Refactoring in Naive Form

.gitignore

@@ -56,6 +56,9 @@ chains
 # tox/pytest cache
 .cache
 
+# mypy
+.mypy_cache/
+
 # Test output logs
 logs
 ### JetBrains template

py_ecc/BaseCurve.py

@@ -0,0 +1,291 @@
+from abc import (
+    abstractmethod,
+)
+
+from typing import (
+    cast,
+)
+
+from py_ecc.field_elements import (
+    FQP,
+)
+
+from py_ecc.optimized_field_elements import (
+    FQP as optimized_FQP,
+)
+
+from py_ecc.new_typing import (
+    Field,
+    GeneralPoint,
+    Point2D,
+)
+from py_ecc.new_typing import (
+    Optimized_Field,
+    Optimized_Point2D,
+    Optimized_Point3D,
+)
+
+
+class BaseCurve:
+    # Name of the curve can be "bn128" or "bls12_381"
+    curve_name = None
+    curve_order = None
+    # Curve is y**2 = x**3 + b
+    b = None
+    # Twisted curve over FQ**2
+    b2 = None
+    # Extension curve over FQ**12; same b value as over FQ
+    b12 = None
+    # Generator for curve over FQ
+    G1 = None
+    # Generator for twisted curve over FQ2
+    G2 = None
+    # Generator for twisted curve over FQ12
+    G12 = None
+    # Point at infinity over FQ
+    Z1 = None
+    # Point at infinity for twisted curve over FQ2
+    Z2 = None
+
+    def __init__(self, curve_properties, curve_name):
+        self.curve_name = curve_name
+        self.curve_order = curve_properties[curve_name]["curve_order"]
+        self.b = curve_properties[curve_name]["b"]
+        self.b2 = curve_properties[curve_name]["b2"]
+        self.b12 = curve_properties[curve_name]["b12"]
+        self.G1 = curve_properties[curve_name]["G1"]
+        self.G2 = curve_properties[curve_name]["G2"]
+        self.G12 = self.twist(cast(Point2D[FQP], self.G2))
+        self.Z1 = curve_properties[curve_name]["Z1"]
+        self.Z2 = curve_properties[curve_name]["Z2"]
+
+    def is_inf(self, pt: GeneralPoint[Field]) -> bool:
+        """
+        Check if a point is the point at infinity
+        """
+        return pt is None
+
+    def is_on_curve(self, pt: Point2D[Field], b: Field) -> bool:
+        """
+        Check that a point is on the curve
+        """
+        if self.is_inf(pt):
+            return True
+        x, y = pt
+        return y**2 == x**3 + b
+
+    def double(self, pt: Point2D[Field]) -> Point2D[Field]:
+        """
+        Elliptic Curve Doubling (P+P).
+        """
+        x, y = pt
+        m = (3 * x**2) / (2 * y)
+        newx = m**2 - 2 * x
+        newy = -m * newx + m * x - y
+        return (newx, newy)
+
+    def add(self,
+            p1: Point2D[Field],
+            p2: Point2D[Field]) -> Point2D[Field]:
+        """
+        Elliptic curve addition.
+        """
+        if p1 is None or p2 is None:
+            return p1 if p2 is None else p2
+        x1, y1 = p1
+        x2, y2 = p2
+        if x2 == x1 and y2 == y1:
+            return self.double(p1)
+        elif x2 == x1:
+            return None
+        else:
+            m = (y2 - y1) / (x2 - x1)
+        newx = m**2 - x1 - x2
+        newy = -m * newx + m * x1 - y1
+        assert newy == (-m * newx + m * x2 - y2)
+        return (newx, newy)
+
+    def multiply(self, pt: Point2D[Field], n: int) -> Point2D[Field]:
+        """
+        Elliptic curve point multiplication.
+        """
+        if n == 0:
+            return None
+        elif n == 1:
+            return pt
+        elif not n % 2:
+            # print(n//2)
+            return self.multiply(self.double(pt), n // 2)
+        else:
+            # print(n//2)
+            return self.add(self.multiply(self.double(pt), n // 2), pt)
+
+    def eq(self, p1: GeneralPoint[Field], p2: GeneralPoint[Field]) -> bool:
+        """
+        Check if 2 points are equal.
+        """
+        return p1 == p2
+
+    def neg(self, pt: Point2D[Field]) -> Point2D[Field]:
+        """
+        Gives the reflection of point wrt x-axis (P => -P).
+        """
+        if pt is None:
+            return None
+        x, y = pt
+        return (x, -y)
+
+    @abstractmethod
+    def twist(self, pt: Point2D[FQP]) -> Point2D[FQP]:
+        """
+        'Twist' a point in E(FQ2) into a point in E(FQ12)
+        """
+        raise NotImplementedError("Must be implemented by subclasses")
+
+
+class BaseOptimizedCurve:
+    # Name of the curve can be "bn128" or "bls12_381"
+    curve_name = None
+    curve_order = None
+    # Curve is y**2 = x**3 + b
+    b = None
+    # Twisted curve over FQ**2
+    b2 = None
+    # Extension curve over FQ**12; same b value as over FQ
+    b12 = None
+    # Generator for curve over FQ
+    G1 = None
+    # Generator for twisted curve over FQ2
+    G2 = None
+    # Generator for curve over FQ12
+    G12 = None
+    # Point at infinity over FQ
+    Z1 = None
+    # Point at infinity for twisted curve over FQ2
+    Z2 = None
+
+    def __init__(self, curve_properties, curve_name):
+        self.curve_name = curve_name
+        self.curve_order = curve_properties[curve_name]["curve_order"]
+        self.b = curve_properties[curve_name]["b"]
+        self.b2 = curve_properties[curve_name]["b2"]
+        self.b12 = curve_properties[curve_name]["b12"]
+        self.G1 = curve_properties[curve_name]["G1"]
+        self.G2 = curve_properties[curve_name]["G2"]
+        self.G12 = self.twist(cast(Optimized_Point3D[optimized_FQP], self.G2))
+        self.Z1 = curve_properties[curve_name]["Z1"]
+        self.Z2 = curve_properties[curve_name]["Z2"]
+
+    def is_inf(self, pt: Optimized_Point3D[Optimized_Field]) -> bool:
+        """
+        Check if a point is the point at infinity
+        """
+        return pt[-1] == (type(pt[-1]).zero(self.curve_name))
+
+    def is_on_curve(self, pt: Optimized_Point3D[Optimized_Field], b: Field) -> bool:
+        """
+        Check that a point is on the curve defined by y**2 == x**3 + b
+        """
+        if self.is_inf(pt):
+            return True
+        x, y, z = pt
+        return y**2 * z == x**3 + (b * z**3)
+
+    def double(self, pt: Optimized_Point3D[Optimized_Field]) -> Optimized_Point3D[Optimized_Field]:
+        """
+        Elliptic curve doubling
+        """
+        x, y, z = pt
+        W = 3 * x * x
+        S = y * z
+        B = x * y * S
+        H = W * W - 8 * B
+        S_squared = S * S
+        newx = 2 * H * S
+        newy = W * (4 * B - H) - 8 * y * y * S_squared
+        newz = 8 * S * S_squared
+        return (newx, newy, newz)
+
+    def add(self,
+            p1: Optimized_Point3D[Optimized_Field],
+            p2: Optimized_Point3D[Optimized_Field]) -> Optimized_Point3D[Optimized_Field]:
+        """
+        Elliptic curve addition
+        """
+        one, zero = type(p1[0]).one(self.curve_name), type(p1[0]).zero(self.curve_name)
+        if p1[2] == zero or p2[2] == zero:
+            return p1 if p2[2] == zero else p2
+        x1, y1, z1 = p1
+        x2, y2, z2 = p2
+        U1 = y2 * z1
+        U2 = y1 * z2
+        V1 = x2 * z1
+        V2 = x1 * z2
+        if V1 == V2 and U1 == U2:
+            return self.double(p1)
+        elif V1 == V2:
+            return (one, one, zero)
+        U = U1 - U2
+        V = V1 - V2
+        V_squared = V * V
+        V_squared_times_V2 = V_squared * V2
+        V_cubed = V * V_squared
+        W = z1 * z2
+        A = U * U * W - V_cubed - 2 * V_squared_times_V2
+        newx = V * A
+        newy = U * (V_squared_times_V2 - A) - V_cubed * U2
+        newz = V_cubed * W
+        return (newx, newy, newz)
+
+    def multiply(self,
+                 pt: Optimized_Point3D[Optimized_Field],
+                 n: int) -> Optimized_Point3D[Optimized_Field]:
+        """
+        Elliptic curve point multiplication
+        """
+        if n == 0:
+            return (
+                type(pt[0]).one(self.curve_name),
+                type(pt[0]).one(self.curve_name),
+                type(pt[0]).zero(self.curve_name)
+            )
+        elif n == 1:
+            return pt
+        elif not n % 2:
+            return self.multiply(self.double(pt), n // 2)
+        else:
+            return self.add(self.multiply(self.double(pt), int(n // 2)), pt)
+
+    def eq(self,
+           p1: Optimized_Point3D[Optimized_Field],
+           p2: Optimized_Point3D[Optimized_Field]) -> bool:
+        """
+        Check if 2 points are equal.
+        """
+        x1, y1, z1 = p1
+        x2, y2, z2 = p2
+        return x1 * z2 == x2 * z1 and y1 * z2 == y2 * z1
+
+    def normalize(self,
+                  pt: Optimized_Point3D[Optimized_Field]) -> Optimized_Point2D[Optimized_Field]:
+        """
+        Convert the Jacobian Point to a normal point
+        """
+        x, y, z = pt
+        return (x / z, y / z)
+
+    def neg(self, pt: Optimized_Point3D[Optimized_Field]) -> Optimized_Point3D[Optimized_Field]:
+        """
+        Gives the reflection of point wrt x-axis (P => -P).
+        """
+        if pt is None:
+            return None
+        x, y, z = pt
+        return (x, -y, z)
+
+    @abstractmethod
+    def twist(self, pt: Optimized_Point3D[optimized_FQP]) -> Optimized_Point3D[optimized_FQP]:
+        """
+        'Twist' a point in E(FQ2) into a point in E(FQ12)
+        """
+        raise NotImplementedError("Must be implemented by subclasses")