有限域上模逆电路的可逆逻辑设计

Design of Modular Inversion Circuits Using Reversible Logic on Galois Field

为了进一步提高加密系统的可靠性，提出了一种新颖的可逆逻辑门，利用它和存在的可逆门，设计了模逆电路所需的基本模块，并在有限域上设计了基于可逆逻辑的模逆电路。根据量子代价和延迟对其基本模块进行了性能评估，结果证明构建模逆电路的基本模块比现有可逆电路的性能提高5%-20%。以有限域GF（23）上求二进制多项式的乘法逆元为例，对提出的模逆电路进行建模仿真，结果表明电路的逻辑结构正确，性能可靠。提出的设计可用于加密算法的量子电路系统。

In order to improve the reliability of encryption system, this paper proposes a novel reversible logic gate, constructs some basic modules of modular inversion circuit by using the proposed gate and some existing reversible gates, and also designs the modular inversion circuit by using reversible logic on Galois field. Then, this paper evaluates the performance of basic modules in terms of quantum cost and delay. The results show that the performance is improved by 5%to 20%compared with the existing counterparts. Taking the calculation of binary polynomial multi-plication inverse element in GF（23） as an example, simulation results indicate that the logic structure of proposed modular inversion circuit is correct and its performance is reliable. The proposed design is suitable to the field of quantum circuit system for encryption algorithm.