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.
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.
In this paper, we construct a lattice based (t, n) threshold multi-stage secret sharing (MSSS) scheme according to Ajtai's construction for one-way functions. In an MSSS scheme, the authorized subsets of participants can recover a subset of secrets at each stage while other secrets remain undisclosed. In this paper, each secret is a vector from a t-dimensional lattice and the basis of each lattice is kept private. A t-subset of n participants can recover the secret(s) using their assigned shares. Using a lattice based one-way function, even after some secrets are revealed, the computational security of the unrecovered secrets is provided against quantum computers. The scheme is multi-use in the sense that to share a new set of secrets, it is sufficient to renew some public information such that a new share distribution is no longer required. Furthermore, the scheme is verifiable meaning that the participants can verify the shares received from the dealer and the recovered secrets from the combiner, using public information.
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.
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.
This article deals with designing an efficient post-quantum lattice based encryption scheme that relies on the multi-authority Ciphertext-Policy Attribute-Based Encryption (CP-ABE). The security of the proposed scheme is based on the hardness of the ring learning with errors (RLWE) problem. The construction of the proposed scheme is done using the Shamir's threshold secret sharing along with the Lagrange interpolation during the key generation and decryption processes in order to achieve the segmentation and restoration of private keys. A comparative study with the existing state of art schemes has been performed to show the feasibility and efficiency of the proposed scheme. Furthermore, experiments on the proposed scheme have been conducted to illustrate the computational time required during the key generation, encryption and decryption processes.
Threshold public key encryption is a cryptographic primitive where a secret key of an organization is distributed among special members called decryption servers (insiders) and a certain threshold number of insiders must cooperate to decrypt any ciphertext. Threshold public key encryption with an additional randomized algorithm Tsplit is called resplittable threshold public key encryption (RTPKE). Cryptographic primitive RTPKE was introduced by Hanaoka et al. [Generic construction of chosen ciphertext secure proxy re-encryption, in CT-RSA, San Francisco, CA, USA, LNCS, O. Dunkelman, ed., Springer-Verlag, Heidelberg, 2012, pp. 349–364] in a generic construction of chosen ciphertext attack secure proxy re-encryption scheme. In MIST 2013 conference Singh et al. [Lattice based efficient threshold public key encryption scheme, J. Wirel. Mob. Netw. Ubiquitous Comput. Dependable Appl. (JoWUA) 4(4) (2013), pp. 93–107] presented lattice-based RTPKE scheme based on Regev's LWE [On lattices, learning with errors, random linear codes, and cryptography, in STOC, Baltimore, MD, USA, H.N. Gabow and R. Fagin, eds., ACM, University of Wales, Cardiff, 2005, pp. 84–93] assumption. In this paper, we propose lattice-based RTPKE scheme in the identity-based setting.
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.