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So the calculations for secp256k1 affirm to the formula y² = (x³ * ax * b) mod p of which is said to be impossible to calculate (as is) because of arbitrary large numbers involved.

Hypothetically if one was to be able to calculate arbitrary values while going about the formula y² = (x³ * ax * b) mod p under this exact mathematical context /formula flow -- (meaning no use of ADD(), DOUBLE() functions as popularly adopted whilst calculating publicKey coordinates.)

Q1. What would this equate to?

Q2. Where does G ^ k come in ( in regards to the formula y² = (x³ * ax * b) mod p)?

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    The equation is y^2 = x^3 + a*x + b (mod p) (and for secp256k1, a=0 and b=7). Further, it is absolutely trivial to solve it, any computer algebra software package can do that for you. The difficulty of solving the discrete logarithm (finding how many times point addition was performed to go from one point to another) has nothing to do with the difficulty of solving this equation. Aug 5, 2023 at 1:15

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