With the standardization of post-quantum signature schemes such as Dilithium and Falcon, lattice-based ring signatures have become a promising tool for anonymous authentication and privacy-preserving encryption in big data environments. Specifically, the DualRing-LB scheme (CRYPTO’ 21), despite its short signatures and elegant structure, suffers from the large public key size, which dominates its communication cost and hinders scalability. There are two methods to reduce the public key size: the first is a compression technique, and the second is the bimodal distribution. The former discards the lower bits of the public key while the latter utilizes a smaller modulus. However, the unforgeability proof of DualRing-LB is incompatible with these methods because they lead to a rapid increase in the norm bound of the module short integer solution (or MSIS) problem, thereby significantly reducing security. In this paper, we follow the original security method of DualRing-LB and apply the trapdoor sampling technique to derive a tighter upper bound of MSIS problem, yielding a fixed security level independent of the ring size. The new proof result enables the use of both the compression technique and the bimodal distribution to enhance the communication efficiency of lattice-based DualRing schemes. Based on this result, we propose three practical lattice-based instantiations that reduce the public key size by 56%, 67%, 50%, compared to DualRing-LB, respectively, and achieve overall size reductions of at least 52%, 56%, 38%, respectively, across different ring sizes. Our results can contribute to lightweight, privacy-preserving cryptographic mechanisms for secure data sharing and authentication in large-scale distributed systems.
With the standardization of post-quantum signature schemes such as Dilithium and Falcon, lattice-based ring signatures have become a promising tool for anonymous authentication and privacy-preserving encryption in big data environments. Specifically, the DualRing-LB scheme (CRYPTO’ 21), despite its short signatures and elegant structure, suffers from the large public key size, which dominates its communication cost and hinders scalability. There are two methods to reduce the public key size: the first is a compression technique, and the second is the bimodal distribution. The former discards the lower bits of the public key while the latter utilizes a smaller modulus. However, the unforgeability proof of DualRing-LB is incompatible with these methods because they lead to a rapid increase in the norm bound of the module short integer solution (or MSIS) problem, thereby significantly reducing security. In this paper, we follow the original security method of DualRing-LB and apply the trapdoor sampling technique to derive a tighter upper bound of MSIS problem, yielding a fixed security level independent of the ring size. The new proof result enables the use of both the compression technique and the bimodal distribution to enhance the communication efficiency of lattice-based DualRing schemes. Based on this result, we propose three practical lattice-based instantiations that reduce the public key size by 56%, 67%, 50%, compared to DualRing-LB, respectively, and achieve overall size reductions of at least 52%, 56%, 38%, respectively, across different ring sizes. Our results can contribute to lightweight, privacy-preserving cryptographic mechanisms for secure data sharing and authentication in large-scale distributed systems.
Alongside the growth of technology is the increasing demand for security of data and communication channels. As attacking power grows, devices become smaller and data expands, the security needs to be stronger yet less resource-consuming than ever before. Public key cryptography (PKC) is used in the majority of today's communications systems. The security of public-key cryptographic schemes, such as RSA and elliptic curve cryptography (ECC), is based on underlying mathematical problems such as factoring large integers or solving the discrete log problem. However, the discovery of Shor's Algorithm in 1994 insinuates that these schemes will be insecure when a full-scale quantum computer is developed, as these problems will be solvable in polynomial time. Therefore attention has moved towards post-quantum, or quantum-safe, cryptography (QSC). In 2016, the National Institute of Standards and Technology (NIST) announced the beginning of their efforts to migrate to QSC, a standardisation process which has involved the cryptographic community worldwide. There are five main types of QSC being considered for standardisation; lattice-based, code-based, multivariate-based, hash-based and isogeny-based. Lattice-based cryptography (LBC) offers a promising alternative to today's classical approaches. Hard problems based on lattices are believed to be unsolvable, even by a quantum-computer, in a feasible amount of time. In 1995, Ajtai showed that the average case complexity of these problems is at least as hard as solving the problems in the worst case. Furthermore, lattice-based schemes are the only remaining contender in the NIST process to provide the important primitives of encryption, key encapsulation and digital signature schemes (DSSs). A well-recognised open problem surrounding quantum-safe cryptography is its increase in bandwidth and computational complexity in comparison to existing cryptography. However, in comparison to other quantum-safe schemes, LBC has been shown to be relatively efficient. In this thesis, novel software designs of lattice-based schemes are presented and shown to be competitive with existing PKC. Additionally, physical attacks are considered and countermeasures are incorporated into the designs. DSSs are required for authentication, integrity and non-repudiation of data. This thesis provides an evaluation of three leading signature schemes, BLISS-B, Dilithium and \textsc{Falcon}, which vary in terms of their key features, such as the sampling processes used, and the structure of the lattices. Physical attacks on the three schemes are considered and the effect on performance of appropriate attack countermeasures is evaluated. A novel fault attack on the NIST candidate \textsc{Falcon} is also proposed. A further advantage of LBC is the ability to support cryptographic primitives with extended capabilities to facilitate certificate management and compute on encrypted data. The complexity of today's technology advances mean applications require more sophisticated primitives, which contrastingly are required to run on even smaller platforms. This thesis presents novel quantum-safe advanced cryptographic schemes, specifically lattice-based identity-based encryption (IBE) and hierarchical identity-based encryption (HIBE). IBE removes the need for certificate management, as a user's public key depends on their public identity. IBE is currently used in vital applications such as emergency services communication and so the development of a high-performance quantum-safe alternative is imperative. This thesis also introduces the first scalable HIBE scheme based on lattices. The first HIBE scheme based on structured lattices, Latte, was proposed by the National Centre for Cyber Security (NCSC) in 2017. However, the public key and ciphertext sizes increased with each delegation and hence it was not feasible to scale the algorithm. Skinny Latte, proposed in this thesis, remedies this issue by fixing the dimension of the lattice, thereby making public key and ciphertext sizes constant. This research also shows that it is practical for real-world deployment. Overall, this thesis demonstrates that lattice-based cryptography is practical for real-world applications. It considers both theoretical and physical attacks, and presents novel designs of advanced quantum-safe cryptographic primitives, which have only yet been realised by lattices.
Conventional public-key cryptographic systems are increasingly threatened by advances in quantum computing, accelerating the need for robust post-quantum cryptographic solutions. Among these, Falcon, a compact lattice-based digital signature scheme, has emerged as a leading candidate in the NIST post-quantum standardization process due to its efficiency and theoretical security grounded in hard lattice problems. This work introduces Falcon-M, a modified version of the Falcon algorithm that significantly reduces implementation complexity. It does so by replacing Falcon’s intricate trapdoor-based key-generation mechanism with a simplified approach that utilizes randomized polynomial Gaussian sampling and fast Fourier transform (FFT) operations. Falcon-M incorporates SHA-512 hashing and discrete Gaussian sampling to preserve cryptographic soundness and statistical randomness while maintaining the core structure of Falcon’s signing and verification processes. We formally specify the Falcon-M algorithm, provide an updated pseudocode, and offer a comparative analysis with the original Falcon in terms of algorithmic complexity, security assumptions, and implementation overhead. Additionally, we present formal lemmas and theorems to ensure correctness and define theoretical bounds on forgery resistance. Although Falcon-M does not rely on a formal cryptographic trapdoor, we demonstrate that it achieves strong practical security based on assumptions related to the Short Integer Solution (SIS) problem. Falcon-M is thus well-suited for lightweight post-quantum applications, particularly in resource-constrained environments, such as embedded systems and Internet-of-Things (IoT) platforms.
Ring signature enables the members to sign anonymously without a manager, it has many online applications, such as e-voting, e-money, whistle blowing etc. As a promising post-quantum candidate, lattice-based cryptography attracts much attention recently. Several efficient lattice-based ring signatures have been naturally constructed from lattice basis delegation, but all of them have large verification key sizes. Our observation finds that a new concept called the split- small integer solution(SIS) problem introduced by Nguyen et al. at PKC’15 is excellent in reducing the public key sizes of lattice-based ring signature schemes from basis delegation. In this research, we first define an extended concept called the extended split-SIS problem, and then prove that the hardness of the extended problem is as hard as the approximating shortest independent vectors problem(SIVP) problem within certain polynomial factor. Moreover, we present an improved ring signature and prove that it is anonymous and unforgeable against the insider corruption. Finally, we give two other improved existing ring signature schemes from lattices. In the end, we show the comparison with the original scheme in terms of the verification key sizes. Our research data illustrate that the public key sizes of the proposed schemes are reduced significantly.
Although the current lattice-based ring signcryption scheme resists quantum attacks,it has large key storage and high encryption/decryption time.The linkable lattice ring signcryption scheme not only can protect signer anonymity,but also can determine whether two signatures are generated by the same signer.Thus,based on the compact Gaussian sampling algorithm and rejection sampling technique,the identity-based linkable ring signcryption scheme is constructed on the NTRU lattice.Firstly,the system master key is generated using the trapdoor generation algorithm on the NTRU lattice.Then private keys of ring members are obtained based on the compact Gaussian sampling algorithm.Finally,the user signature is generated using rejection sampling,and the key encapsulation mechanism encrypts the signature.Security proof in the random oracle model (ROM) that DRLWE and NTRU small integer solutions are difficult to solve ensures confidentiality,unforgeability,unconditional anonymity,and linkability.Performance analysis shows that compared to the lattice-based ring signcryption and linkable ring signature schemes on NTRU,the proposed scheme has a smaller public key and lower encryption/decryption cost,greatly improving efficiency.
With the rapid expansion of consumer electronics and the Internet of Things (IoT) ecosystem, ensuring secure communication in resource-constrained edge devices has become a critical challenge, especially under the threat of quantum attacks. Although lattice-based cryptographic schemes provide post-quantum security, they often suffer from large key storage and high computational overhead, limiting their applicability in edge environments. To address these challenges, we propose an identity-based linkable ring signcryption scheme constructed on the post quantum Lattice cryptography, tailored for edge-enabled IoT systems. The scheme employs a trapdoor generation algorithm to establish the master keys, utilizes compact Gaussian sampling to derive private keys for ring members, and integrates rejection sampling to generate user signatures with strong anonymity. Furthermore, a key encapsulation mechanism ensures identity protection during encryption. Security analysis under the Random Oracle Model (ROM) demonstrates the scheme's resistance to forgery and its linkability property. Performance evaluation shows that the proposed approach achieves smaller public keys, reduced encryption/decryption costs, and enhanced efficiency, making it well-suited for lightweight IoT and consumer electronics applications in the post-quantum era.
A myriad of conditional privacy-preserving signature (CPPS) schemes have emerged recently, aiming to secure communication data while preserving user privacy. However, many of these schemes, relying on classical mathematical problems and identity based cryptographic mechanism, suffer from key escrow vulnerabilities and are susceptible to quantum attacks. In this paper, we propose a lattice based conditional privacy-preserving certificateless signature scheme. By leveraging the ring small integer solution problem and the decisional compact knapsack problem, our scheme demonstrates robust resistance against quantum attacks with high asymptotic efficiency. We utilize certificateless signature to circumvent the key escrow issue inherent in identity based CPPS schemes. While ensuring conditional privacy preservation, we enhance the security and efficiency of the signature process through a rejection sampling algorithm based on the bimodal Gaussian distribution. Furthermore, our security analysis demonstrates resilience against type I and type II adversaries, meeting diverse security requirements such as traceability and unlinkability. Through a comparative analysis of communication traffic, we observe commendable efficiency in signature generation, making our scheme particularly suitable for wireless communication scenarios. Finally, we detail implementation strategies tailored for drone networks, enhancing the practicality and relevance of our contributions in wireless communication contexts.