Fractal: Post-Quantum And Transparent Recursive Proofs From Holography

We present a new methodology to efficiently realize recursive composition of succinct non-interactive arguments of knowledge (SNARKs). Prior to this work, the only known methodology relied on pairing-based SNARKs instantiated on cycles of pairing-friendly elliptic curves, an expensive algebraic object. Our methodology does not rely on any special algebraic objects and, moreover, achieves new desirable properties: it is post-quantum and it is transparent (the setup is public coin).We exploit the fact that recursive composition is simpler for SNARKs with preprocessing, and the core of our work is obtaining a preprocessing zkSNARK for rank-1 constraint satisfiability (R1CS) that is postquantum and transparent. We obtain this latter by establishing a connection between holography and preprocessing in the random oracle model, and then constructing a holographic proof for R1CS.We experimentally validate our methodology, demonstrating feasibility in practice. (The full version of this work is available at https://ia. cr/2019/1076.)