Certificateless cryptography solves the certificate management problem in public-key cryptography and the key-escrow problem in identity-based cryptography. Xie et al. proposed a certificateless signature scheme using NTRU lattices. They proved that their scheme was existential unforgeable for Type I and Type II adversaries under the intractability of the Small Integer Solution (SIS) problem on NTRU lattices in the random oracle model. Subsequently, Hung et al. proposed a revocable certificateless signature scheme on NTRU lattices that gave a revocation method via public channels to revoke illegal or compromised users. They also proved that their scheme was existential unforgeable for Type I, Type II and Type III adversaries under the intractability of the SIS problem. Recently, Wang et al. proposed a certificateless aggregate signature scheme from bilinear pairings and Rezaeibagha et al. proposed a new lightweight certificateless scheme for Industrial Internet of Things from bilinear pairings. The security of their schemes was proven for Type I and Type II adversaries under the intractability of some mathematical problems. In this paper, we show that the two schemes on NTRU lattices are insecure against Type I or Type II adversaries. We also point out invalidity of Wang et al.'s scheme and vulnerability of Rezaeibagha et al.'s scheme against Type I attacks. We then suggest some improvements to prevent our attacks.
Certificateless cryptography solves the certificate management problem in public-key cryptography and the key-escrow problem in identity-based cryptography. Xie et al. proposed a certificateless signature scheme using NTRU lattices. They proved that their scheme was existential unforgeable for Type I and Type II adversaries under the intractability of the Small Integer Solution (SIS) problem on NTRU lattices in the random oracle model. Subsequently, Hung et al. proposed a revocable certificateless signature scheme on NTRU lattices that gave a revocation method via public channels to revoke illegal or compromised users. They also proved that their scheme was existential unforgeable for Type I, Type II and Type III adversaries under the intractability of the SIS problem. Recently, Wang et al. proposed a certificateless aggregate signature scheme from bilinear pairings and Rezaeibagha et al. proposed a new lightweight certificateless scheme for Industrial Internet of Things from bilinear pairings. The security of their schemes was proven for Type I and Type II adversaries under the intractability of some mathematical problems. In this paper, we show that the two schemes on NTRU lattices are insecure against Type I or Type II adversaries. We also point out invalidity of Wang et al.'s scheme and vulnerability of Rezaeibagha et al.'s scheme against Type I attacks. We then suggest some improvements to prevent our attacks.
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.
The enormous benefits of Internet of Things (IoT) technology have driven its deployment in various applications. Additionally, the development of quantum computers has directed attention towards lattice-based cryptography. Consequently, the computational capabilities of quantum computers pose a threat to the security of the existing IoT signature mechanisms. Quantum computers are proficient at unraveling the complexity bound of computationally hard problems like the integer factorization problem (IFP) and the discrete logarithm problem (DLP). As a result, security is an essential requirement for the IoT communication network against quantum attacks. The amalgamation of certificateless public key cryptosystems (CL-PKC) and lattice-based cryptography (LBC) is one of the solution for alleviating these security menaces. Lucidly, CL-PKC prevents key escrow issues and key management problems; LBC prevents quantum attacks. The Shortest Integer Solution (SIS) problem, which the NTRU lattices offer, serves as the basis for this paper’s introduction of a certificateless signature mechanism for IoT environments. By adopting the Random Oracle Model, we demonstrated the security of the suggested mechanism against Type 1 and Type 2 attackers. Furthermore, security analysis and performance evaluation demonstrate robust communication, as evidenced by metrics such as the computational cost of CL-Sign and CL-Verify phases at 536μs, 376.81μs and communication cost of KGC at 418 bits, CL-Sign at 532 bits and CL-Verify at 446 bits. Also, we calculate the cost of single-message signature generation and verification on an IoT device. These results show that the suggested mechanism’s security and computational efficiency are more reliable, and efficient than other relevant competing frameworks.
The certificateless cryptography solves the certificate management and key escrow problems in the Internet of Things. However, these schemes are no longer safe in the quantum environment. Lattice cryptography has become the main method to solve quantum security. At present, only a few lattice-based certificateless signature schemes have been proposed and the use of the trapdoor function limits the efficiency of the lattice cryptography, and the security of these schemes can only reach existential unforgeability. We construct a lattice-based certificateless signature scheme based on Lyubashevsky's signature scheme. The security of our scheme can reach strong unforgeability and the computational efficiency of our scheme is lower than the previous schemes.
Certificateless public key cryptography has appealing features,namely it does not require the use of certificates and does not have a private key escrow feature.This paper describes a certificateless key agreement protocol based on bilinear pairings.The identity authentication in the protocol depends on a digital signature scheme.This paper proves the security of the signature scheme.The results show that in the random oracle model with the discrete logarithm assumption,the signature scheme resists existential forgeries against adaptive chosen-message attacks.The results farther show that the protocol preserves the desired security properties,including known-key security,unknown key-share resilience,perfect forward secrecy,key-compromise impersonation resilience and leakage of ephemeral private key resilience.The protocol requires much lower computation overhead than related protocols,since it uses fewer bilinear pairing operations and no modular exponentiation.
Although most existing linkable ring signature schemes on lattice can effectively resist quantum attacks, they still have the disadvantages of excessive time and storage overhead. This paper constructs an identity-based linkable ring signature (LRS) scheme over NTRU lattice by employing the technologies of trapdoor generation and rejection sampling. The security of this scheme relies on the small integer solution (SIS) problem on NTRU lattice. We prove that this scheme has unconditional anonymity, unforgeability, and linkability under the random oracle model (ROM). Through the performance analysis, this scheme has a shorter size of public/private keys, and when the number of ring members is small (such as N ≤ 8 ), this scheme has a shorter signature size compared with other existing latest lattice-based LRS schemes. The computational efficiency of signature has also been further improved since it only involves multiplication in the polynomial ring and modular operations of small integers. Finally, we implemented our scheme and other similar schemes, and it is shown that the time for the signature generation and verification of this scheme decreases roughly by 44.951% and 33.503%, respectively.
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.