In this proposal, I aim to construct practical protocols for device-independent quantum cryptography. In particular, my goals are to improve over the current constructions with respect to round complexity, verifiability and reliability, and to construct new cryptographic schemes for robust outsourcing quantum computation.
As a first step, I showed classical verification for any quantum computation can be performed non-interactively and in zero-knowledge. The protocol results from a sequence of significant improvements to the first classical verification protocol of Mahadev. First, I showed that the sampling of randomness can be made instance-independent, and thus can be performed in an offline setup phase. Next, I established a parallel repetition theorem to reduce the soundness error at an optimal rate. Finally, the round complexity can be reduced by Fiat-Shamir transform in the quantum-accessible random oracle model. As a consequence, I gave the first classical non-interactive zero-knowledge for QMA.
In the next step, I plan to integrate the aforementioned verification procedure to construct schemes for robust outsourcing quantum computation, including (i) a non-interactive randomness expansion protocol for extracting uniformly random bits of arbitrarily polynomial size, and (ii) a classically verifiable fully homomorphic encryption for quantum circuits. Furthermore, I will study efficient protocols for near-term devices.
Dept rep: Dr. Michael Hicks
Members: Dr. Gorjan Alagic
Shih-Han Hung is a graduate student in the Department of Computer Science at the University of Maryland. His research aims to understand the power of quantum computation. He is interested in quantum cryptography, verification of quantum computation and quantum algorithms.