Use custom polynomial

da/kzg_rs/kzg.py

@@ -15,7 +15,7 @@ def bytes_to_polynomial(b: bytearray) -> Polynomial:
     Convert bytes to list of BLS field scalars.
     """
     assert len(b) % BYTES_PER_FIELD_ELEMENT == 0
-    return Polynomial([int(bytes_to_bls_field(b)) for b in batched(b, int(BYTES_PER_FIELD_ELEMENT))])
+    return Polynomial([int(bytes_to_bls_field(b)) for b in batched(b, int(BYTES_PER_FIELD_ELEMENT))], BLS_MODULUS)
 
 
 def g1_linear_combination(polynomial: Polynomial[BLSFieldElement], global_parameters: Sequence[G1]) -> Commitment:
@@ -27,7 +27,7 @@ def g1_linear_combination(polynomial: Polynomial[BLSFieldElement], global_parame
     assert len(polynomial) <= len(global_parameters)
     point = reduce(
         bls.add,
-        (bls.multiply(g, p) for g, p in zip(global_parameters, polynomial.coef)),
+        (bls.multiply(g, p) for g, p in zip(global_parameters, polynomial)),
         bls.Z1()
     )
     return Commitment(bls.G1_to_bytes48(point))
@@ -44,8 +44,7 @@ def generate_element_proof(
         global_parameters: Sequence[G1]
 ) -> Proof:
     # compute a witness polynomial in that satisfies `witness(x) = (f(x)-v)/(x-u)`
-    f_x_v = polynomial - Polynomial([polynomial.eval(int(element)) % BLS_MODULUS])
-    x_u = Polynomial([-element, BLSFieldElement(1)])
-    witness = f_x_v // x_u
-    witness = Polynomial(list(BLSFieldElement(int(x) % BLS_MODULUS) for x in reversed(witness) if x != inf))
+    f_x_v = polynomial - Polynomial([polynomial.eval(int(element)) % BLS_MODULUS], BLS_MODULUS)
+    x_u = Polynomial([-element, BLSFieldElement(1)], BLS_MODULUS)
+    witness, _ = f_x_v / x_u
     return g1_linear_combination(witness, global_parameters)

da/kzg_rs/poly.py

@@ -1,22 +1,69 @@
-from typing import Self, List
-from eth2spec.eip7594.mainnet import BLS_MODULUS
-import numpy as np
-from sympy import ntt, intt
+class Polynomial[T]:
+    def __init__(self, coefficients, modulus):
+        self.coefficients = coefficients
+        self.modulus = modulus
 
+    def __repr__(self):
+        return "Polynomial({}, modulus={})".format(self.coefficients, self.modulus)
 
-class Polynomial[T](np.polynomial.Polynomial):
-    def __init__(self, coef, domain=None, window=None, symbol="x"):
-        self.coef = coef
-        super().__init__(coef, domain, window, symbol)
+    def __add__(self, other):
+        return Polynomial(
+            [(a + b) % self.modulus for a, b in zip(self.coefficients, other.coefficients)],
+            self.modulus
+        )
 
-    def eval(self, x: T) -> T:
-        return np.polyval(self, x)
+    def __sub__(self, other):
+        return Polynomial(
+            [(a - b) % self.modulus for a, b in zip(self.coefficients, other.coefficients)],
+            self.modulus
+        )
 
-    def evaluation_form(self, modulus=BLS_MODULUS) -> Self:
-        return Polynomial(intt(reversed(self), prime=modulus))
+    def __mul__(self, other):
+        result = [0] * (len(self.coefficients) + len(other.coefficients) - 1)
+        for i in range(len(self.coefficients)):
+            for j in range(len(other.coefficients)):
+                result[i + j] = (result[i + j] + self.coefficients[i] * other.coefficients[j]) % self.modulus
+        return Polynomial(result, self.modulus)
 
-    # def __truediv__(self, other):
-    #     return Polynomial(list(reversed(np.polydiv(list(reversed(self.coef)), list(reversed(other.coef))))))
+    def divide(self, other):
+        if not isinstance(other, Polynomial):
+            raise ValueError("Unsupported type for division.")
+
+        dividend = list(self.coefficients)
+        divisor = list(other.coefficients)
+
+        quotient = []
+        remainder = dividend
+
+        while len(remainder) >= len(divisor):
+            factor = remainder[-1] * pow(divisor[-1], -1, self.modulus) % self.modulus
+            quotient.insert(0, factor)
+
+            # Subtract divisor * factor from remainder
+            for i in range(len(divisor)):
+                remainder[len(remainder) - len(divisor) + i] -= divisor[i] * factor
+                remainder[len(remainder) - len(divisor) + i] %= self.modulus
+
+            # Remove leading zeros from remainder
+            while remainder and remainder[-1] == 0:
+                remainder.pop()
+
+        return Polynomial(quotient, self.modulus), Polynomial(remainder, self.modulus)
+
+    def __truediv__(self, other):
+        return self.divide(other)
+
+    def __neg__(self):
+        return Polynomial([-1 * c for c in self.coefficients], self.modulus)
+
+    def __len__(self):
+        return len(self.coefficients)
+
+    def __iter__(self):
+        return iter(self.coefficients)
 
     def __getitem__(self, item):
-        return self.coef[item]
+        return self.coefficients[item]
+
+    def eval(self, element):
+        return sum(pow(x, i)*element for i, x in enumerate(self.coefficients))

da/test_kzg.py

@@ -29,3 +29,4 @@ class TestKZG(TestCase):
         commit = kzg.bytes_to_commitment(rand_bytes, GLOBAL_PARAMETERS)
         poly = kzg.bytes_to_polynomial(rand_bytes)
         proof = kzg.generate_element_proof(poly[0], poly, GLOBAL_PARAMETERS)
+        self.assertEqual(len(proof), 48)