I have 2 key pairs $(x_1, y_1)$, $(x_2, y_2)$.
I also have $a = $random 256-bit array and $b = $256-bit of defined values from me.
I know the values for $(x_1, y_1)$, $x_2$ and $b$. But I miss the value of $y_2$ (private key).
I have the following term:
// * = scalarmult_vartime (a * sha512 (a + b) [0-32]) + x1 = x2
Can I solve this equation for $y_2$? $a$ is flexible, so maybe it can be derived from $b$?
Of course, I know that I can not get a private key from a public bookmark, but in this case the publickey is the sum of the addition of a publickey (to which I know the private key) with a value defined to me.
(This is a simplified version of ECC Curve25519: How to generate this kind of private key? / Strange key exchange mechanism)