Shockwave+

Overview

Shockwave is a variant of Brakedown that uses Reed-Solomon code instead of a linear-time encodable code. Shockwave+ is an extension of Shockwave that works over all finite fields by using ECFFT instead of FFT for low-degree extension of polynomial evaluations.

Brakedown has a linear-time prover and is field-agnostic (i.e. works over all finite fields), but its proofs are concretely larger than Shockwave’s.

Shockwave provides shorter proofs and lower verification time but requires an FFT-friendly field to achieve $O (n\log{n})$ proving time.

Shockwave+ inherits the smaller proofs of Shockwave and is also field-agnostic. It uses the EXTEND operation from ECFFT to run Reed-Solomon encoding in $n\log{n}$ time.

Crates shockwave_plus contains the prover/verifier for a zero-knowledge proof of R1CS satisfiability. It’s based on the PIOP from Spartan, and uses the multilinear polynomial commitment scheme implemented in tensor_pcs.

Zero-Knowledge

We use the zero-knowledge sum-check protocol from Libra to transform the Spartan PIOP into a zero-knowledge PIOP. And use a technique from BCG+17 to make the polynomial commitment scheme zero-knowledge.

The EXTEND operation is implemented in a separate crate ecfft and is used in tensor_pcs.

Benchmarks

TBD

Future work

• Support richer frontends (CCS, PLONKish).
• Employ self-recursion techniques from Vortex/Orion to make the proofs smaller.

Run tests

cargo test