Homomorphic encryption of the k=2 Bernstein–Vazirani algorithm

IF 2 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-22 DOI:10.1088/1751-8121/ad6c04

Pablo Fernández, Miguel A Martin-Delgado

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引用次数: 0

Abstract

We introduce a class of circuits that solve a particular case of the Bernstein–Vazirani recursive problem for second-level recursion. This class of circuits allows for the implementation of the oracle using a number of T-gates that grows linearly with the number of qubits in the problem. We find an application of this scheme to quantum homomorphic encryption (QHE), which is an important cryptographic technology useful for delegated quantum computing, allowing a remote server to perform quantum computations on encrypted quantum data, so that the server cannot know anything about the client’s data. Liang’s QHE schemes are suitable for circuits with a polynomial number of gates

T/T†

. Thus, the simplified circuits we have constructed can be evaluated homomorphically in an efficient manner.

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k=2 伯恩斯坦-瓦齐拉尼算法的同态加密

我们介绍了一类电路，它能解决伯恩斯坦-瓦齐拉尼递归问题的一个特殊情况，即二级递归问题。这一类电路允许使用与问题中的量子比特数呈线性增长的 T 门来实现神谕。我们发现这一方案在量子同态加密（QHE）中的应用，QHE 是一种重要的加密技术，可用于委托量子计算，允许远程服务器对加密的量子数据进行量子计算，这样服务器就无法知道客户数据的任何信息。梁的 QHE 方案适用于具有多项式门数 T/T† 的电路。因此，我们构建的简化电路可以高效地进行同态评估。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Physics A: Mathematical and Theoretical 物理-物理：数学物理

CiteScore

4.10

自引率

14.30%

发文量

542

审稿时长

1.9 months

期刊介绍： Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.