Design and implementation of a parallel Stein algorithm based on a ternary optical computer

The Stein algorithm is used to solve the problem that the Euclidean algorithm is inefficient when dealing with large integers, and it is widely used in mathematics, physics, and cryptography. When the algorithm is implemented on a traditional electronic computer, the problems of slow computation speed, low computational efficiency, and large space occupation become more evident with the increase in the number of integer bits and the improvement of precision demands. The ternary optical computer (TOC), with low power consumption, abundant data bits, ease of expansion, and bitwise reconstruction, can solve these problems. In this study, a parallel Stein algorithm based on TOC is proposed by analyzing the Stein algorithm and identifying the parts of the algorithm that can be computed in parallel. The algorithm employs the parity judge to determine the parity of the data and calculates the intra-group greatest common divisor of each group of data in parallel by reconstructing the composite arithmetic and MSD multiplier, with the final value being the greatest common divisor of all the data. By analyzing the energy consumption and clock cycles of the parallel algorithm and through experimental verification, it is concluded that the parallel Stein algorithm based on TOC exhibits good time performance and operational efficiency, fully leveraging the advantages of TOC in computing.