Recent advances in quantum-computing technology have threatened the security of classical cryptographic algorithms. This initiated research on Post-Quantum Cryptography (PQC), and the National Institute of Standards and Technology (NIST) PQC standardization is in progress. Coping with the current situation in which the security of existing cryptographic algorithms is already in question and that of new cryptographic algorithms is not yet certain, there has been active research on hybrid schemes combining two algorithms such that the security of the combined scheme is based on both underlying algorithms. For digital signatures, a naive solution for a hybrid scheme is to simply concatenate a classical signature and a quantum-resistant signature. In this paper, however, we propose a compact hybrid signature construction method that combines two randomized signatures such that the size of the combined signature is shorter than that of naive concatenation. Our construction allows for selective verification, which provides backward compatibility and conformance with existing regulations. We demonstrate the feasibility of the proposed method by combining ECDSA P-256 and Falcon-512, which are representative classical and post-quantum signature schemes, respectively. We prove that the combined signature is existentially unforgeable against an adaptive chosen-message attack, even if one of the underlying signature schemes is completely broken and only the other one remains secure. Through experiments on a desktop PC and Raspberry Pi 3 Model B, we verify that the proposed method effectively reduces the combined signature size with negligible computational overhead. Our experimental results demonstrate the proposed method is also applicable to PQC-PQC combinations.
Recent advances in quantum-computing technology have threatened the security of classical cryptographic algorithms. This initiated research on Post-Quantum Cryptography (PQC), and the National Institute of Standards and Technology (NIST) PQC standardization is in progress. Coping with the current situation in which the security of existing cryptographic algorithms is already in question and that of new cryptographic algorithms is not yet certain, there has been active research on hybrid schemes combining two algorithms such that the security of the combined scheme is based on both underlying algorithms. For digital signatures, a naive solution for a hybrid scheme is to simply concatenate a classical signature and a quantum-resistant signature. In this paper, however, we propose a compact hybrid signature construction method that combines two randomized signatures such that the size of the combined signature is shorter than that of naive concatenation. Our construction allows for selective verification, which provides backward compatibility and conformance with existing regulations. We demonstrate the feasibility of the proposed method by combining ECDSA P-256 and Falcon-512, which are representative classical and post-quantum signature schemes, respectively. We prove that the combined signature is existentially unforgeable against an adaptive chosen-message attack, even if one of the underlying signature schemes is completely broken and only the other one remains secure. Through experiments on a desktop PC and Raspberry Pi 3 Model B, we verify that the proposed method effectively reduces the combined signature size with negligible computational overhead. Our experimental results demonstrate the proposed method is also applicable to PQC-PQC combinations.
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.
The accelerated advancements in quantum computing substantially threaten classical cryptographic systems, particularly those that rely on RSA, ECC, and other public key encryption methods. Particularly Shor's method shows how easily conventional cryptographic techniques might be broken; therefore quick development of quantum resistant substitutes is necessary. Rising as a potential answer with cryptographic algorithms meant to resist quantum attacks is post quantum cryptography (PQC). Nonetheless, performance trade-offs, compatibility problems, and the absence of standardized implementations make the shift to completely quantum-safe cryptographic systems very difficult. Hybrid PQC systems that combine conventional and quantum resistant cryptographic mechanisms have been suggested as a workable method for tackling these difficulties so guaranteeing security in the post quantum future. Emphasizing their security, performance, and practical implementations, this review article offers a thorough study of hybrid PQC methods. The resistance of many hybrid cryptographic models including lattice-based, code-based, and multivariate cryptographic techniques against quantum attacks is comprehensively investigated in this work methodologically, we review current PQC hybrid models, evaluate their computing efficiency, and examine security criteria grounded on recent research and standardizing initiatives like those under NIST. Our results show that hybrid PQC models create difficulties in terms of key management, computational overhead, and implementation complexity even if they improve security by reducing risks related with both conventional and quantum attacks. A comparative study shows among several hybrid systems the trade-offs in terms of encryption speed, key sizes, and resource use. Moreover showing the feasibility of PQC hybridizing in IoT, cloud computing, and block chain security are pragmatic uses of PQC hybridizing in which case appropriate protocols are needed for broad acceptance. At last, our work emphasizes the significant contribution hybrid PQC models provide in the transitional period producing a quantum secure environment. To enable basic integration into the present digital infrastructure, future research should focus on improving the efficiency of hybrid cryptosystems, optimizing key exchange mechanisms, and regulating standardization concerns. The findings of this study support the present discussion on post quantum security and provide data for academics and corporate leaders aiming for the next generation of cryptographic solutions. https://doi.org/10.5281/zenodo.17873992
Post Quantum Cryptography (sometimes referred to as a quantum-proof, quantum-safe or quantum-resistant) refers to cryptographic algorithms (usually public-key algorithms) that are thought to be secure against an attack by a quantum computer. PQC is all about preparing for the era of quantum computing by updating existing mathematical-based algorithms and standards. The cryptographic community is working on post-quantum cryptography in order to provide alternatives using hard mathematical problems that cannot be broken by quantum computers. A hybrid scheme is recommended to ease the transition into the post-quantum era. A hybrid scheme is a combination of a traditional and a post-quantum scheme. The resulting scheme is at least as secure as one of the schemes used. In hybrid key establishment, two independent key exchanges are performed one with a traditional scheme like ECDHE and one with a post-quantum scheme like NewHope [1]. In this paper, we propose possible best-fit hybrid digital signatures.
Since the security of post-quantum cryptography (PQC) algorithms is based on the hardness of mathematical problems, while the security of quantum key distribution (QKD) relies on the fundamental principles of quantum physics, each approach possesses distinct advantages and limitations that can complement one another. Consequently, recent studies have proposed hybrid schemes that combine QKD and PQC to establish a dual-layered security model. In response to this trend, this study proposes hybrid schemes that integrate QKD with the National Institute of Standards and Technology (NIST) standardized PQC algorithms. These hybrid schemes include two core components: a hybrid QKD-PQC key exchange protocol and a hybrid QKD-PQC digital signature scheme. For the hybrid key exchange protocol, this study combines Module-Lattice-based Key Encapsulation Mechanisms (ML-KEM) with QKD protocols, specifically BB84 and E91, to construct a secure key exchange protocol. In the design of the hybrid digital signature scheme, this study utilizes Module-Lattice-based Digital Signature Algorithms (ML-DSA) and Stateless Hash-based Digital Signature Algorithms (SLH-DSA) to generate signature reconstruction values. These values are verified using confirmation codes transmitted via the BB84 and E91 protocols. The proposed hybrid key exchange protocol is evaluated by examining the shared secret key it produces, particularly with respect to entropy and whether the output is independent and identically distributed (IID). Furthermore, the computation time and message lengths of the proposed hybrid schemes are evaluated.
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.
Hybrid cryptographic protocol was proposed by integrating quantum-safe algorithms (Kyber and Dilithium) together with a classical ECDSA-based signature scheme to verify secure proof on blockchain. Since quantum computers pose some loopholes in existing cryptography algorithms, the proposed mechanism addresses those vulnerabilities by maintaining compatibility with the existing infrastructure. The protocol integrates post-quantum key exchange to derive shared secrets securely. The shared secrets are used to enable hybrid encryption for efficient data protection. Additionally, the implementation uses a dual-signature approach, using quantum safe and classical signatures. These signatures are combined to ensure robust and tamper-resistant proof verification. The deployed solution validates its feasibility and efficiency for smart contract-based verification. The protocol maintains backward compatibility with existing systems while providing strong resistance to quantum attacks. Benchmark results demonstrate the system’s scalability and robustness under high transaction loads, with efficient gas usage for on-chain proof validation. This approach paves the way for post-quantum secure applications, including verifiable proofs, secure key exchanges, and decentralized systems resilient to quantum adversaries.