arXiv 1810.011662018-10quant-phcs.CCcs.CR

一种适用于多项式规模电路的量子同态加密方案

A quantum homomorphic encryption scheme for polynomial-sized circuits

Li Yu

备注：: 29 pages, 2 figures. Revised Section VIII, among other minor fixes

摘要：

量子同态加密（QHE）是一种加密方法，它允许使用另一方提供的程序对一方的私有数据进行量子计算，而不会向另一方透露有关数据或程序的大量信息。众所周知，用于不受限制大小的电路的信息理论上安全的QHE将需要指数资源，并且已经构造了用于多项式大小的量子线路的高效计算安全的QHE方案。在本文中，我们首先提出了一个QHE方案的多项式深度的电路类型的基础上，rebit量子计算形式主义。该方案保证了受限类型数据的完全安全。然后，我们提出了一个更大的类的多项式深度的量子线路，其中有部分数据隐私的QHE计划。两种方案都具有良好的电路保密性。我们还提出了一个交互式QHE方案与渐近数据隐私，然而，电路的隐私是不好的，在这个意义上说，谁提供的数据的一方可以欺骗和了解电路。我们表明，这种作弊通常会影响评估的正确性或导致偏离协议。因此，在具有嵌入式验证的交互式方案中，欺骗可以被对方捕获。这种带有验证的方案在数据隐私方面有一个小缺点。最后，我们展示了一些方法，实现一些不平凡的数据隐私和电路隐私的水平，而不诉诸允许提前终止，在QHE问题和经典功能的安全评估。在这些方案中，纠缠和经典通信成本是多项式的电路大小和安全参数（如果有的话）。

英文摘要：

Quantum homomorphic encryption (QHE) is an encryption method that allows quantum computation to be performed on one party's private data with the program provided by another party, without revealing much information about the data nor about the program to the opposite party. It is known that information-theoretically-secure QHE for circuits of unrestricted size would require exponential resources, and efficient computationally-secure QHE schemes for polynomial-sized quantum circuits have been constructed. In this paper we first propose a QHE scheme for a type of circuits of polynomial depth, based on the rebit quantum computation formalism. The scheme keeps the restricted type of data perfectly secure. We then propose a QHE scheme for a larger class of polynomial-depth quantum circuits, which has partial data privacy. Both schemes have good circuit privacy. We also propose an interactive QHE scheme with asymptotic data privacy, however, the circuit privacy is not good, in the sense that the party who provides the data could cheat and learn about the circuit. We show that such cheating would generally affect the correctness of the evaluation or cause deviation from the protocol. Hence the cheating can be caught by the opposite party in an interactive scheme with embedded verifications. Such scheme with verification has a minor drawback in data privacy. Finally, we show some methods which achieve some nontrivial level of data privacy and circuit privacy without resorting to allowing early terminations, in both the QHE problem and in secure evaluation of classical functions. The entanglement and classical communication costs in these schemes are polynomial in the circuit size and the security parameter (if any).

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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