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Lattice-based Threshold Secret Sharing Algorithm

ZHANG Hongjun,LIU Ke,MOU Zhansheng

Published Jun 1, 2016• 0 citations
Publisher

Abstract

The secret sharing algorithm based on the traditional mathematical assumption is difficult to resist the attack of the quantum algorithm.Therefore,a lattice-based threshold secret sharing algorithm is proposed.The basic process of the secret sharing strategy is analyzed,which is divided into public key generation,share generation and secret reconstruction.The threshold secret sharing algorithm based on lattice is discussed.The algorithm can be reduced to the closest vector problem,and its security is analyzed.Calculation results prove that the algorithm is correct and safe.

DOI
10.3969/j.issn.1000-3428.2016.06.024

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The secret sharing algorithm based on the traditional mathematical assumption is difficult to resist the attack of the quantum algorithm.Therefore,a lattice-based threshold secret sharing algorithm is proposed.The basic process of the secret sharing strategy is analyzed,which is divided into public key generation,share generation and secret reconstruction.The threshold secret sharing algorithm based on lattice is discussed.The algorithm can be reduced to the closest vector problem,and its security is analyzed.Calculation results prove that the algorithm is correct and safe.
In this paper, we introduce a method of threshold secret sharing scheme in which secret reconstruction is based on celebrated Babai lattice algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there is no quantum threats to these channels. One solution for this problem can be utilization of lattice cryptosystems for these channels which requires designing lattice based secret sharing schemes. We indicate that our scheme is asymptotically correct. Moreover, we analyze the security of our scheme by giving a quantitative proof of security from the view point of information theory.
In this paper, we introduce a method of threshold secret sharing scheme (TSSS) in which secret reconstruction is based on Babai's nearest plane algorithm. In order to supply secure public channels for transmitting shares to parties, we need to ensure that there are no quantum threats to these channels. A solution to this problem can be utilization of lattice-based cryptosystems for these channels which requires designing lattice-based TSSSs. We investigate the effect of lattice dimension on the security and correctness of the proposed scheme. Moreover, we prove that for a fixed lattice dimension the proposed scheme is asymptotically correct. We also give a quantitative proof of security from information theoretic viewpoint.
In this paper, a variant of (t, n) threshold secret sharing scheme is realized using a lattice model. Due to the potential quantum attacks in the future, we need to construct a secure channels for transmitting secret shares. Such channels could be modeled by a lattice based public key cryptosystem whose security is based on the worst case hardness of lattice problems. Therefore, we propose a lattice based threshold secret sharing scheme that is compatible with the platform on which the cryptosystem is built. It is shown that the proposed scheme is correct and asymptotically perfect from information theoretic point of view.
Abstract This paper proposed a quantum secret sharing scheme over lattice-based threshold encryption: it integrates resplittable threshold public key encryption (RTPKE) and utilizes a lattice-based private key share transmission mechanism to enhance the security of the share distribution process. By leveraging the dynamic key management features of RTPKE, the scheme can flexibly adjust key distribution as required when participants change. During the quantum secret reconstruction process, the decoy particles do not need to be detected by eavesdroppers when transmitted between participants. Instead, this task is performed by a semi-trusted third party (TP), reducing resource consumption and communication overhead. The decoy particles are not chosen from a fixed quantum bases but are instead in completely random quantum bases, making it impossible for an eavesdropper to obtain the correct result through conventional measurements. The probability of the eavesdropper escaping detection after measuring any decoy particle is nearly zero. After each participant performs a unitary operation, they randomly shuffle the sequence of decoy and information particles. When the particles are transmitted back to the TP, the TP uses the sequence information recorded by the participants to restore the original order and extract the information particles, effectively defending against forgery-replay attacks and potential threats from dishonest participants.
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.
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.