Hi - I work on proof systems for Mina. Our proof system does not require any trusted setup. It uses a polynomial commitment scheme based on the setupless scheme used in bulletproofs (the version we use is close to the one described in this paper https://eprint.iacr.org/2020/499.pdf), which is based on the hardness of discrete-log.
Some SNARKs use pairing-based polynomial commitment schemes, which require a trusted setup (and some require a trusted setup for other reasons.)
plonk based proof system can take advantage of an existing universal setup (like Powers of Tau ceremony). I’d be curious to know more about how Mina approaches this though.
