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# nova-study |
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Implementation of [Nova](https://eprint.iacr.org/2021/370.pdf) using [arkworks-rs](https://github.com/arkworks-rs/) just for learning purposes. |
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> Warning: Implementation from scratch to learn the internals of Nova. Do not use in production. |
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This repo is an ongoing implementation, not to be used but just to understand and experiment with the internals of the scheme and try experimental combinations. |
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Thanks to [levs57](https://twitter.com/levs57) for clarifications on the Nova folding. |
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#![allow(non_snake_case)]
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#![allow(non_camel_case_types)]
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#![allow(non_upper_case_globals)]
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#![allow(unused)] // TMP
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mod nifs;
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mod pedersen;
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mod r1cs;
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mod transcript;
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mod utils;
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use ark_ec::AffineRepr;
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use ark_std::ops::Add;
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use std::marker::PhantomData;
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use crate::pedersen::Commitment;
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use crate::r1cs::*;
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use crate::transcript::Transcript;
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use crate::utils::*;
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// Phi: φ in the paper (later 𝖴), a folded instance
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pub struct Phi<C: AffineRepr> {
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cmE: Commitment<C>,
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u: C::ScalarField,
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cmW: Commitment<C>,
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x: Vec<C::ScalarField>,
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}
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// FWit: Folded Witness
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pub struct FWit<C: AffineRepr> {
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E: Vec<C::ScalarField>,
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rE: C::ScalarField,
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W: Vec<C::ScalarField>,
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rW: C::ScalarField,
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}
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pub struct NIFS<C: AffineRepr> {
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_phantom: PhantomData<C>,
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}
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impl<C: AffineRepr> NIFS<C> {
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pub fn fold_witness(
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r: C::ScalarField,
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fw1: FWit<C>,
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fw2: FWit<C>,
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T: Vec<C::ScalarField>,
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) -> FWit<C> {
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let r2 = r * r;
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let E: Vec<C::ScalarField> = vec_add(
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// TODO this syntax will be simplified with future operators impl
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vec_add(fw1.E, vector_elem_product(&T, &r)),
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vector_elem_product(&fw2.E, &r2),
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);
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let rE = fw1.rE + r * fw2.rE;
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let W = vec_add(fw1.W, vector_elem_product(&fw2.W, &r));
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let rW = fw1.rW + r * fw2.rW;
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FWit::<C> {
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E: E.into(),
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rE,
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W: W.into(),
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rW,
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}
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}
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pub fn fold_instance(
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r: C::ScalarField,
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phi1: Phi<C>,
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phi2: Phi<C>,
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cmT: Commitment<C>,
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) -> Phi<C> {
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let r2 = r * r;
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let cmE = phi1.cmE.cm + cmT.cm.mul(r) + phi2.cmE.cm.mul(r2);
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let u = phi1.u + r * phi2.u;
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let cmW = phi1.cmW.cm + phi2.cmW.cm.mul(r);
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let x = vec_add(phi1.x, vector_elem_product(&phi2.x, &r));
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Phi::<C> {
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cmE: Commitment::<C> {
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cm: cmE.into(),
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r: phi1.cmE.r,
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},
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u,
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cmW: Commitment::<C> {
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cm: cmW.into(),
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r: phi1.cmW.r,
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},
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x,
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}
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}
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}
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use crate::pedersen;
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use ark_ff::fields::PrimeField;
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use core::ops::Add;
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// this file contains an abstraction of R1CS struct, to later be plugged from arkworks
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// ConstraintSystem or something similar.
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pub struct R1CS<F: PrimeField> {
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pub A: Vec<Vec<F>>,
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pub B: Vec<Vec<F>>,
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pub C: Vec<Vec<F>>,
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}
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pub struct RelaxedR1CS<F: PrimeField> {
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pub ABC: R1CS<F>,
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pub u: F,
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pub E: F,
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}
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impl<F: PrimeField> R1CS<F> {
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pub fn relax(self) -> RelaxedR1CS<F> {
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RelaxedR1CS::<F> {
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ABC: self,
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u: F::one(),
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E: F::zero(),
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}
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}
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}
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impl<F: PrimeField> RelaxedR1CS<F> {
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pub fn fold(self, other: Self, r: F) -> Self {
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unimplemented!();
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}
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}
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