More efficient SM9 algorithm based on bilinear pair optimization processing

Abstract

Currently, SM9 algorithm has received more and more attention as a new cryptographic product. The SM9 algorithm encryption and decryption principle relies on the mapping relationship on the elliptic curve. Although this mapping relationship improves the security, it will slightly reduce the efficiency. The goal of this article is to improve the efficiency of the SM9 algorithm. Different from the traditional assembly line acceleration method, we decided to start with the basic operation of the algorithm itself. There is a bilinear pairing operation on the elliptic curve, which completes the point to point on the elliptic curve. The calculation complexity directly determines the SM9 algorithm. For this reason, we propose two new bilinear pair processing methods. The former uses the properties of isomorphic mapping to transfer the operations involved in the calculation of bilinear pairs from a large feature domain to a small feature domain, reducing the number of operations on the feature domain. The latter is for special operations in the bilinear pairing process, adding intermediate variables to convert them into low-time-consuming multiplication operations. According to the traditional Miller algorithm, the calculation of bilinear pairs requires 900 multiplication time units. Our solution can reduce this value to 700 and 800 multiplication time units respectively. In addition, the two algorithms have not changed the mapping relationship of the bilinear pair. On the premise of ensuring the correct mapping relationship, the efficiency of the SM9 algorithm is improved.