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The cryptonote whitepaper uses a G constant, as a base point, to calculate various operations, but I don't understand where this constant actually comes from. Is it just a random point on an elliptical curve?

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G is defined in the definition of the signature scheme, Edwards-curve Digital Signature Algorithm (EdDSA)in the case of Cryptonote and Monero.

As explained in this answer in crypo.SE :

the base point is chosen pretty arbitrarily. As described in the Ed25519 paper, it arises from the choice u=9 in the original Curve25519 paper

The details of this choice are probably out of the scope of Monero.SE and more suited to crypto.SE.

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