Elliptic curve cryptography is an essential cryptography which is widely used in data encryption, key agreement, digital signature, and other applications. Scalar multiplication is the fundamental operation in all ECC schemes, such as ECDSA, ECIES, and ECMQV. Even a slight improvement of scalar multiplication is precious. Various methods have been proposed for improving efficiency of the scalar multiplication, including the windows method, the NAF method, and the w-NAF method. However, the endeavour in this direction almost exhausted in the past several years since it is hard to find a method substantially better than the w-NAF method. This paper focuses on the scalar multiplication algorithm for the case when the scalar is a pseudo-random number. A faster pseudo-random scalar multiplication method is proposed based on a group isomorphism between the pseudo-random number group and elliptic curve point group. Experimental results show that the proposed method can considerably reduce the computation time compared with those traditional methods. The pseudo-random scalar multiplication accounts for a significant proportion of total scalar multiplication operations in almost all ECC schemes. Therefore, the proposed method is promising and applicable for various ECC applications in the fields such as Internet of things, edge computing, and swarm robotics.

椭圆曲线密码学是必不可少的密码学，广泛用于数据加密，密钥协商，数字签名和其他应用程序中。标量乘法是所有ECC方案（例如ECDSA，ECIES和ECMQV）中的基本操作。标量乘法即使略有改善也是很宝贵的。已经提出了用于提高标量乘法的效率的各种方法，包括窗口方法，NAF方法和w-NAF方法。但是，由于很难找到一种比w-NAF方法更好的方法，因此在过去的几年中，几乎没有朝着这个方向努力。本文针对标量为伪随机数的情况，重点研究了标量乘法算法。提出了一种基于伪随机数组和椭圆曲线点组之间的同构性的伪随机标量乘法方法。实验结果表明，与传统方法相比，该方法可以大大减少计算时间。在几乎所有ECC方案中，伪随机标量乘法都占总标量乘法运算的很大一部分。因此，所提出的方法是有希望的，并且可以应用于诸如物联网，边缘计算和群体机器人技术领域中的各种ECC应用。在几乎所有ECC方案中，伪随机标量乘法都占总标量乘法运算的很大一部分。因此，所提出的方法是有希望的，并且可以应用于诸如物联网，边缘计算和群体机器人技术领域中的各种ECC应用。在几乎所有ECC方案中，伪随机标量乘法都占总标量乘法运算的很大一部分。因此，所提出的方法是有希望的，并且可以应用于诸如物联网，边缘计算和群体机器人技术领域中的各种ECC应用。