I came across a post stating that Monero uses the Borromean Ring Signature scheme to hide the amounts. So what signature scheme is used to sign the transactions?

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Pedersen Commitments of Monero output amounts are published, instead of publishing the actual amounts in the clear. Borromean Ring Signatures are used for range proofs on those Pedersen Commitments, which prove the amounts are not negative.

Monero signs transactions with MLSAG signatures. See https://lab.getmonero.org/pubs/MRL-0005.pdf

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