论文标题
减少基于量子FLT的反转电路的深度
Reducing the Depth of Quantum FLT-Based Inversion Circuit
论文作者
论文摘要
在过去的几年中，量子计算和密码分析的工作已大大增加。还提出了量子算术电路的各种构造，作为现场的重要组成部分之一。但是，尽管在实现量子算法中使用了必不可少的有限场反转研究，例如用于椭圆曲线离散对手问题（ECDLP）的Shor's算法。在这项研究中，我们建议减少现有量子费马特的小定理（FLT）基于二元有限场的反转电路的深度。特别是，我们建议采用完整的瀑布方法，以将ITOH-TSUJII的FLT变体转换为相应的量子电路，并删除Banegas等人先前工作中使用的反向平方操作，从而减少了CNOT GATES（CNOT计数）的数量，从而有助于减少整体深度和栅极计数。此外，通过首先在Qiskit Quantum计算机模拟器中构建我们的方法和以前的工作来比较成本并执行资源分析。我们的方法可以作为时间效率实施的替代方法。
Works on quantum computing and cryptanalysis has increased significantly in the past few years. Various constructions of quantum arithmetic circuits, as one of the essential components in the field, has also been proposed. However, there has only been a few studies on finite field inversion despite its essential use in realizing quantum algorithms, such as in Shor's algorithm for Elliptic Curve Discrete Logarith Problem (ECDLP). In this study, we propose to reduce the depth of the existing quantum Fermat's Little Theorem (FLT)-based inversion circuit for binary finite field. In particular, we propose follow a complete waterfall approach to translate the Itoh-Tsujii's variant of FLT to the corresponding quantum circuit and remove the inverse squaring operations employed in the previous work by Banegas et al., lowering the number of CNOT gates (CNOT count), which contributes to reduced overall depth and gate count. Furthermore, compare the cost by firstly constructing our method and previous work's in Qiskit quantum computer simulator and perform the resource analysis. Our approach can serve as an alternative for a time-efficient implementation.
