With the rapid development of quantum computing technology, traditional collaborative signature schemes based on RSA and elliptic curve cryptography face significant security challenges. This paper proposes a lattice-based certificateless collaborative signature scheme (L-CCS) to address the security and efficiency requirements of multi-party collaboration in intelligent computing and network systems. By leveraging lattice problems such as the Small Integer Solution and Learning With Errors, our scheme ensures post-quantum security. The L-CCS eliminates the need for a trusted Key Generation Center and a dedicated aggregator, enhancing decentralization and system robustness. Our construction achieves existential unforgeability under adaptive chosen-message attacks in the random oracle model. Furthermore, we provide a practical implementation optimized for large-scale data sharing, demonstrating sublinear scalability in signature size and computation time.
With the rapid development of quantum computing technology, traditional collaborative signature schemes based on RSA and elliptic curve cryptography face significant security challenges. This paper proposes a lattice-based certificateless collaborative signature scheme (L-CCS) to address the security and efficiency requirements of multi-party collaboration in intelligent computing and network systems. By leveraging lattice problems such as the Small Integer Solution and Learning With Errors, our scheme ensures post-quantum security. The L-CCS eliminates the need for a trusted Key Generation Center and a dedicated aggregator, enhancing decentralization and system robustness. Our construction achieves existential unforgeability under adaptive chosen-message attacks in the random oracle model. Furthermore, we provide a practical implementation optimized for large-scale data sharing, demonstrating sublinear scalability in signature size and computation time.
Certificateless signcryption can simultaneously provide certificateless signature and encryption. In recent years, many certificateless signcryption schemes have been proposed. However, these schemes are based on traditional mathematical theory and not have the ability of resisting the quantum computing attacks. Up to now, lattice-based certificateless signature or encryption schemes have been proposed; however, these schemes only have one function and cannot fulfill two functions of certificateless signature and encryption at the same time. In consideration of this reason, in this article, a certificateless signcryption scheme from lattice (L-CLSS) is constructed. L-CLSS has three advantages. First, in the random oracle model, it is provably indistinguishable against adaptive ciphertext-chosen attacks under the intractability of the learning with errors (LWE) problem and unforgeable against adaptive message-chosen attacks under the hardness of small integer solution (SIS) problem. Second, comparison with the cryptographic algorithms under the difficulty of large integer decomposition, L-CLSS can resist the quantum computing attacks. Third, L-CLSS has higher computation efficiency and a lower communication cost than the existing schemes.
Certificateless signatures (CLS) are noticeable because they may resolve the key escrow problem in ID-based signatures and break away the management problem regarding certificate in conventional signatures. However, the security of the mostly previous CLS schemes relies on the difficulty of solving discrete logarithm or large integer factorization problems. These two problems would be solved by quantum computers in the future so that the signature schemes based on them will also become insecure. For post-quantum cryptography, lattice-based cryptography is significant due to its efficiency and security. However, no study on addressing the revocation problem in the existing lattice-based CLS schemes is presented. In this paper, we focus on the revocation issue and present the first revocable CLS (RCLS) scheme over lattices. Based on the short integer solution (SIS) assumption over lattices, the proposed lattice-based RCLS scheme is shown to be existential unforgeability against adaptive chosen message attacks. By performance analysis and comparisons, the proposed lattice-based RCLS scheme is better than the previously proposed lattice-based CLS scheme, in terms of private key size, signature length and the revocation mechanism.
With the rapid development of electronic information technology, digital signature has become an indispensable part of our lives. Traditional public key certificate cryptosystems cannot overcome the limitations of certificate management. Identity-based cryptosystems can avoid the certificate management issues. The development of quantum computers has brought serious challenges to traditional cryptography. Post-quantum cryptography research is imperative. At present, almost all post-quantum identity-based signature (IBS) schemes are constructed using Gaussian sampling or trapdoor technologies. However, these two technologies have a great impact on computational efficiency. To overcome this problem, we construct an IBS scheme on lattices by employing Lyubashevsky’s signature scheme. Based on the shortest vector problem on lattices, our scheme does not use Gaussian sampling or trapdoor technologies. In the random oracle model, it is proved that our scheme is strongly unforgeable against adaptive chosen messages and identity attacks. The security level of our scheme is strongly unforgeable, which is a higher level than the existential unforgeability of other schemes. Compared with other efficient schemes, our scheme has advantages in computation complexity and security.
Electronic voting (e-voting) systems have gained prominence as secure, efficient, and scalable alternatives to traditional paper-based voting. However, the advent of quantum computing poses a serious threat to classical cryptographic techniques like Rivest–Shamir–Adleman and elliptic curve cryptography, which are commonly used in securing e-voting platforms. This creates an urgent need for post-quantum cryptographic solutions that can preserve the core security properties of confidentiality, integrity, verifiability, and unforgeability under quantum attacks. This chapter addresses these challenges by introducing post-quantum lattice-based signcryption scheme for electronic voting (PQLS-EVote), a novel signcryption scheme based on lattice-based cryptography. The scheme leverages the hardness of the learning with errors (LWE) and short integer solution (SIS) problems to achieve post-quantum security. A major novelty of PQLS-EVote lies in its use of rejection sampling to optimize ring signature generation, minimizing computational overhead. Additionally, a ( https://www.w3.org/1998/Math/MathML" display="inline"> t , n ) threshold mechanism is incorporated to ensure decentralized trust and fault tolerance. Security is formally analyzed in the random oracle model. Performance evaluation and comparison with existing schemes confirm that PQLS-EVote achieves strong security guarantees, improved efficiency, and scalability, making it a promising candidate for secure quantum-resistant e-voting systems.
The advancement of quantum computing threatens classical cryptographic systems, such as RSA and ECDSA, which can be broken by quantum algorithms like Shor's algorithm. This necessitates the development of post-quantum cryptographic systems resistant to quantum attacks. Lattice-based cryptography, particularly the Learning with Errors (LWE) and Learning with Rounding (LWR) problems, is a promising approach. This paper presents a threshold signature scheme based on the Kryzhovnik signature, an adaptation of the Crystals-Dilithium scheme for LWR. The scheme leverages the hardness of the Module Learning with Rounding (MLWR) and Module Short Integer Solution (MSIS) problems to ensure post-quantum security. It allows a group of N participants to collaboratively generate a signature, requiring at least t participants to create a valid signature, preventing forgery by individual participants. The scheme uses Shamir's Secret Sharing, ensuring the shared secret is never stored explicitly. Key advantages include efficiency, security, and threshold-based access control, making it suitable for IoT and other resource-constrained environments.
Proxy re-signature enables transitive authentication of digital identities across different domains and has significant application value in areas such as digital rights management, cross-domain certificate validation, and distributed system access control. However, most existing proxy re-signature schemes, which are predominantly based on traditional public-key cryptosystems, face security vulnerabilities and certificate management bottlenecks. While identity-based schemes alleviate some issues, they introduce key escrow concerns. Certificateless schemes effectively resolve both certificate management and key escrow problems but remain vulnerable to quantum computing threats. To address these limitations, this paper constructs an efficient post-quantum certificateless proxy re-signature scheme based on algebraic lattices. Building upon algebraic lattice theory and leveraging the Dilithium algorithm, our scheme innovatively employs a lattice basis reduction-assisted parameter selection strategy to mitigate the potential algebraic attack vectors inherent in the NTRU lattice structure. This ensures the security and integrity of multi-party communication in quantum-threat environments. Furthermore, the scheme significantly reduces computational overhead and optimizes signature storage complexity through structured compression techniques, facilitating deployment on resource-constrained devices like Internet of Things (IoT) terminals. We formally prove the unforgeability of the scheme under the adaptive chosen-message attack model, with its security reducible to the hardness of the corresponding underlying lattice problems.