1# Shockwave+
 2
 3## Overview
 4
 5Shockwave is a variant of [Brakedown](https://eprint.iacr.org/2021/1043) 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](https://arxiv.org/pdf/2107.08473.pdf) instead of FFT for low-degree extension of polynomial evaluations.
 6
 7Brakedown 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.
 8
 9Shockwave provides shorter proofs and lower verification time but requires an FFT-friendly field to achieve $O (n\log{n})$ proving time. 
10
11Shockwave+ inherits the smaller proofs of Shockwave and is also *field-agnostic*. It uses the EXTEND operation from [ECFFT](https://arxiv.org/pdf/2107.08473.pdf) to run Reed-Solomon encoding in $n\log{n}$ time.
12
13**Crates**
14[shockwave_plus](/shockwave_plus/) contains the prover/verifier for a zero-knowledge proof of R1CS satisfiability. It’s based on the PIOP from [Spartan](https://eprint.iacr.org/2019/550.pdf), and uses the multilinear polynomial commitment scheme implemented in [tensor_pcs](/tensor_pcs/).
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16**Zero-Knowledge**
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18We 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](https://eprint.iacr.org/2017/872.pdf) to make the polynomial commitment scheme zero-knowledge.
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22The EXTEND operation is implemented in a separate crate [ecfft](https://github.com/DanTehrani/ecfft) and is used in [tensor_pcs](/tensor_pcs/).
23
24## Benchmarks
25
26TBD
27
28## Future work
29
30- [ ]  Support richer frontends (CCS, PLONKish).
31- [ ]  Employ *self-recursion* techniques from [Vortex](https://eprint.iacr.org/2022/1633.pdf)/[Orion](https://eprint.iacr.org/2022/1010.pdf) to make the proofs smaller.
32
33## Run tests
34```bash
35cargo test
36```