Implement fft_g1

nomos-da/kzgrs/Cargo.toml

@@ -15,6 +15,7 @@ ark-poly = { version = "0.4.2" }
 ark-poly-commit = { version = "0.4.0" }
 ark-serialize = { version = "0.4" }
 blst = "0.3.11"
+derive_more = "0.99"
 num-bigint = "0.4.4"
 thiserror = "1.0.58"
 num-traits = "0.2.18"

nomos-da/kzgrs/src/fft.rs

@@ -0,0 +1,49 @@
+use ark_bls12_381::{Fr, G1Affine};
+use ark_ec::CurveGroup;
+
+pub fn fft_g1(vals: &[G1Affine], roots_of_unity: &[Fr]) -> Vec<G1Affine> {
+    if vals.len() == 1 {
+        return vals.to_vec();
+    }
+    let half_roots: Vec<_> = roots_of_unity.iter().step_by(2).copied().collect();
+
+    let l = fft_g1(
+        vals.iter()
+            .step_by(2)
+            .copied()
+            .collect::<Vec<_>>()
+            .as_slice(),
+        half_roots.as_slice(),
+    );
+
+    let r = fft_g1(
+        vals.iter()
+            .skip(1)
+            .step_by(2)
+            .copied()
+            .collect::<Vec<_>>()
+            .as_slice(),
+        half_roots.as_slice(),
+    );
+
+    let y_times_root = r
+        .into_iter()
+        .cycle()
+        .enumerate()
+        .map(|(i, y)| (y * roots_of_unity[i % vals.len()]).into_affine());
+
+    l.into_iter()
+        .cycle()
+        .take(vals.len())
+        .zip(y_times_root)
+        .enumerate()
+        .map(|(i, (x, y_times_root))| {
+            if i < vals.len() / 2 {
+                x + y_times_root
+            } else {
+                x - y_times_root
+            }
+            .into_affine()
+        })
+        .collect()
+}

nomos-da/kzgrs/src/fk20.rs

@@ -0,0 +1,20 @@
+use crate::{GlobalParameters, Polynomial, Proof};
+use ark_bls12_381::{Bls12_381, Fq, Fr, G1Affine, G1Projective};
+use ark_ec::mnt4::G1Prepared;
+use ark_ec::{AffineRepr, CurveGroup};
+
+use ark_poly::univariate::DensePolynomial;
+use ark_poly::{EvaluationDomain, Radix2EvaluationDomain};
+use num_traits::Zero;
+fn toeplitz1(global_parameters: &GlobalParameters, polynomial_degree: usize) -> Vec<G1Projective> {
+    debug_assert_eq!(global_parameters.powers_of_g.len(), polynomial_degree);
+    debug_assert!(polynomial_degree.is_power_of_two());
+    unimplemented!()
+}
+
+pub fn fk20_batch_generate_elements_proofs(
+    polynomial: &DensePolynomial<Fr>,
+    global_parameters: &GlobalParameters,
+) -> Vec<Proof> {
+    unimplemented!()
+}

nomos-da/kzgrs/src/lib.rs

@@ -1,4 +1,6 @@
 pub mod common;
+mod fft;
+mod fk20;
 pub mod global_parameters;
 pub mod kzg;
 pub mod rs;