PayneJoe / PNova

Plonkish Nova implementation along with advanced features

PNova

As we know the original Nova implementation is based on R1CS. Our target is to implement a plonkish versioned NOVA, folding multiple Customer Gate/Lookup instances into one respectively. Thereafter, we can feed the folded instances into the relaxed Plonk SNARK.

Intuition About Plonkish Nova

Few Thoughts

• Jellyfish(TurboPlonk/UltraPlonk) supporting relaxed plonkish circuit SAT
• KZG pcs for primary proof over BN254 curve, and IPA pcs for secondary proof over Grumpkin curve
• Poseidon Circuit based Jellyfish
• Keccak Transcript
• Native verification for final first proof (Bn254 curve)
• Non-native verification for final secondary proof (Grumpkin curve)

Details About Implementation

Before intensive coding we will give more comprehensive details as much as possible, including some attestation code:

• Thinking in Folding Scheme: Cross Term in R1CS
• Thinking in Folding Scheme: Cross Term in Plonk
• Thinking in Folding Scheme: Cycle Curves
• Plonk From Scratch

Roadmap

Features	Status	Repo	Doc
Stage One
Uncompressed Relaxed UltraPlonk Backend/Frontend	Ongoing	relaxed-stage-1	Relaxed Plonk Step by Step
Compressed Relaxed UltraPlonk Backend/Frontend	Ongoing
Stage Two
Uncompressed NIFS	Ongoing	ark-nifs	Plonkish Nova
Uncompressed Cycle-Curve Circuits	TODO
Support PLookup/LogUp Folding	TODO
Stage Three
compressed NIFS	TODO
Compressed Cycle-Curve Circuits	TODO
Stage Four
Cycle-fold Delegated Circuit	TODO
Improving logUp Argument with GKR	TODO
Memory Check Based Lookup Argument	TODO
GKR Based Permutation Check	TODO

Progress of Specific Task

Day	Task	Status
11/08/23	Relaxed Plonk / Data Structure	$\checkmark$
11/10/23	Relaxed Plonk / Frontend Dev	$\checkmark$
11/12/23	Relaxed Plonk / Frontend Testing	$\checkmark$
11/15/23	Relaxed Plonk / Backend Dev	$\checkmark$
12/05/23	Transcript Dev	$\checkmark$
12/06/23	Poseidon RO Dev	$\checkmark$
12/07/23	PCS Dev	$\checkmark$
12/08/23	NIFS Dev	-
12/08/23	Poseidon Circuit RO Dev	-
12/08/23	Cycle Circuit Dev	-
12/09/23	Refactor ark-nifs (arkworks + jellyfish)	$\checkmark$
12/10/23	In-depth of secondary(delegation) circuit	-

References

[1] NOVA: https://eprint.iacr.org/2021/370.pdf

[2] CycleFold: https://eprint.iacr.org/2023/1192.pdf

[3] Protostar: https://eprint.iacr.org/2023/620.pdf

[4] Multivariate lookup: https://eprint.iacr.org/2022/1530.pdf

[5] Cached quotients: https://eprint.iacr.org/2022/1763.pdf

[6] Improving logUp argument with GKR: https://eprint.iacr.org/2023/1284.pdf