So I'm trying to figure out how ringCT works, but with so much data that needs to be used to make a transaction, how does Monero keep transactions from being seen if they are spent or not in ring signatures?
For example, lets say we have a transaction A that has a Pedersen commitment like,
54315648671857041765176828750544187674052177887109727513765797498108209248246, 15377053119273270820956237130367905799861881946971335076519717600451380609362, I will reference this point as A.
Now, we have A, but lets say we want to make two new transactions to split A. B and C will be those transactions.
In order to check all inputs = all outputs, we need to add every input and every output commitment to see if they equal up.
So basically, A = B + C, where B and C are a commitments.
But to do that publicly would expose A? Meaning we just need to find a transaction in the ring with an output that's commitment is A.
Even if we had more transactions, we would still need all transactions commitments to add them together, meaning anyone can see them in the transaction.
So what does Monero do to not let that happen? I would imagine it somehow hides the commitments but how is that possible? Without publicly exposing A there's no way to validate coins.