Rust implementation of extension field elements multiplication

hydra/garaga/hints/ecip.py

@@ -107,12 +107,8 @@ def zk_ecip_hint(
     if ec_group_class == G1Point and use_rust:
         pts = []
         c_id = Bs[0].curve_id
-        if c_id == CurveID.BLS12_381:
-            nb = 48
-        else:
-            nb = 32
         for pt in Bs:
-            pts.extend([pt.x.to_bytes(nb, "big"), pt.y.to_bytes(nb, "big")])
+            pts.extend([pt.x, pt.y])
         field_type = get_field_type_from_ec_point(Bs[0])
         field = get_base_field(c_id.value, field_type)
 

hydra/garaga/hints/extf_mul.py

@@ -1,6 +1,7 @@
 import operator
 from functools import reduce
 
+from garaga import garaga_rs
 from garaga.algebra import ModuloCircuitElement, Polynomial, PyFelt
 from garaga.definitions import (
     direct_to_tower,
@@ -19,29 +20,13 @@ def nondeterministic_extension_field_mul_divmod(
     curve_id: int,
     extension_degree: int,
 ) -> tuple[list[PyFelt], list[PyFelt]]:
-
-    Ps = [Polynomial(P) for P in Ps]
     field = get_base_field(curve_id)
-
-    P_irr = get_irreducible_poly(curve_id, extension_degree)
-
-    z_poly = reduce(operator.mul, Ps)  #  Π(Pi)
-    z_polyq, z_polyr = divmod(z_poly, P_irr)
-
-    z_polyr_coeffs = z_polyr.get_coeffs()
-    z_polyq_coeffs = z_polyq.get_coeffs()
-    # assert len(z_polyq_coeffs) <= (
-    #     extension_degree - 1
-    # ), f"len z_polyq_coeffs={len(z_polyq_coeffs)}, degree: {z_polyq.degree()}"
-    assert (
-        len(z_polyr_coeffs) <= extension_degree
-    ), f"len z_polyr_coeffs={len(z_polyr_coeffs)}, degree: {z_polyr.degree()}"
-
-    # Extend polynomials with 0 coefficients to match the expected lengths.
-    # TODO : pass exact expected max degree when len(Ps)>2.
-    z_polyq_coeffs += [field(0)] * (extension_degree - 1 - len(z_polyq_coeffs))
-    z_polyr_coeffs += [field(0)] * (extension_degree - len(z_polyr_coeffs))
-
+    ps = [[c.value for c in P] for P in Ps]
+    q, r = garaga_rs.nondeterministic_extension_field_mul_divmod(
+        curve_id, extension_degree, ps
+    )
+    z_polyq_coeffs = [field(c) for c in q] if len(q) > 0 else [field.zero()]
+    z_polyr_coeffs = [field(c) for c in r] if len(r) > 0 else [field.zero()]
     return (z_polyq_coeffs, z_polyr_coeffs)
 
 

tools/garaga_rs/src/ecip/core.rs

@@ -3,118 +3,89 @@ use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bls12_381::fiel
 use lambdaworks_math::elliptic_curve::short_weierstrass::curves::bn_254::field_extension::BN254PrimeField;
 use lambdaworks_math::field::element::FieldElement;
 use lambdaworks_math::field::traits::IsPrimeField;
-use lambdaworks_math::traits::ByteConversion;
 
 use crate::ecip::curve::{SECP256K1PrimeField, SECP256R1PrimeField, X25519PrimeField};
 use crate::ecip::ff::FF;
 use crate::ecip::g1point::G1Point;
 use crate::ecip::rational_function::FunctionFelt;
 use crate::ecip::rational_function::RationalFunction;
+use crate::io::parse_field_elements_from_list;
 
 use num_bigint::{BigInt, BigUint, ToBigInt};
 
 use super::curve::CurveParamsProvider;
 
 pub fn zk_ecip_hint(
-    list_bytes: Vec<Vec<u8>>,
+    list_values: Vec<BigUint>,
     list_scalars: Vec<BigUint>,
     curve_id: usize,
 ) -> Result<[Vec<String>; 5], String> {
     match curve_id {
         0 => {
-            let list_felts: Vec<FieldElement<BN254PrimeField>> = list_bytes
-                .into_iter()
-                .map(|x| {
-                    FieldElement::<BN254PrimeField>::from_bytes_be(&x)
-                        .map_err(|e| format!("Byte conversion error: {:?}", e))
-                })
-                .collect::<Result<Vec<FieldElement<BN254PrimeField>>, _>>()?;
+            let list_felts = parse_field_elements_from_list::<BN254PrimeField>(&list_values)?;
 
             let points: Vec<G1Point<BN254PrimeField>> = list_felts
                 .chunks(2)
                 .map(|chunk| G1Point::new(chunk[0].clone(), chunk[1].clone()))
                 .collect();
 
-            let scalars: Vec<Vec<i8>> = extract_scalars::<BN254PrimeField>(list_scalars);
-            Ok(run_ecip::<BN254PrimeField>(points, scalars))
+            let dss: Vec<Vec<i8>> = construct_digits_vectors::<BN254PrimeField>(list_scalars);
+            Ok(run_ecip::<BN254PrimeField>(points, dss))
         }
         1 => {
-            let list_felts: Vec<FieldElement<BLS12381PrimeField>> = list_bytes
-                .into_iter()
-                .map(|x| {
-                    FieldElement::<BLS12381PrimeField>::from_bytes_be(&x)
-                        .map_err(|e| format!("Byte conversion error: {:?}", e))
-                })
-                .collect::<Result<Vec<FieldElement<BLS12381PrimeField>>, _>>()?;
+            let list_felts = parse_field_elements_from_list::<BLS12381PrimeField>(&list_values)?;
 
             let points: Vec<G1Point<BLS12381PrimeField>> = list_felts
                 .chunks(2)
                 .map(|chunk| G1Point::new(chunk[0].clone(), chunk[1].clone()))
                 .collect();
 
-            let scalars: Vec<Vec<i8>> = extract_scalars::<BLS12381PrimeField>(list_scalars);
-            Ok(run_ecip::<BLS12381PrimeField>(points, scalars))
+            let dss: Vec<Vec<i8>> = construct_digits_vectors::<BLS12381PrimeField>(list_scalars);
+            Ok(run_ecip::<BLS12381PrimeField>(points, dss))
         }
         2 => {
-            let list_felts: Vec<FieldElement<SECP256K1PrimeField>> = list_bytes
-                .into_iter()
-                .map(|x| {
-                    FieldElement::<SECP256K1PrimeField>::from_bytes_be(&x)
-                        .map_err(|e| format!("Byte conversion error: {:?}", e))
-                })
-                .collect::<Result<Vec<FieldElement<SECP256K1PrimeField>>, _>>()?;
+            let list_felts = parse_field_elements_from_list::<SECP256K1PrimeField>(&list_values)?;
 
             let points: Vec<G1Point<SECP256K1PrimeField>> = list_felts
                 .chunks(2)
                 .map(|chunk| G1Point::new(chunk[0].clone(), chunk[1].clone()))
                 .collect();
 
-            let scalars: Vec<Vec<i8>> = extract_scalars::<SECP256K1PrimeField>(list_scalars);
-            Ok(run_ecip::<SECP256K1PrimeField>(points, scalars))
+            let dss: Vec<Vec<i8>> = construct_digits_vectors::<SECP256K1PrimeField>(list_scalars);
+            Ok(run_ecip::<SECP256K1PrimeField>(points, dss))
         }
         3 => {
-            let list_felts: Vec<FieldElement<SECP256R1PrimeField>> = list_bytes
-                .into_iter()
-                .map(|x| {
-                    FieldElement::<SECP256R1PrimeField>::from_bytes_be(&x)
-                        .map_err(|e| format!("Byte conversion error: {:?}", e))
-                })
-                .collect::<Result<Vec<FieldElement<SECP256R1PrimeField>>, _>>()?;
+            let list_felts = parse_field_elements_from_list::<SECP256R1PrimeField>(&list_values)?;
 
             let points: Vec<G1Point<SECP256R1PrimeField>> = list_felts
                 .chunks(2)
                 .map(|chunk| G1Point::new(chunk[0].clone(), chunk[1].clone()))
                 .collect();
 
-            let scalars: Vec<Vec<i8>> = extract_scalars::<SECP256R1PrimeField>(list_scalars);
-            Ok(run_ecip::<SECP256R1PrimeField>(points, scalars))
+            let dss: Vec<Vec<i8>> = construct_digits_vectors::<SECP256R1PrimeField>(list_scalars);
+            Ok(run_ecip::<SECP256R1PrimeField>(points, dss))
         }
         4 => {
-            let list_felts: Vec<FieldElement<X25519PrimeField>> = list_bytes
-                .into_iter()
-                .map(|x| {
-                    FieldElement::<X25519PrimeField>::from_bytes_be(&x)
-                        .map_err(|e| format!("Byte conversion error: {:?}", e))
-                })
-                .collect::<Result<Vec<FieldElement<X25519PrimeField>>, _>>()?;
+            let list_felts = parse_field_elements_from_list::<X25519PrimeField>(&list_values)?;
 
             let points: Vec<G1Point<X25519PrimeField>> = list_felts
                 .chunks(2)
                 .map(|chunk| G1Point::new(chunk[0].clone(), chunk[1].clone()))
                 .collect();
 
-            let scalars: Vec<Vec<i8>> = extract_scalars::<X25519PrimeField>(list_scalars);
-            Ok(run_ecip::<X25519PrimeField>(points, scalars))
+            let dss: Vec<Vec<i8>> = construct_digits_vectors::<X25519PrimeField>(list_scalars);
+            Ok(run_ecip::<X25519PrimeField>(points, dss))
         }
         _ => Err(String::from("Invalid curve ID")),
     }
 }
 
-fn extract_scalars<F: IsPrimeField + CurveParamsProvider<F>>(list: Vec<BigUint>) -> Vec<Vec<i8>> {
+fn construct_digits_vectors<F: IsPrimeField + CurveParamsProvider<F>>(
+    list: Vec<BigUint>,
+) -> Vec<Vec<i8>> {
     let mut dss_ = Vec::new();
 
-    for i in 0..list.len() {
-        let scalar_biguint = list[i].clone();
+    for scalar_biguint in list {
         let neg_3_digits = neg_3_base_le(scalar_biguint);
         dss_.push(neg_3_digits);
     }

tools/garaga_rs/src/ecip/curve.rs

@@ -5,10 +5,12 @@ use lambdaworks_math::field::fields::montgomery_backed_prime_fields::{
     IsModulus, MontgomeryBackendPrimeField,
 };
 
+use crate::ecip::polynomial::Polynomial;
 use lambdaworks_math::field::traits::IsPrimeField;
 use lambdaworks_math::unsigned_integer::element::U256;
 use num_bigint::BigUint;
 use std::cmp::PartialEq;
+use std::collections::HashMap;
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
 pub enum CurveID {
@@ -72,6 +74,21 @@ pub struct CurveParams<F: IsPrimeField> {
     pub g_y: FieldElement<F>,
     pub n: FieldElement<F>, // Order of the curve
     pub h: u32,             // Cofactor
+    pub irreducible_polys: HashMap<usize, &'static [i8]>,
+}
+
+pub fn get_irreducible_poly<F: IsPrimeField + CurveParamsProvider<F>>(
+    ext_degree: usize,
+) -> Polynomial<F> {
+    let coeffs = (F::get_curve_params().irreducible_polys)[&ext_degree];
+    fn lift<F: IsPrimeField>(c: i8) -> FieldElement<F> {
+        if c >= 0 {
+            FieldElement::from(c as u64)
+        } else {
+            -FieldElement::from(-c as u64)
+        }
+    }
+    return Polynomial::new(coeffs.iter().map(|x| lift::<F>(*x)).collect());
 }
 
 /// A trait that provides curve parameters for a specific field type.
@@ -99,6 +116,7 @@ impl CurveParamsProvider<SECP256K1PrimeField> for SECP256K1PrimeField {
                 "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",
             ),
             h: 1,
+            irreducible_polys: HashMap::from([]), // Provide appropriate values here
         }
     }
 }
@@ -122,6 +140,7 @@ impl CurveParamsProvider<SECP256R1PrimeField> for SECP256R1PrimeField {
                 "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
             ),
             h: 1,
+            irreducible_polys: HashMap::from([]), // Provide appropriate values here
         }
     }
 }
@@ -143,6 +162,7 @@ impl CurveParamsProvider<X25519PrimeField> for X25519PrimeField {
                 "1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED",
             ),
             h: 8,
+            irreducible_polys: HashMap::from([]), // Provide appropriate values here
         }
     }
 }
@@ -158,6 +178,10 @@ impl CurveParamsProvider<BN254PrimeField> for BN254PrimeField {
             g_y: FieldElement::from_hex_unchecked("2"), // Replace with actual 'g_y'
             n: FieldElement::from_hex_unchecked("1"),   // Replace with actual 'n'
             h: 1,                                       // Replace with actual 'h'
+            irreducible_polys: HashMap::from([
+                (6, [82, 0, 0, -18, 0, 0, 1].as_slice()),
+                (12, [82, 0, 0, 0, 0, 0, -18, 0, 0, 0, 0, 0, 1].as_slice()),
+            ]),
         }
     }
 }
@@ -173,6 +197,10 @@ impl CurveParamsProvider<BLS12381PrimeField> for BLS12381PrimeField {
             g_y: FieldElement::from_hex_unchecked("2"), // Replace with actual 'g_y'
             n: FieldElement::from_hex_unchecked("1"),   // Replace with actual 'n'
             h: 1,                                       // Replace with actual 'h'
+            irreducible_polys: HashMap::from([
+                (6, [2, 0, 0, -2, 0, 0, 1].as_slice()),
+                (12, [2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1].as_slice()),
+            ]),
         }
     }
 }

tools/garaga_rs/src/ecip/polynomial.rs

@@ -80,6 +80,10 @@ impl<F: IsPrimeField> Polynomial<F> {
         Polynomial::new(vec![FieldElement::<F>::zero()])
     }
 
+    pub fn one() -> Self {
+        Polynomial::new(vec![FieldElement::<F>::one()])
+    }
+
     pub fn mul_with_ref(&self, other: &Polynomial<F>) -> Polynomial<F> {
         if self.degree() == -1 || other.degree() == -1 {
             return Polynomial::zero();
@@ -142,7 +146,7 @@ impl<F: IsPrimeField> Polynomial<F> {
         for (i, coeff) in self.coefficients.iter().enumerate().skip(1) {
             let u_64 = i as u64;
             let degree = &FieldElement::<F>::from(u_64);
-            new_coeffs[i - 1] = *(&coeff) * degree;
+            new_coeffs[i - 1] = coeff * degree;
         }
         Polynomial::new(new_coeffs)
     }

tools/garaga_rs/src/extf_mul.rs

@@ -0,0 +1,30 @@
+use crate::ecip::{
+    curve::{get_irreducible_poly, CurveParamsProvider},
+    polynomial::{pad_with_zero_coefficients_to_length, Polynomial},
+};
+use lambdaworks_math::field::traits::IsPrimeField;
+
+// Returns (Q(X), R(X)) such that Π(Pi)(X) = Q(X) * P_irr(X) + R(X), for a given curve and extension degree.
+// R(X) is the result of the multiplication in the extension field.
+// Q(X) is used for verification.
+pub fn nondeterministic_extension_field_mul_divmod<F: IsPrimeField + CurveParamsProvider<F>>(
+    ext_degree: usize,
+    ps: Vec<Polynomial<F>>,
+) -> (Polynomial<F>, Polynomial<F>) {
+    let mut z_poly = Polynomial::one();
+    for poly in ps {
+        z_poly = z_poly.mul_with_ref(&poly);
+    }
+
+    let p_irr = get_irreducible_poly(ext_degree);
+
+    let (z_polyq, mut z_polyr) = z_poly.divmod(&p_irr);
+    assert!(z_polyr.coefficients.len() <= ext_degree);
+
+    // Extend polynomial with 0 coefficients to match the expected length.
+    if z_polyr.coefficients.len() < ext_degree {
+        pad_with_zero_coefficients_to_length(&mut z_polyr, ext_degree);
+    }
+
+    (z_polyq, z_polyr)
+}

tools/garaga_rs/src/io.rs

@@ -0,0 +1,24 @@
+use lambdaworks_math::field::element::FieldElement;
+use lambdaworks_math::field::traits::IsPrimeField;
+use lambdaworks_math::traits::ByteConversion;
+use num_bigint::BigUint;
+
+pub fn parse_field_elements_from_list<F: IsPrimeField>(
+    coeffs: &[BigUint],
+) -> Result<Vec<FieldElement<F>>, String>
+where
+    FieldElement<F>: ByteConversion,
+{
+    let length = (F::field_bit_size() + 7) / 8;
+    coeffs
+        .iter()
+        .map(|x| {
+            let bytes = x.to_bytes_be();
+            let pad_length = length.saturating_sub(bytes.len());
+            let mut padded_bytes = vec![0u8; pad_length];
+            padded_bytes.extend(bytes);
+            FieldElement::from_bytes_be(&padded_bytes)
+                .map_err(|e| format!("Byte conversion error: {:?}", e))
+        })
+        .collect()
+}