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Comment by jxm262 | Hacker News Reader

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.

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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

Technical Requirements: https://tools.ietf.org/html/rfc5639#section-2.2

That was... an awesome explanation :)

Thank you

"The simplicity of these parameters gives the NSA / NIST very little wiggle room to create a deliberately bad curve. And even the specific values of 0, 7 and 977 can be justified by security and efficiency constraints, so the chance that Bitcoin’s elliptic curve parameters were chosen with any malicious intent is very low indeed" [1]

[1] http://bitcoinmagazine.com/7781/satoshis-genius-unexpected-w...

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