Families of SNARK-friendly 2-chains of elliptic curves

In this talk, we first are interested in families of 2-chains in which the BW6-761 curve would fall. We present a family of BW6 curves from any BLS12 curve and derive generic formulas, in terms of the BLS12 curve seed u, and integer parameters ht,hy. We extend this work to a 2-chain family of BW6 curves from BLS24 curves. To achieve higher levels of security in the target finite field of the outer curves, we compare a larger field characteristic thanks to larger parameters ht,hy, to the larger embedding degrees 8 and 12 obtained with Cocks-Pinch curves. Finally, we argue that the BLS12 and BLS24 based families are respectively tailored for Groth’16 and KZG-based SNARKs recursive proof composition, and we present a short list of curves with an optimized implementation along with benchmarks.