two version of R2R are here HEAD master

1 files changed, 181 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/ellipticcurve/math.py b/.venv/lib/python3.12/site-packages/ellipticcurve/math.py
new file mode 100644
index 00000000..981ab4e7
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+++ b/.venv/lib/python3.12/site-packages/ellipticcurve/math.py
@@ -0,0 +1,181 @@
+from .point import Point
+
+
+class Math:
+
+    @classmethod
+    def modularSquareRoot(cls, value, prime):
+        return pow(value, (prime + 1) // 4, prime)
+
+    @classmethod
+    def multiply(cls, p, n, N, A, P):
+        """
+        Fast way to multily point and scalar in elliptic curves
+
+        :param p: First Point to mutiply
+        :param n: Scalar to mutiply
+        :param N: Order of the elliptic curve
+        :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p)
+        :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p)
+        :return: Point that represents the sum of First and Second Point
+        """
+        return cls._fromJacobian(
+            cls._jacobianMultiply(cls._toJacobian(p), n, N, A, P), P
+        )
+
+    @classmethod
+    def add(cls, p, q, A, P):
+        """
+        Fast way to add two points in elliptic curves
+
+        :param p: First Point you want to add
+        :param q: Second Point you want to add
+        :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p)
+        :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p)
+        :return: Point that represents the sum of First and Second Point
+        """
+        return cls._fromJacobian(
+            cls._jacobianAdd(cls._toJacobian(p), cls._toJacobian(q), A, P), P,
+        )
+
+    @classmethod
+    def inv(cls, x, n):
+        """
+        Extended Euclidean Algorithm. It's the 'division' in elliptic curves
+
+        :param x: Divisor
+        :param n: Mod for division
+        :return: Value representing the division
+        """
+        if x == 0:
+            return 0
+
+        lm = 1
+        hm = 0
+        low = x % n
+        high = n
+
+        while low > 1:
+            r = high // low
+            nm = hm - lm * r
+            nw = high - low * r
+            high = low
+            hm = lm
+            low = nw
+            lm = nm
+
+        return lm % n
+
+    @classmethod
+    def _toJacobian(cls, p):
+        """
+        Convert point to Jacobian coordinates
+
+        :param p: First Point you want to add
+        :return: Point in Jacobian coordinates
+        """
+        return Point(p.x, p.y, 1)
+
+    @classmethod
+    def _fromJacobian(cls, p, P):
+        """
+        Convert point back from Jacobian coordinates
+
+        :param p: First Point you want to add
+        :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p)
+        :return: Point in default coordinates
+        """
+        z = cls.inv(p.z, P)
+        x = (p.x * z ** 2) % P
+        y = (p.y * z ** 3) % P
+
+        return Point(x, y, 0)
+
+    @classmethod
+    def _jacobianDouble(cls, p, A, P):
+        """
+        Double a point in elliptic curves
+
+        :param p: Point you want to double
+        :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p)
+        :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p)
+        :return: Point that represents the sum of First and Second Point
+        """
+        if p.y == 0:
+            return Point(0, 0, 0)
+
+        ysq = (p.y ** 2) % P
+        S = (4 * p.x * ysq) % P
+        M = (3 * p.x ** 2 + A * p.z ** 4) % P
+        nx = (M**2 - 2 * S) % P
+        ny = (M * (S - nx) - 8 * ysq ** 2) % P
+        nz = (2 * p.y * p.z) % P
+
+        return Point(nx, ny, nz)
+
+    @classmethod
+    def _jacobianAdd(cls, p, q, A, P):
+        """
+        Add two points in elliptic curves
+
+        :param p: First Point you want to add
+        :param q: Second Point you want to add
+        :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p)
+        :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p)
+        :return: Point that represents the sum of First and Second Point
+        """
+        if p.y == 0:
+            return q
+        if q.y == 0:
+            return p
+
+        U1 = (p.x * q.z ** 2) % P
+        U2 = (q.x * p.z ** 2) % P
+        S1 = (p.y * q.z ** 3) % P
+        S2 = (q.y * p.z ** 3) % P
+
+        if U1 == U2:
+            if S1 != S2:
+                return Point(0, 0, 1)
+            return cls._jacobianDouble(p, A, P)
+
+        H = U2 - U1
+        R = S2 - S1
+        H2 = (H * H) % P
+        H3 = (H * H2) % P
+        U1H2 = (U1 * H2) % P
+        nx = (R ** 2 - H3 - 2 * U1H2) % P
+        ny = (R * (U1H2 - nx) - S1 * H3) % P
+        nz = (H * p.z * q.z) % P
+
+        return Point(nx, ny, nz)
+
+    @classmethod
+    def _jacobianMultiply(cls, p, n, N, A, P):
+        """
+        Multily point and scalar in elliptic curves
+
+        :param p: First Point to mutiply
+        :param n: Scalar to mutiply
+        :param N: Order of the elliptic curve
+        :param P: Prime number in the module of the equation Y^2 = X^3 + A*X + B (mod p)
+        :param A: Coefficient of the first-order term of the equation Y^2 = X^3 + A*X + B (mod p)
+        :return: Point that represents the sum of First and Second Point
+        """
+        if p.y == 0 or n == 0:
+            return Point(0, 0, 1)
+
+        if n == 1:
+            return p
+
+        if n < 0 or n >= N:
+            return cls._jacobianMultiply(p, n % N, N, A, P)
+
+        if (n % 2) == 0:
+            return cls._jacobianDouble(
+                cls._jacobianMultiply(p, n // 2, N, A, P), A, P
+            )
+
+        return cls._jacobianAdd(
+            cls._jacobianDouble(cls._jacobianMultiply(p, n // 2, N, A, P), A, P), p, A, P
+        )