This paper studies information-theoretically secure quantum homomorphic encryption (QHE) schemes of classical data. Previous works on information-theoretically secure QHE schemes (like Childs'05, Liang'13, and others) are typically based on the Quantum-One-Time-Pad (QOTP) approach of Ambainis et al. [AMTdW'00]. There, the encryption of a bit is a qubit, randomly selected from a set of four possible qubits. This paper takes a different approach and presents the RBE (Random-Basis Encryption) scheme -- a QHE scheme in which the encryption of a bit is a qubit, randomly selected from a set of an immense number of qubits. Second, this paper studies weak measurements (WM) and presents a WM-based attack on legacy QOTP-based Quantum Key Distribution (QKD) protocols. Then, we use the RBE scheme to construct a QKD protocol and argue that this protocol is resilient to such WM-based attacks. Finally, this paper raises the following question. Entanglement is an essential resource in quantum information and quantum computation research. Hence, once generated, how can its owner secure entangled systems of qubits? We inspect possible QOTP-based solutions, suggest an RBE-based solution, and discuss some of the benefits of the latter.

翻译：本文研究了经典数据的信息论安全量子同态加密（QHE）方案。以往关于信息论安全QHE方案的研究（如Childs'05、Liang'13等）通常基于Ambainis等人[AMTdW'00]提出的量子一次性密码本（QOTP）方法。在该方法中，一个比特的加密结果是一个从四个可能量子比特中随机选取的量子比特。本文采用不同思路，提出了RBE（随机基加密）方案——一种QHE方案，其中每个比特的加密结果是一个从海量可能量子比特中随机选取的量子比特。其次，本文研究了弱测量（WM），并提出了一种基于弱测量的攻击方法，可针对传统基于QOTP的量子密钥分发（QKD）协议。随后，我们利用RBE方案构建了一个QKD协议，并论证该协议能够抵御此类基于弱测量的攻击。最后，本文提出以下问题：纠缠是量子信息与量子计算研究中的核心资源。那么，一旦生成纠缠，其所有者如何保护纠缠量子比特系统的安全？我们考察了可能的基于QOTP的解决方案，提出了一种基于RBE的解决方案，并讨论了后者的若干优势。