From 61c848f055f0f65d3fc38ace35d2796c359ede02 Mon Sep 17 00:00:00 2001
From: arnaucube <root@arnaucube.com>
Date: Sun, 5 Mar 2023 10:42:17 +0100
Subject: [PATCH] Add poly split, start prover

---
 src/lib.rs | 100 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 100 insertions(+)
 create mode 100644 src/lib.rs

diff --git a/src/lib.rs b/src/lib.rs
new file mode 100644
index 0000000..d7a846e
--- /dev/null
+++ b/src/lib.rs
@@ -0,0 +1,100 @@
+#![allow(non_snake_case)]
+
+pub mod merkletree;
+use merkletree::{MerkleTreePoseidon as MT, Params as MTParams};
+
+use ark_ff::PrimeField;
+use ark_poly::{univariate::DensePolynomial, UVPolynomial};
+use ark_std::log2;
+use ark_std::marker::PhantomData;
+use ark_std::ops::Mul;
+use ark_std::{rand::Rng, UniformRand};
+
+pub struct FRI<F: PrimeField, P: UVPolynomial<F>> {
+    _f: PhantomData<F>,
+    _poly: PhantomData<P>,
+}
+
+impl<F: PrimeField, P: UVPolynomial<F>> FRI<F, P> {
+    pub fn new() -> Self {
+        Self {
+            _f: PhantomData,
+            _poly: PhantomData,
+        }
+    }
+
+    pub fn split(p: &P) -> (P, P) {
+        // let d = p.degree() + 1;
+        let d = p.coeffs().len();
+        if (d != 0) && (d & (d - 1) != 0) {
+            println!("d={:?}", d);
+            panic!("d should be a power of 2");
+        }
+
+        let coeffs = p.coeffs();
+        let odd: Vec<F> = coeffs.iter().step_by(2).cloned().collect();
+        let even: Vec<F> = coeffs.iter().skip(1).step_by(2).cloned().collect();
+
+        return (
+            P::from_coefficients_vec(odd),
+            P::from_coefficients_vec(even),
+        );
+    }
+
+    pub fn prove<R: Rng>(rng: &mut R, p: &P) -> (Vec<F>, [F; 2]) {
+        // f_0(x) = fL_0(x^2) + x fR_0(x^2)
+        let mut f_i1 = p.clone();
+
+        // TODO challenge a_0
+        let mut f_is: Vec<P> = Vec::new();
+        f_is.push(p.clone());
+        let mut commitments: Vec<F> = Vec::new();
+        let mut mts: Vec<MT<F>> = Vec::new();
+        while f_i1.degree() > 1 {
+            let alpha_i = F::from(3_u64); // TODO: WIP, defined by Verifier (well, hash transcript)
+
+            let (fL_i, fR_i) = Self::split(&f_i1);
+
+            // compute f_{i+1}(x) = fL_i(x) + alpha_i * fR_i(x)
+            let aux = DensePolynomial::from_coefficients_slice(fR_i.coeffs());
+            f_i1 = fL_i.clone() + P::from_coefficients_slice(aux.mul(alpha_i).coeffs());
+            f_is.push(f_i1.clone());
+        }
+        let (fL_i, fR_i) = Self::split(&f_i1);
+        let constant_fL_l: F = fL_i.coeffs()[0].clone();
+        let constant_fR_l: F = fR_i.coeffs()[0].clone();
+
+        // TODO evaluate f_i(z^{2^i})
+        let evals: Vec<F> = Vec::new();
+
+        (evals, [constant_fL_l, constant_fR_l])
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use ark_ff::Field;
+    use ark_std::UniformRand;
+    pub type Fr = ark_bn254::Fr; // scalar field
+    use ark_poly::univariate::DensePolynomial;
+    use ark_poly::Polynomial;
+
+    #[test]
+    fn test_split() {
+        let mut rng = ark_std::test_rng();
+        let deg = 7;
+        let p = DensePolynomial::<Fr>::rand(deg, &mut rng);
+        assert_eq!(p.degree(), deg);
+
+        type FRIC = FRI<Fr, DensePolynomial<Fr>>;
+        let (pL, pR) = FRIC::split(&p);
+
+        // check that f(z) == fL(x^2) + x * fR(x^2), for a rand z
+        let z = Fr::rand(&mut rng);
+        assert_eq!(
+            p.evaluate(&z),
+            pL.evaluate(&z.square()) + z * pR.evaluate(&z.square())
+        );
+    }
+}