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Question about ECC Point Addition



I have a question about ECC Point addition from the intro document in the
grin repository:

Under "Transacting with MimbleWimble" a new curve G is introduced:

> For these reasons, we introduce a second ECC curve *G* and a
> private key *r* used as a *blinding factor*.

And this curve G is used for Point addition:

> r*G + v*H

Two questions, are G and H in the same group in secp256k1? That seems to be
the construction Greg Maxwell made in his Confidential Transactions paper
for Pedersen Commitments:

If it is not, then is G a different curve altogether? As in, not secp256k1?
In that case, how is Point Addition defined between points on different


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