Distributed cloud computing provides an opportunity for users, companies, and public organisations to compute with low cost and high efficiency. Meanwhile, information in local computers is now transferred to distributed cloud platforms, where users' information is much easier to obtain and be tampered with by malicious participants. Fortunately, threshold cryptographical schemes can improve robustness against malicious participants in group. However, threshold cryptographical schemes against quantum attack are the main barrier of cloud security in a 'post-quantum' world. This paper focuses on the research of threshold cryptography against quantum attack. We present a more efficient lattice-based secret sharing algorithm (LB-SSA), where each sharer can independently generate his public key and secret key without interactivity. We also present two applications of LB-SSA: a multi-authority identity-based encryption (MA-IBE) scheme from lattices and a threshold decryption scheme from lattices. To the best of our knowledge, our MA-IBE is the first lattice-based IBE scheme under multiple authorities.
Distributed cloud computing provides an opportunity for users, companies, and public organisations to compute with low cost and high efficiency. Meanwhile, information in local computers is now transferred to distributed cloud platforms, where users' information is much easier to obtain and be tampered with by malicious participants. Fortunately, threshold cryptographical schemes can improve robustness against malicious participants in group. However, threshold cryptographical schemes against quantum attack are the main barrier of cloud security in a 'post-quantum' world. This paper focuses on the research of threshold cryptography against quantum attack. We present a more efficient lattice-based secret sharing algorithm (LB-SSA), where each sharer can independently generate his public key and secret key without interactivity. We also present two applications of LB-SSA: a multi-authority identity-based encryption (MA-IBE) scheme from lattices and a threshold decryption scheme from lattices. To the best of our knowledge, our MA-IBE is the first lattice-based IBE scheme under multiple authorities.
As the most popular cryptographic scheme in the post-quantum field, lattices have received extensive attention and research. Not only do they provide quantum-resistant security, they also enable the construction of complex applications. Currently, lattice cryptography schemes based on different difficult problems have been applied in different fields. The threshold secret sharing (TSS) scheme is an important field of cryptography and has important application value and development prospects in key protection, secure multi-party computation, privacy protection, etc. However, with the rapid development of quantum computing, many existing cryptography-underlying technologies are facing huge difficulties and challenges. Therefore, post-quantum TSS has important research significance and value for the future development of cryptography. In this paper, we summarize the existing secret sharing schemes based on lattice-hard problems and the relevant applications of these schemes in the post-quantum realm. We classify existing lattice-based TSS according to different functions and introduce typical solutions. To the best of our knowledge, this is the first review paper on lattice-based TSS schemes.
In this paper, we propose a threshold increasing algorithm for a (t; n) latticebased Threshold Multi-Stage Secret Sharing (TMSSS) scheme. To realize the changeability feature, we use the zero addition protocol to construct a new (t0; n) TMSSS scheme. Therefore, the new scheme enjoys the signi cant feature of threshold changeability along with the inherited features of being multi-stage, multi-use, and veri able derived fromour previously proposed lattice-based TMSSS scheme. Furthermore, we use the improved TMSSS scheme to propose a threshold decryption algorithm for the Learning With Error (LWE) based public key encryption scheme based on the study of Lindner and Peikert. For threshold decryption, each authorized subset of participants decrypts the ciphertext partially and sends the result to the combiner. The combiner can decrypt the ciphertext using the partial decryptions. The security of both schemes is based on hardness of lattice problems, i.e. LWE and Inhomogeneous Small Integer Solution (ISIS) problems, which are believed to resist against the quantum algorithms. The proposed schemes are eficient, especially on the participants' side, making them suitable for the applications in which the participants have limited processing capacities.
Public-key cryptography is an indispensable component used in almost all of our present-day digital infrastructure. However, most if not all of it is predominantly built upon hardness guarantees of number theoretic problems that can be broken by large-scale quantum computers in the future. Sensing the imminent threat from continued advances in quantum computing, NIST has recently initiated a global-level standardization process for quantum resistant public-key cryptographic primitives such as public-key encryption, digital signatures, and key encapsulation mechanisms. While the process received proposals from various categories of post-quantum cryptography, lattice-based cryptography features most prominently among all the submissions. Lattice-based cryptography offers a very attractive alternative to traditional public-key cryptography mainly due to the variety of lattice-based schemes offering varying flavors of security and efficiency guarantees. In this article, we survey the evolution of lattice-based key-sharing schemes (public-key encryption and key encapsulation schemes) and cover various aspects ranging from theoretical security guarantees, general algorithmic frameworks, practical implementation aspects, and physical attack security, with special focus on lattice-based key-sharing schemes competing in the NIST’s standardization process.
In public-key encryption, a long-term private key can be an easy target for hacking and deserves extra protection. One way to enhance its security is to share the long-term private key among multiple (say n) distributed servers; any threshold number (t, t ≤ n) of these servers are needed to collectively use the shared private key without reconstructing it. As a result, an attacker who has compromised less than t servers will still not be able to reconstruct the shared private key. In this thesis, we studied threshold decryption schemes for lattice-based public-key en- cryption, which is one of the most promising post-quantum public-key encryption schemes. We developed threshold decryption schemes for Stinson’s, the standard NTRU, and NTRU with Ring Learning with Errors (R-LWE) cryptosystems. Prototype implementations were developed for validating the functionality of these threshold decryption schemes. Our de- signs achieve heuristic security, and its security is supported by mechanisms similar to that of R-LWE.
Public-key cryptography is an indispensable component used in almost all of our present-day digital infrastructure. However, most if not all of it is predominantly built upon hardness guarantees of number theoretic problems that can be broken by large-scale quantum computers in the future. Sensing the imminent threat from continued advances in quantum computing, NIST has recently initiated a global-level standardization process for quantum resistant public-key cryptographic primitives such as public-key encryption, digital signatures, and key encapsulation mechanisms. While the process received proposals from various categories of post-quantum cryptography, lattice-based cryptography features most prominently among all the submissions. Lattice-based cryptography offers a very attractive alternative to traditional public-key cryptography mainly due to the variety of lattice-based schemes offering varying flavors of security and efficiency guarantees. In this article, we survey the evolution of lattice-based key-sharing schemes (public-key encryption and key encapsulation schemes) and cover various aspects ranging from theoretical security guarantees, general algorithmic frameworks, practical implementation aspects, and physical attack security, with special focus on lattice-based key-sharing schemes competing in the NIST’s standardization process.
The rise of cloud computing has transformed data storage and processing but introduced new vulnerabilities, especially with the impending threat of quantum computing. Traditional cryptographic methods, though currently effective, are at risk of being compromised by quantum attacks. This research aims to develop a quantum-resistant security framework for cloud environments, combining lattice-based cryptography with Quantum Key Distribution (QKD) protocols, particularly the E91 protocol, for secure key management. The framework also incorporates quantum authentication protocols to enhance user identity verification, protecting against unauthorized access and tampering. The proposed solution balances robust security with practical implementation, ensuring scalability and efficiency in real-world cloud environments. Performance evaluations indicate an encryption time of approximately 30 milliseconds, outperforming existing methods such as RSA and DES. This research contributes to the development of future-proof cryptographic standards, addressing both current security challenges and emerging quantum computing threats. By leveraging quantum mechanics, the framework strengthens cloud-based data protection, providing a resilient solution against evolving cyber risks. The results hold significant promise for advancing cloud security, laying the groundwork for next-generation encryption techniques that can withstand the threats posed by quantum computing.