Elliptic curves and SNARKs — Past, present and future.

Elliptic curves are used in many proof systems. Some systems (e.g. Bulletproofs) use plain curves (e.g. ed25519). Some (e.g. Groth16, KZG-PLONK) use pairing-friendly curves (e.g. BLS12-381). Some recursive systems require pairing-friendly 2-cycle (e.g. MNT4/6) or 2-chains (e.g. BLS12-377/BW6-761). Some other recursive/folding systems require plain 2-cycle (e.g. Pasta). In this talk we will go through the difference between these curves and why there isn’t a silver bullet curve for all scenarios.