一种求解椭圆曲线离散对数问题的新方法
A new method for solving the elliptic curve discrete logarithm problem
AI总结：
本文提出利用初始子式（initial minors）和Schur补求解椭圆曲线离散对数问题的新范式，并通过代码验证，成功解决了阶数高达$2^{50}$的群上的问题。
摘要：
椭圆曲线离散对数问题被视为一种安全的密码学原语。本文旨在提出一种攻击椭圆曲线离散对数问题的范式转变。在本文中，我们将论证初始子式（initial minors）是解决该问题的一种可行途径。本文将介绍该攻击所需的必要算法。我们编写了代码，利用Schur补（Schur complements）来验证初始子式的猜想。我们能够解决阶数高达$2^{50}$的群上的该问题。
英文摘要：
The elliptic curve discrete logarithm problem is considered a secure cryptographic primitive. The purpose of this paper is to propose a paradigm shift in attacking the elliptic curve discrete logarithm problem. In this paper, we will argue that initial minors are a viable way to solve this problem. This paper will present necessary algorithms for this attack. We have written a code to verify the conjecture of initial minors using Schur complements. We were able to solve the problem for groups of order up to $2^{50}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
