Pedersen commitments in Monero use two different generator points to ensure security. One point masks the amount while the other point, with an unknown factor, ensures that the commitment remains secure. If the factor were known, it could potentially compromise the security by linking the commitments to the actual amounts.
If switch H to G and reduce the original equation we get this
C = (y + b)*G
using this it seems like everything should still work just fine. we still have the pseudo random mask y and shouldn't be able to calculate b from C. where would the vulnerability be if we could reduce the original equation like this?
