<p>I'd recommend the first three chapters of Jimmy Song's Programming Bitcoin <a href="https://github.com/jimmysong/programmingbitcoin" rel="nofollow noreferrer">book</a> (also available to purchase on Amazon and other book sellers). <a href="https://github.com/jimmysong/programmingbitcoin/blob/master/ch01.asciidoc" rel="nofollow noreferrer">Chapter 1</a> goes through introductory finite fields math, <a href="https://github.com/jimmysong/programmingbitcoin/blob/master/ch02.asciidoc" rel="nofollow noreferrer">Chapter 2</a> explains elliptic curves including the elliptic curve Bitcoin uses (secp256k1) and then <a href="https://github.com/jimmysong/programmingbitcoin/blob/master/ch03.asciidoc" rel="nofollow noreferrer">Chapter 3</a> covers elliptic curve cryptography including how to create and verify a ECDSA signature.</p>

CC BY-SA 4.0
2022-06-25T09:06:00.693Z
2022-06-25T09:06:00.693Z
Michael Folkson
<p>I would suggest starting with <a href="https://bitcoin.page" rel="nofollow noreferrer">Jameson Lopp's Page</a> and <a href="https://river.com/learn/" rel="nofollow noreferrer">River Learn</a>, which has a glossary defining terms like <a href="https://river.com/learn/terms/e/ecdsa/" rel="nofollow noreferrer">ECDSA</a>, <a href="https://river.com/learn/terms/s/secp256k1/" rel="nofollow noreferrer">secp256k1</a>, <a href="https://river.com/learn/terms/s/signature-digital-signature-algorithm-dsa/" rel="nofollow noreferrer">Digital Signature Algorithms</a>, <a href="https://river.com/learn/terms/s/sha-256/" rel="nofollow noreferrer">SHA-256</a>, <a href="https://river.com/learn/terms/s/script-bitcoin/" rel="nofollow noreferrer">Bitcoin Script</a>, and <a href="https://river.com/learn/terms/p/proof-of-work-pow/" rel="nofollow noreferrer">Proof-of-Work</a>.</p>

CC BY-SA 4.0
2022-01-26T07:52:05.390Z
2022-01-26T07:52:05.390Z
Sachin Meier
<p>A bit of a background about me ; Computer Engineer but during my studies i didn't dive too deep into the maths , especially the maths that makes the blockchain and cryptography work</p>
<p>looking for advice from any senior or experienced researchers or practitioners in this field to give me some advice and point me towards the correct direction</p>
<p>E.g one example of the type of math i am looking for = so you know how the term Elliptic Curve Cryptography (ECDSA) keeps coming up all the time ?</p>
<p>i know very little about how exactly are the private keys <strong>extracted from an elliptic curve</strong> - i'd like to understand how exactly are we able to derive something as vital as a <strong>wallet private key</strong> from an elliptic curve .. how does this work to help Bitcoin or any blockchain become secure ? That's what i want to understand through the math !</p>
<p>if you can outline exactly which math topics i need to revise and learn - i would be thankful !</p>
<p>P.S : suggestions for any useful and relevant online courses are most welcome !</p>

CC BY-SA 4.0
2021-12-08T19:35:35.793Z
ecdsa allows people to sign transactions to prove that they authored them and not anyone else without revealing their private key. https://www.maximintegrated.com/en/design/technical-documents/tutorials/5/5767.html does this help?
MCCCS
<private-key><signature><ecdsa>
Curious about the Math that makes Bitcoin/Blockchain work ! Any good resources to learn it?
Muhammad Yasir
# Curious about the Math that makes Bitcoin/Blockchain work ! Any good resources to learn it?

(Asked by: username_0 on 2021-12-08)

A bit of a background about me ; Computer Engineer but during my studies i didn't dive too deep into the maths , especially the maths that makes the blockchain and cryptography work

looking for advice from any senior or experienced researchers or practitioners in this field to give me some advice and point me towards the correct direction

E.g one example of the type of math i am looking for = so you know how the term Elliptic Curve Cryptography (ECDSA) keeps coming up all the time ?

i know very little about how exactly are the private keys **extracted from an elliptic curve** - i'd like to understand how exactly are we able to derive something as vital as a **wallet private key** from an elliptic curve .. how does this work to help Bitcoin or any blockchain become secure ? That's what i want to understand through the math !

if you can outline exactly which math topics i need to revise and learn - i would be thankful !

P.S : suggestions for any useful and relevant online courses are most welcome !

**Tags:** private-key, signature, ecdsa

> **Comments:**
> **username_1**: ecdsa allows people to sign transactions to prove that they authored them and not anyone else without revealing their private key. https://www.maximintegrated.com/en/design/technical-documents/tutorials/5/5767.html does this help?  

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## 2 answers

### Answer by username_2 on 2022-06-25. Score: 2

I'd recommend the first three chapters of Jimmy Song's Programming Bitcoin [book](https://github.com/jimmysong/programmingbitcoin) (also available to purchase on Amazon and other book sellers). [Chapter 1](https://github.com/jimmysong/programmingbitcoin/blob/master/ch01.asciidoc) goes through introductory finite fields math, [Chapter 2](https://github.com/jimmysong/programmingbitcoin/blob/master/ch02.asciidoc) explains elliptic curves including the elliptic curve Bitcoin uses (secp256k1) and then [Chapter 3](https://github.com/jimmysong/programmingbitcoin/blob/master/ch03.asciidoc) covers elliptic curve cryptography including how to create and verify a ECDSA signature.


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### Answer by username_3 on 2022-01-26. Score: 0

I would suggest starting with [Jameson Lopp's Page](https://bitcoin.page) and [River Learn](https://river.com/learn/), which has a glossary defining terms like [ECDSA](https://river.com/learn/terms/e/ecdsa/), [secp256k1](https://river.com/learn/terms/s/secp256k1/), [Digital Signature Algorithms](https://river.com/learn/terms/s/signature-digital-signature-algorithm-dsa/), [SHA-256](https://river.com/learn/terms/s/sha-256/), [Bitcoin Script](https://river.com/learn/terms/s/script-bitcoin/), and [Proof-of-Work](https://river.com/learn/terms/p/proof-of-work-pow/).


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