Hey folks
I wanted to share something cool I found while messing around with summation polynomials and automorphisms.
So, S₃ Perfect-Square Discriminant
If you take:
x2 = β * x1 (where β³ = 1 when j = 0)
then the discriminant of the S₃ polynomial in z turns out to be:
Δ = 16 * (x₁³ + b)² (mod p)
Is this something that's used in algorithms like Pollard Rho? I need more info on this since I'm just starting out with cryptography.
I mean any kind of scheme you can just cube x and get a value which is the same for P, P*lamba, P*lambda^2, essentially giving you 3x the effective table size but the speedup is only useful when the point in question is equally likely to be found in one of those groups. When people DLP solve on secp256k1 it's always in a restricted range because the whole group is far far far too large. So the only way someone is going to be able to successfully solve P=xG is when x is in some small range, generally... there are real cases (and lots of silly challenges) where that happens, for the automorphism to be useful the restriction needs to be x is in [range]*{1,lambda,lambda^2} which is a lot more contrived than x being in a range to begin with.
Chat GPT cannot count: https://www.facebook.com/reel/1138880084809988
It cannot even solve ECDLP for small examples: https://bitcointalk.org/index.php?topic=5459153.0
That's a fortunate case. I asked it to count 1 to 100 and it skipped 6. It also repeated lots of numbers and skipped random gaps after them, so that must be a clue to the secrets of the multiverse.
So what I get, is that 6 does not exist, and arithmetic as we know it is wrong, ok?
Though I don't see how this would be an issue for most people that ask it to break crypto.