
The Math Behind Bitcoin - typedweb
http://www.coindesk.com/math-behind-bitcoin/
======
Beldur
Original article: [http://blog.chain.com/post/95218566791/the-math-behind-
bitco...](http://blog.chain.com/post/95218566791/the-math-behind-bitcoin)

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jxm262
Thanks for this. As someone new to bitcoin, this helped explained things a bit
for me, but also leaves me with many more questions.

Sorry if this is a stupid question, but can someone explain the part
explaining b?

    
    
        y2 = x3 + ax + b
        For a = 0 and b = 7 (the version used by bitcoin)
    

Can someone please explain why b is set to 7? Is there some other articles
that explain this in a little more depth?

I'm finding references to Secp256k1 (SEC 2: Recommended Elliptic Curve Domain
Parameters), but am struggling to understand it.

~~~
tveita
You have a list of requirements when generating an curve. Some of the
requirements are needed so the equations you use have solutions, while some
are there to prevent known attacks that take advantage of the structure of the
curve.

The numbers should be choosen using a nothing-up-my-sleeves strategy, to prove
that you haven't chosen them to enable an attack that isn't public knowledge
yet. So you typically choose the first number that match all requirements,
either counting sequentially, or using a preagreed pseudorandom sequence, like
the Brainpool curves.

See for example the requirements used by the Brainpool curves - each
requirement has a rationale.

Security requirements:
[https://tools.ietf.org/html/rfc5639#section-2.1](https://tools.ietf.org/html/rfc5639#section-2.1)

Technical Requirements:
[https://tools.ietf.org/html/rfc5639#section-2.2](https://tools.ietf.org/html/rfc5639#section-2.2)

~~~
jxm262
That was... an awesome explanation :)

Thank you

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goodbyegti
Another explanation which may be of interest:

[http://www.michaelnielsen.org/ddi/how-the-bitcoin-
protocol-a...](http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-
actually-works/)

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cirosantilli
Lol that image is so "kids, math is cool, like the Matrix":
[http://media.coindesk.com/2014/10/math-behind-
bitcoin.jpg](http://media.coindesk.com/2014/10/math-behind-bitcoin.jpg)

