An Exploration of Secure Circular Multi-Party Quantum Computation

Abstract

Multi party quantum computation (MPQC) is any quantum cryptographic protocol where multiple untrusted users collaborate to perform calculations on their combined data without revealing their private information. MPQC is not guaranteed information-theoretically secure by the laws of quantum mechanics, and thus finding schemes for MPQC that ensure a high degree of security is an ongoing research task. In this thesis, we examine an approach for MPQC protocols that employs a circular structure. The circular structure minimizes the amount of information transmitted from user to user, increasing efficiency and security. This makes it a good structure for MPQC.

We address three main topics related to circular MPQC. First, we build a quantum circuit to practically implement an existing circular MPQC protocol. We demonstrate feasibility and reasonable efficiency in the circuit model. Second, we examine the security of circular MPQC. We consider the protocol's vulnerabilities to outside and inside attacks. After identifying weaknesses in the scheme, we suggest two improvements to increase security. The first involves inserting random data values into the protocol, and the second involves the help of a semi-trusted third party. Finally, given that quantum computers are not currently commercially available, we explore options for multiparty computation using classical resources and cloud-based quantum computing. We modify the circular MPQC protocol to function for fully classical clients using blind quantum computing. Our method proposes a semi-trusted intermediate server to use post-selection to simulate entanglement between two quantum servers.