Liu Jianmei, Wang Hong, Ma Zhi, Duan Qianheng, Fei Yangyang, Meng Xiangdong
State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou 450001, China.
Henan Key Laboratory of Network Cryptography Technology, Zhengzhou 450001, China.
Entropy (Basel). 2022 Jul 9;24(7):955. doi: 10.3390/e24070955.
In this paper, we consider the optimization of the quantum circuit for discrete logarithm of binary elliptic curves under a constrained connectivity, focusing on the resource expenditure and the optimal design for quantum operations such as the addition, binary shift, multiplication, squaring, inversion, and division included in the point addition on binary elliptic curves. Based on the space-efficient quantum Karatsuba multiplication, the number of CNOTs in the circuits of inversion and division has been reduced with the help of the Steiner tree problem reduction. The optimized size of the CNOTs is related to the minimum degree of the connected graph.
在本文中，我们考虑了在受限连通性下用于二元椭圆曲线离散对数的量子电路优化问题，重点关注资源消耗以及二元椭圆曲线上点加法中包含的加法、二进制移位、乘法、平方、求逆和除法等量子操作的最优设计。基于空间高效的量子Karatsuba乘法，借助斯坦纳树问题简化，求逆和除法电路中的CNOT门数量得以减少。CNOT门的优化规模与连通图的最小度数相关。
