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Reading the BIP 32 section of how to generate Public child key from Public parent key, I got stuck in the following:

The returned child key Ki is point(parse256(IL)) + Kpar.

As I could understand point(p) is the Elliptical Curve multiplication which will output X and Y coords, so how can I add them with Kpar? Also, it should return me a Compressed public key right?

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A public key is an elliptic curve point. So K_par is also an elliptic curve point. You can then just do a EC point add to add the point given by point(p) with K_par to get a new point, which is also a public key.

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  • So if I have K_par as compressed I need to recover Y value using ModPow(a, (p+1)/4, p) ?
    – Allan Romanato
    Apr 8, 2020 at 20:32
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    @AllanRomanato Yes, converting a compressed serialization of a point to a point requires recovering the Y coordinate (and negating if necessary, to make the oddness match up).
    – Pieter Wuille
    Apr 8, 2020 at 20:42
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The addition operation in that context refers to the Elliptic Curve group operation ("point addition").

The child key returned is a point, not a serialization. So the question of whether it's compressed or not is not technically relevant. In practice, every time a serialization of a point is used in BIP32, it is compressed though.

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