One of the modern directions in the field of information security is post-quantum cryptography. Its purpose is to develop new quantum-resistant cryptographic algorithms. An important section of post-quantum cryptography is electronic digital signature algorithms. There are a number of different approaches to designing post-quantum signatures. One of the main approaches to designing post-quantum cryptographic digital signature algorithms is hash-based post-quantum digital signature schemes. Hash-based post-quantum digital signature schemes are one of the main types of post-quantum cryptographic digital signature algorithms. They are quite efficient and provably secure. Their reliable security has been established against both classical and quantum attacks. There are many types of digital signatures for solving various information security problems, such as group signatures, ring signatures, blind signatures, verifiably encrypted signatures, etc. This paper proposes a new cryptographic protocol of verifiably encrypted signature with possibility of verification after a specified time based on the post-quantum cryptographic algorithm of hash-based digital signature, TANBA-SPHINCS+. The protocol is an efficient combination of the postquantum digital signature algorithm TANBA-SPHINCS+, the cryptographic protocol providing data encryption for a specified time, ECTLC, and the verifiably encrypted signature scheme.
One of the modern directions in the field of information security is post-quantum cryptography. Its purpose is to develop new quantum-resistant cryptographic algorithms. An important section of post-quantum cryptography is electronic digital signature algorithms. There are a number of different approaches to designing post-quantum signatures. One of the main approaches to designing post-quantum cryptographic digital signature algorithms is hash-based post-quantum digital signature schemes. Hash-based post-quantum digital signature schemes are one of the main types of post-quantum cryptographic digital signature algorithms. They are quite efficient and provably secure. Their reliable security has been established against both classical and quantum attacks. There are many types of digital signatures for solving various information security problems, such as group signatures, ring signatures, blind signatures, verifiably encrypted signatures, etc. This paper proposes a new cryptographic protocol of verifiably encrypted signature with possibility of verification after a specified time based on the post-quantum cryptographic algorithm of hash-based digital signature, TANBA-SPHINCS+. The protocol is an efficient combination of the postquantum digital signature algorithm TANBA-SPHINCS+, the cryptographic protocol providing data encryption for a specified time, ECTLC, and the verifiably encrypted signature scheme.
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.
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
In order to meet the challenges brought by quantum computing, research on post-quantum cryptography has been carried out comprehensively. Among them, the most influential one is the post-quantum cryptography algorithm standardization project initiated by NIST. In July 2022, NIST announced that the Dilithium, Falcon, and SPHINCS+ algorithms were selected as candidate schemes for the standardization of post-quantum cryptographic digital signatures. The OQS project team is committed to promoting the transition of existing security protocols to standardized post-quantum algorithms and is currently the mainstream open-source post-quantum project. This paper improves the post-quantum hybrid digital signature scheme used by the OQS project team. Firstly, the hybrid digital signature scheme used in this project is studied, and it is found that there are security risks. Subsequently, an enhanced scheme is constructed and implemented using the hybrid algorithm combiner proposed by Nina Bindel et al., solving the security issues. The unforgeability and 2 -non-separability of the enhanced scheme are verified through formal analysis, and forward compatibility is achieved. The enhanced scheme shows obvious advantages in key generation efficiency and signature verification efficiency. Under some algorithms, the speed of signature verification of the improved scheme is 60 % of the original scheme. Meanwhile, the enhanced scheme also demonstrates stability in terms of time and storage overhead. Finally, the TLS1.3 protocol PSK mechanism is implemented using the enhanced scheme. This is the first implementation of post-quantum algorithm security protection in the PSK mechanism of the TLS protocol. This scheme can resist man-in-the-middle attacks while meeting the requirements of forward compatibility.
Information security is a fundamental and urgent issue in the digital transformation era. Cryptographic techniques and digital signatures have been applied to protect and authenticate relevant information. However, with the advent of quantum computers and quantum algorithms, classical cryptographic techniques have been in danger of collapsing because quantum computers can solve complex problems in polynomial time. Stemming from that risk, researchers worldwide have stepped up research on post-quantum algorithms to resist attack by quantum computers. In this review paper, we survey studies in recent years on post-quantum cryptography (PQC) and provide statistics on the number and content of publications, including a literature overview, detailed explanations of the most common methods so far, current implementation status, implementation comparisons, and discussion on future work. These studies focused on essential public cryptography techniques and digital signature schemes, and the US National Institute of Standards and Technology (NIST) launched a competition to select the best candidate for the expected standard. Recent studies have practically implemented the public key encryption/key encapsulation mechanism (PKE/KEM) and digital signature schemes on different hardware platforms and applied various optimization measures based on other criteria. Along with the increasing number of scientific publications, the recent trend of PQC research is increasingly evident and is the general trend in the cryptography industry. The movement opens up a promising avenue for researchers in public key cryptography and digital signatures, especially on algorithms selected by NIST.
Abstract It is viewed as revolutionary technology, offering incredible potential in terms of computing power within different scientific and industrial sectors. Quantum computers provide remarkable computing power; however, they also present significant security risks to existing public-key cryptography systems used to secure digital communication, online banking systems, government, medical applications, cloud computing systems, and IoT systems. Security of commonly used encryption schemes like RSA, DH, and ECC depends on mathematical problems that are impossible for classical computers to solve but can be easily resolved with the help of powerful enough quantum computers by using Shor’s algorithm. Furthermore, Grover’s algorithm makes exhaustive search attacks much faster, thus effectively lowering the security level of symmetric encryption schemes since it provides the speed-up for brute-force attacks. Post-Quantum Cryptography (PQC) turned out to be an effective and scalable method to protect digital data from attacks using quantum computing. In contrast to quantum cryptography, which requires a special quantum communication channel, PQC uses classical cryptographic algorithms that cannot be broken down by either classical or quantum computer due to certain mathematical problems. This research paper offers an extensive exploration of post-quantum cryptography through the analysis of the development of quantum computing, weaknesses of current cryptographic techniques, and mathematics behind quantum-resistant algorithms. Moreover, this paper explores the major classes of PQC techniques such as lattice-based, code-based, hash-based, multivariate, and isogeny-based cryptography and provides details about their security and application. Moreover, the report gives an overview of the NIST Post-Quantum Cryptography Standardization Project and analyzes recent standardizations of quantum-proof algorithms to be utilized in future digital infrastructures. Keywords: Post-Quantum Encryption, Quantum Security, Quantum-Proof Public-Key Cryptography, Lattice-Based Security Protocols, ML-KEM Key Encapsulation Mechanism, ML-DSA Digital Signature Algorithm, NIST Post-Quantum Cryptography, Contemporary Cybersecurity, Secure Communications, Cryptographic Algorithms.
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.