From 69d0f5c5baff8d0d76dbae153ca43c51ff85a2d9 Mon Sep 17 00:00:00 2001
From: arnaucube <root@arnaucube.com>
Date: Thu, 27 Jul 2023 23:30:34 +0200
Subject: [PATCH] add pow_i & pow_i_over_x methods

---
 src/lib.rs         |  1 +
 src/protogalaxy.rs | 90 ++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 91 insertions(+)
 create mode 100644 src/protogalaxy.rs

diff --git a/src/lib.rs b/src/lib.rs
index 609383e..e24a480 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -4,5 +4,6 @@
 #![allow(dead_code)] // TMP
 
 pub mod pedersen;
+pub mod protogalaxy;
 pub mod transcript;
 pub mod utils;
diff --git a/src/protogalaxy.rs b/src/protogalaxy.rs
new file mode 100644
index 0000000..280fc43
--- /dev/null
+++ b/src/protogalaxy.rs
@@ -0,0 +1,90 @@
+use ark_crypto_primitives::sponge::Absorb;
+use ark_ec::{CurveGroup, Group};
+use ark_ff::fields::PrimeField;
+use ark_std::log2;
+use ark_std::{One, Zero};
+use std::marker::PhantomData;
+use std::ops::Add;
+
+use ark_poly::{univariate::SparsePolynomial, Polynomial};
+
+use crate::pedersen::{Commitment, Params as PedersenParams, Pedersen, Proof as PedersenProof};
+use crate::transcript::Transcript;
+use crate::utils::*;
+
+// naive impl of pow_i for betas, assuming that betas=(b, b^2, b^4, ..., b^{2^{t-1}})
+fn pow_i<F: PrimeField>(i: usize, betas: &Vec<F>) -> F {
+    // WIP check if makes more sense to do it with ifs instead of arithmetic
+
+    let n = 2_u64.pow(betas.len() as u32);
+    let b = bit_decompose(i as u64, n as usize);
+
+    let mut r: F = F::one();
+    for (j, beta_i) in betas.iter().enumerate() {
+        let mut b_j = F::zero();
+        if b[j] {
+            b_j = F::one();
+        }
+        r *= (F::one() - b_j) + b_j * betas[j];
+    }
+    r
+}
+
+fn pow_i_over_x<F: PrimeField>(i: usize, betas: &Vec<F>, deltas: &Vec<F>) -> SparsePolynomial<F> {
+    assert_eq!(betas.len(), deltas.len());
+
+    let n = 2_u64.pow(betas.len() as u32);
+    let b = bit_decompose(i as u64, n as usize);
+
+    let mut r: SparsePolynomial<F> =
+        SparsePolynomial::<F>::from_coefficients_vec(vec![(0, F::one())]); // start with r(x) = 1
+    for (j, beta_i) in betas.iter().enumerate() {
+        if b[j] {
+            let curr: SparsePolynomial<F> =
+                SparsePolynomial::<F>::from_coefficients_vec(vec![(0, betas[j]), (1, deltas[j])]);
+            r = r.mul(&curr);
+        }
+    }
+    r
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::pedersen::Pedersen;
+    use crate::transcript::poseidon_test_config;
+    use ark_bls12_381::{Fr, G1Projective};
+    use ark_std::One;
+    use ark_std::UniformRand;
+
+    #[test]
+    fn test_pow_i() {
+        let mut rng = ark_std::test_rng();
+        let t = 4;
+        let n = 16;
+        let beta = Fr::rand(&mut rng);
+        let betas = powers_of_beta(beta, t);
+        let not_betas = all_powers(beta, n);
+
+        for i in 0..n {
+            assert_eq!(pow_i(i, &betas), not_betas[i]);
+        }
+    }
+
+    #[test]
+    fn test_pow_i_over_x() {
+        let mut rng = ark_std::test_rng();
+        let t = 3;
+        let n = 8;
+        // let beta = Fr::rand(&mut rng);
+        // let delta = Fr::rand(&mut rng);
+        let beta = Fr::from(3);
+        let delta = Fr::from(5);
+        let betas = powers_of_beta(beta, t);
+        let deltas = powers_of_beta(delta, t);
+
+        // for i in 0..n {
+        //     dbg!(pow_i_over_x(i, &betas, &deltas));
+        // }
+    }
+}