There’s a maximum of 115,792,089,237,316,195,423,570,985,008,687,907,853,269,984,665,640,564,039,457,584,007,913,129,639,936 private keys to choose from.
Take as many as you need.
Discussion
Vitor once said that all private keys, hence all possible Nostr accounts that will exist, already exist. They're just waiting for people to use them (I think about this sometimes)
Hello, how do you find out? Is there any information about it? something with binomial coefficients somehow? how do you calculate it? unfortunately, I can't find anything about it. Thank you!
A private key is 256 bits long, if my math is right that gives you 2^256 combinations because each bit can be either one or zero.
It’s basically 2 times itself 256 times.
Did that make sense?
Some sequences of bits are not on the secp256k1 curve. Some are reflections of the same point and collapse into others. So there are actually less private keys.
Since Satoshi chose this curve, a lot of research has happened in ECC. Bernstein worked out various properties that make a curve "safe", essentially means it is hard for developers to misuse the curve. secp256k1 is not a "safe" curve. https://safecurves.cr.yp.to/
Glad I said maximum in my first post.
Now I wonder how many theoretical reflections one private key may have.
I've assumed it's just 1. But I dunno for sure. If it's just 1, and some have 0, we still have more than half as many private keys. It's still tremendously huge.
Ok. Thanks