The elliptic curve discrete logarithm problem is of fundamental importance in public-key cryptography. It is in use for a long time. Moreover, it is an interesting challenge in computational mathematics. Its solution is supposed to provide interesting research directions. In this paper, we explore ways to solve the elliptic curve discrete logarithm problem. Our results are mostly computational. However, it seems, the methods that we develop and directions that we pursue can provide a potent attack on this problem. This work follows our earlier work, where we tried to solve this problem by finding a zero minor in a matrix over the same finite field on which the elliptic curve is defined. This paper is self-contained.

翻译：椭圆曲线离散对数问题在公钥密码学中具有根本重要性，并长期得到应用。此外，它也是计算数学领域中一项有趣的挑战。解决该问题有望提供有价值的研究方向。本文探索了求解椭圆曲线离散对数问题的多种方法。我们的研究结果主要基于计算层面。然而，我们开发的方法及探索的方向似乎能够为此问题提供有效的攻击手段。本研究延续了我们之前的工作——通过在与椭圆曲线定义域相同的有限域上寻找矩阵的零子式来尝试解决该问题。本文内容自包含。