I don’t really know much about Monero and most of the info below is based on some quick googling, so it may not be very accurate or I may reach to the wrong conclusion.
My understanding is that they use this ring signature scheme to create transactions. In particular, it seems they use Curve25519 as the underlying elliptic curve, which is the same curve used in Ed25519 (aka EdDSA on Curve25519). However, the two signature schemes are fundamentally different, so I think it will not be possible to leverage the tEdDSA protocol used in the IC.
Signatures aside, I think there may be some other challenges. Monero transactions seem to include other things on top of the ring signature (See here for example):
- a ring signature per input;
- a unique key image for every real input of the transaction;
- Pedersen commitments for every input and output;
- Bulletproofs for the outputs.
The above would make it harder to create tx entirely on-chain, as they involve private information, aside from the secret signing key. Doing them on-chain would require a customized MPC protocol, which may not be very scalable in the end. Another thing that it is not very clear to me at this point is what would be the privacy of those on-chain transactions, although this may not actually be a big problem.
Do you happen to know if Monero also supports standard signature schemes like ECDSA/ Ed25519/EdDSA?