Threshold-Based Post-Quantum Secure Verifiable Multi-Secret Sharing for Distributed Storage Blockchain

Abstract

Blockchain systems store transaction data in the form of a distributed ledger where each node stores a copy of all data, which gives rise to storage issues. It is well-known that the tremendous storage and distribution of the block data are common problems in blockchain systems. In the literature, some types of secret sharing schemes are employed to overcome these problems. The secret sharing method is one of the most significant cryptographic protocols used to ensure the privacy of the data. The main purpose of this paper is to improve the recent distributed storage blockchain systems by proposing an alternative secret sharing method. We first propose a secure threshold verifiable multi-secret sharing scheme that has the verification and private communication steps based on post-quantum lattice-based hard problems. We then apply the proposed threshold scheme to the distributed storage blockchain (DSB) system to share transaction data at each block. In the proposed DSB system, we encrypt the data block with the AES-256 encryption algorithm before distributing it among nodes at each block, and both its secret key and the hash value of the block are privately shared among nodes simultaneously by the proposed scheme. Thereafter, in the DSB system, the encrypted data block is encoded by the Reed–Solomon code, and it is shared among nodes. We finally analyze the storage and recovery communication costs and the robustness of the proposed DSB system. We observe that our approach improves effectively the recovery communication cost and makes it more robust compared to the previous DSB systems. It also improves extremely the storage cost of the traditional blockchain systems. Furthermore, the proposed scheme brings to the DSB system the desirable properties such as verification process and secret communication without private channels in addition to the known properties of the schemes used in the previous DSB systems. As a result of the flexibility on the threshold parameter of the scheme, a diverse range of qualified subsets of nodes in the DSB system can privately recover the secret values.

A Quantum Blind Multi-Signature Method for the Industrial Blockchain

“…Hence, the available post-quantum signature schemes are necessary to better meet the security requirements of future blockchain, where most are classic post-quantum signature methods. Because this kind of post-quantum signature schemes do not need to greatly change the classic architecture of the existing industrial blockchain, they have gained a lot of views, such as the post-quantum smart contract [6], post-quantum cryptocurrency scheme [7], post-quantum multi-secret sharing [8], anti-quantum proxy blind signature [9], lattice-based signature scheme [10][11][12], etc.…”

“…The authority of the arbitrator is reduced to be offline in [31], so that it is not compulsory for an arbitrator to verify the signatures. To resist quantum attacks, the authors of [8] considered a threshold-based multi-secret sharing for post-quantum secure blockchain.…”

“…In a multi-party transaction of industrial blockchain, there are multiple traders [1,2,8], as shown in Figure 1. Every transaction is denoted as a unique transaction ID, where each trader should verify the previous quantum signature, and then make his quantum signature before sending the transaction message to the next trader [16,17,30,31].…”

“…Recent anti-quantum technologies can be divided into two main categories. The one kind is the classic anti-quantum technologies, including the post-quantum smart contract [6], post-quantum cryptocurrency scheme [7], post-quantum multi-secret sharing [8], anti-quantum proxy blind signature [9], lattice-based signature scheme [10][11][12], etc. Although these classic anti-quantum technologies are promising to secure the blockchain architecture and digital assets, they suffer from algorithm complexity and environmental vulnerability along with the increasing scale of blockchain.…”

“…Nevertheless, research studies on anti-quantum technologies of blockchain have neglected the multi-signature transactions, which are very popular in industrial blockchain [16,17]. Both classic anti-quantum technologies [6][7][8][9][10][11][12] and quantum antiquantum technologies [13][14][15] cannot be directly used in the multi-signature transactions of blockchain to provide quantum resistance and blockchain scalability. Moreover, the existing multi-signature schemes in blockchain [16,17] cannot both provide anti-quantum security and keep the computational performance and the scalability of blockchain.…”