Understanding ECDSA

Summary

ECDSA attack cryptography ethereum extended euclidean algorithm generating functions signature malleability Understanding ECDSA Prerequisites and audience In this article, we'll try to understand how ECDSA (Elliptic Curve Digital Signature Algorithm) works. The version I have in mind is the one used by the Ethereum blockchain. Since my interest lies in security, we'll also explore the signature malleability attack. I expect you to be familiar with Public Key Cryptography and how it can be used to sign messages, at least conceptually. You'll only need to know basic math, so abstract algebra is not a requirement. I'll introduce the bare minimum as we go. My exposition will be deliberately unsophisticated, favoring ease of understanding over conciseness and elegance. The reader I have in mind is someone dissatisfied with the many superficial, hand-wavy explanations of ECDSA often found in articles and books aimed at developers and auditors, but who doesn't have the time or interest to go all the way down the rabbit hole and learn cryptography in a thorough and systematic way. If you, like me, work in a field where you need to have a working knowledge of multiple disciplines, you'll probably appreciate this kind of compromise. Finally, this might also serve as an introduction to the topic before you turn to more serious and academic literature. Not your typical article You can think of this section as a kind of disclaimer. This article is the result of an exercise where I start from a vague understanding of a topic and try to connect all the dots and fill in all the gaps on my own, without relying on any external sources of information. This means no books, no LLMs, and no internet. For the exercise to be effective, it needs to be written with an audience in mind, forcing you to keep track of what you've already explained and what you can expect the reader to know. It also helps you do a better job because you feel more exposed. Have you ever gone back to something you ...