2

I know that it's important to run sc_reduce() first to filter some invalid scalar when I need a private key.

How about public keys in Monero? How can I ensure its format is right?

Please help to answer it, many thanks!

4

sc_reduce just takes a 256 bit number and reduces it mod 𝑙 to yield a scalar of the correct curve order. Nothing special. Any number between 0 and 𝑙 is a valid scalar.

For a point (which is what a public key is) however, the bytes need to first decode to a point and this can vary based on what format has been used to store the point. Assuming it's a compressed 32 byte point, this will consist of the y coordinate (a scalar) combined with a 1 bit sign (used during recovery). Thus after taking the binary of the y coordinate, one must recover the x coordinate. This is a little more involved but covered perfectly well in [ref]. Having recovered x one can then check the resulting x,y point is actually on the curve with a check such as: (-x*x + y*y - 1 - d*x*x*y*y) % q == 0. In practice, you will be using a tried-and-tested library to do any decoding / point operations.

| improve this answer | |
  • 1
    Thank you very much!! It helps! – Mooooo May 7 at 3:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.