various platforms raging from resource constrained IoT devices to powerful servers connected to the devices for secure communications in post-quantum era. It offers appropriate solutions to find tradeoffs between key sizes, signature lengths, performance, and security for practical applications.