{"id":397172,"date":"2024-06-29T13:17:32","date_gmt":"2024-06-29T13:17:32","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=397172"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=397172","title":{"rendered":"Elliptic curves and ECDSA: everything to know to sign a transaction in Bitcoin from scratch<\/span>"},"content":{"rendered":"
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Elliptic curves are very simple.\u00a0The Elliptic Curves Digital Signature Algorithm (ECDSA), which works on top of their properties, is used in most blockchains like Bitcoin, Ethereum, etc., and is even simpler. But it\u2019s challenging to find a good explanation on the internet and build all the pieces together. But here it is! In this article, we will.<\/p>\n

We will go through all the concepts needed to understand and implement this algorithm \u2014 one by one. By the end of this article, we will have a fully functioning demo\u00a0from scratch<\/strong>, which can extract the\u00a0public key<\/strong>\u00a0from the\u00a0private key<\/strong>,\u00a0sign<\/strong>\u00a0a message, and\u00a0verify<\/strong>\u00a0that the signature is correct. This implementation will\u00a0only<\/strong>\u00a0use the concepts described in this article. Moreover, it will take less than 100 lines of code.<\/p>\n

This article is targeted mainly at developers like myself, who want to finally understand ECDSA, but it will also be very useful for everyone else. It requires knowing no more than middle school math.<\/p>\n

I highly recommend following it step by step. If you want, you can grab a piece of paper and a pen and repeat all the steps in this article. It would be even better! If you\u2019re not a programmer, you can ignore some pieces of code. If you are, I recommend re-writing the code on your own and practicing!<\/p>\n

The article consists of 6 parts; each part uses the concepts of the previous parts (except part 2):<\/p>\n