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Information Sciences

Quantum homomorphic encryption scheme with flexible number of evaluator based on (k, n)-threshold quantum state sharing

Xiu‐Bo Chen, Yiru Sun, Gang Xu, Yixian Yang

Published Jun 6, 2019• 52 citations
Publisher
DOI
10.1016/j.ins.2019.06.009

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Currently, most quantum homomorphic encryption (QHE) schemes only allow a single evaluator (server) to accomplish computation tasks on encrypted data shared by the data owner (user). In addition, the quantum computing capability of the evaluator and the scope of quantum computation it can perform are usually somewhat limited, which significantly reduces the flexibility of the scheme in quantum network environments. In this paper, we propose a novel (t,n)-threshold QHE (TQHE) network scheme based on the Shamir secret sharing protocol, which allows k(t≤k≤n) evaluators to collaboratively perform evaluation computation operations on each qubit within the shared encrypted sequence. Moreover, each evaluator, while possessing the ability to perform all single-qubit unitary operations, is able to perform arbitrary single-qubit gate computation task assigned by the data owner. We give a specific (3, 5)-threshold example, illustrating the scheme's correctness and feasibility, and simulate it on IBM quantum computing cloud platform. Finally, it is shown that the scheme is secure by analyzing encryption/decryption private keys, ciphertext quantum state sequences during transmission, plaintext quantum state sequence, and the result after computations on the plaintext quantum state sequence.
Universal quantum homomorphic encryption based on (k,n)(k, n)(k,n)-threshold quantum state sharing
Quantum homomorphic encryption integrates quantum computing with homomorphic encryption, which allows calculations to be performed directly on encrypted data without decryption on the server side. In this paper, we explore distributed quantum homomorphic encryption, focusing on the coordination of multiple evaluators to achieve evaluation tasks, which not only ensures security but also boosts computational power. Notably, we propose a (k,n)(k, n)(k,n)-threshold universal quantum homomorphic encryption scheme based on quantum state sharing. Each server is capable of executing a universal gate set, including the Clifford gates {X,Y,Z,H,S,CNOT}\{X,Y,Z,H,S,CNOT\}{X,Y,Z,H,S,CNOT} and a non-Clifford T gate. The scheme provides that k evaluation servers chosen from nnn (0<k≤n)(0 < k \leq n)(0<k≤n) cooperate to complete the quantum homomorphic encryption so that the client can get the evaluated plaintext after decryption. Several concrete examples are presented to provide clarity to our solution. We also include security analysis, demonstrating its security against eavesdroppers.
Threshold private set intersection is a basic primitive of secure multiparty computation, which has many important applications in the field of privacy preservation and information security, especially in a ride sharing system, one of the most transforming and innovative technologies enabled by the Internet of Things. In this paper, we propose a new proposal for threshold private set intersection based on quantum homomorphic encryption, in which both the number of users and the designated trusted party are flexible. Furthermore, the complicated computing task can be delegated to a server for processing contributing to the speciality of quantum homomorphic encryption. More importantly, the users’ privacy is perfectly guaranteed because all the calculations are performed on the quantum encrypted data. Therefore, this proposal is more practical compared with the prior work.