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The relevant mathematical function is fixed-base scalar multiplication.
This project contains a crate-per-elliptic curve, and none of them implement scalar multiplication.
Thus I will leave this issue open, noting @str4d has in fact contributed an immaculately written field arithmetic backend for the NIST P-256 elliptic curve, with the caveat that he purposefully was trying to solve the specific problems of point compression and decompression.
I'm not able to find any way to get public key corresponding to any secret key. Is there a way to obtain it?
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