Bitcoins security strength is at 128 bit.
With ECDSA on secp256k1 and a key size of 256 bit, the strength is at 128 bit.
2512 bit is an absurdly large number and completely off. But i guess you meant 512 bit.
ECDSA's security is dependend on the key size. With a key length of 2n bit, the bit strength (security) is at 2n-1 bit.
Of course I meant 512 bit With ECDSA on secp256k1 and a key size of 256 bit, the strength is at 128 bit.
2512 bit is an absurdly large number and completely off. But i guess you meant 512 bit.
ECDSA's security is dependend on the key size. With a key length of 2n bit, the bit strength (security) is at 2n-1 bit.
Sorry I was thinking 2^512 possibilities not bits. And about the 256 bits vs 128 bits, bitcoin security is 256 bit (originally), but as we currently have algorithms that can solve it using just 128 bit search space you can also say that the strength is (currently) 128 bits. Maybe tomorrow it is just 100 bits? Who knows. That is why (in my opinion) it is easier to speak of 256 bits, because it is a number that wont change.
But I disagree with that.
No. That's nothing one can agree or disagree with.
You can either decide to accept or to deny it.
I agree that with the current way of trying to solve the problem, which is just brute forcing (or pollard rho), the search space is what you say.
BUT
IF you want to try to develop smarter algorithms for solving the problem, then you will have to convert the problem to something else first. And in that conversion the difficulty (unfortunately) does change. Because of the mod operator.