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curve.py

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+from py_ecc.fields.field_elements import FQ as Field
+import py_ecc.bn128 as b
+from typing import NewType
+from functools import cache
+from utils import lincomb
+from dataclasses import dataclass
+
+primitive_root = 5
+
+class Scalar(Field):
+    field_modulus = b.curve_order
+
+    # Gets the first root of unity of a given group order
+    @classmethod
+    def root_of_unity(cls, group_order:int):
+        return Scalar(5) ** ((cls.field_modulus - 1) // group_order)
+
+    # Gets the full list of roots of unity of a given group order
+    @classmethod
+    def roots_of_unity(cls, group_order: int):
+        o = [Scalar(1), cls.root_of_unity(group_order)]
+        while len(o) < group_order:
+            o.append(o[-1] * o[1])
+        return o
+
+Base = NewType('Base', b.FQ)
+
+def ec_mul(pt, coeff):
+    if hasattr(coeff, 'n'):
+        coeff = coeff.n
+    return b.multiply(pt, coeff % b.curve_order)
+
+# Elliptic curve linear combination. A truly optimized implementation
+# would replace this with a fast lin-comb algo, see https://ethresear.ch/t/7238
+def ec_lincomb(pairs):
+    return lincomb(
+        [pt for (pt, _) in pairs],
+        [int(n) % b.curve_order for (_, n) in pairs],
+        b.add,
+        b.Z1
+    )
+    # Equivalent to:
+    # o = b.Z1
+    # for pt, coeff in pairs:
+    #     o = b.add(o, ec_mul(pt, coeff))
+    # return o