Our Cryptographic Stack
For all zero-knowledge proofs, we use Bulletproofs. We chose this proving system as it has very low relative prover latency and is fully transparent, meaning that it does not require a trusted setup like Groth16. In addition, it is friendly to collaborative proving, unlike more modern transparent schemes like FRI / STARKs. Bulletproofs are not succinct (so, technically Renegade does not use SNARKs, just NIZKs), but we currently use StarkWare for scalability, so the relatively-high verifier complexity is no issue.
For MPC, we use maliciously-secure two-party SPDZ. We chose a fast secret-sharing-style scheme, as our circuits are arithmetic and we may potentially expand to more than two parties in the future.
For hashes, we use arithmetic-friendly Poseidon everywhere. For cross-proof witness consistency checks, we use Pedersen commitments, as we can save work by re-using the Bulletproof commitments.
For public-key cryptography (used to encrypt matching outputs and to encrypt plaintext wallets to store them on-chain), we use ElGamal, usually combined with Poseidon hashes to turn asymmetric schemes into faster symmetric ones. ElGamal also has the benefit of being key-private, so that third-party observers cannot determine the destination address of any tokens.