With the advent of machine learning and quantum computing, the 21st century has gone from a place of relative algorithmic security, to one of speculative unease and possibly, cyber catastrophe. Modern algorithms like Elliptic Curve Cryptography (ECC) are the bastion of current cryptographic security protocols that form the backbone of consumer protection ranging from Hypertext Transfer Protocol Secure (HTTPS) in the modern internet browser, to cryptographic financial instruments like Bitcoin. And there's been very little work put into testing the strength of these ciphers. Practically the only study that I could find was on side-channel recognition, a joint paper from the University of Milan, Italy and King's College, London\cite{battistello2025ecc}. These algorithms are already considered bulletproof by many consumers, but exploits already exist for them, and with computing power and distributed, federated compute on the rise, it's only a matter of time before these current bastions fade away into obscurity, and it's on all of us to stand up when we notice something is amiss, lest we see such passages claim victims in that process. In this paper, we seek to explore the use of modern language model architecture in cracking the association between a known public key, and its associated private key, by intuitively learning to reverse engineer the public keypair generation process, effectively solving the curve. Additonally, we attempt to ascertain modern machine learning's ability to memorize public-private secp256r1 keypairs, and to then test their ability to reverse engineer the public keypair generation process. It is my belief that proof-for would be equally valuable as proof-against in either of these categories. Finally, we'll conclude with some number crunching on where we see this particular field heading in the future.

翻译：随着机器学习和量子计算的出现，21世纪已从一个相对算法安全的时代，转变为充满推测性不安并可能引发网络灾难的时期。椭圆曲线密码学（ECC）等现代算法是当前密码安全协议的堡垒，构成了从现代互联网浏览器中的超文本传输安全协议（HTTPS）到比特币等加密金融工具的消费者保护体系的支柱。然而，针对这些密码强度测试的研究却极为匮乏。实际上，我能找到的唯一相关研究是关于侧信道识别的，这是意大利米兰大学与伦敦国王学院联合发表的一篇论文\cite{battistello2025ecc}。尽管许多用户认为这些算法已牢不可破，但针对它们的漏洞利用已然存在。随着计算能力以及分布式联合计算的兴起，当前这些安全堡垒逐渐失效只是时间问题。我们每个人都有责任在发现异常时挺身而出，以免在此过程中造成实际损害。本文旨在探索如何利用现代语言模型架构，通过直观学习逆向工程公钥对生成过程来破解已知公钥与其对应私钥之间的关联，从而有效求解曲线方程。此外，我们尝试评估现代机器学习记忆secp256r1公私钥对的能力，并测试其逆向推导公钥对生成过程的效果。我认为，无论在上述哪个方向，证明"可行"与证明"不可行"都具有同等价值。最后，我们将通过具体数据分析对该领域未来发展趋势进行展望。