Data commit

Task/Elliptic-curve-arithmetic/Python/elliptic-curve-arithmetic.py

@@ -0,0 +1,75 @@
+#!/usr/bin/env python3
+
+class Point:
+    b = 7
+    def __init__(self, x=float('inf'), y=float('inf')):
+        self.x = x
+        self.y = y
+
+    def copy(self):
+        return Point(self.x, self.y)
+
+    def is_zero(self):
+        return self.x > 1e20 or self.x < -1e20
+
+    def neg(self):
+        return Point(self.x, -self.y)
+
+    def dbl(self):
+        if self.is_zero():
+            return self.copy()
+        try:
+            L = (3 * self.x * self.x) / (2 * self.y)
+        except ZeroDivisionError:
+            return Point()
+        x = L * L - 2 * self.x
+        return Point(x, L * (self.x - x) - self.y)
+
+    def add(self, q):
+        if self.x == q.x and self.y == q.y:
+            return self.dbl()
+        if self.is_zero():
+            return q.copy()
+        if q.is_zero():
+            return self.copy()
+        try:
+            L = (q.y - self.y) / (q.x - self.x)
+        except ZeroDivisionError:
+            return Point()
+        x = L * L - self.x - q.x
+        return Point(x, L * (self.x - x) - self.y)
+
+    def mul(self, n):
+        p = self.copy()
+        r = Point()
+        i = 1
+        while i <= n:
+            if i&n:
+                r = r.add(p)
+            p = p.dbl()
+            i <<= 1
+        return r
+
+    def __str__(self):
+        return "({:.3f}, {:.3f})".format(self.x, self.y)
+
+def show(s, p):
+    print(s, "Zero" if p.is_zero() else p)
+
+def from_y(y):
+    n = y * y - Point.b
+    x = n**(1./3) if n>=0 else -((-n)**(1./3))
+    return Point(x, y)
+
+# demonstrate
+a = from_y(1)
+b = from_y(2)
+show("a =", a)
+show("b =", b)
+c = a.add(b)
+show("c = a + b =", c)
+d = c.neg()
+show("d = -c =", d)
+show("c + d =", c.add(d))
+show("a + b + d =", a.add(b.add(d)))
+show("a * 12345 =", a.mul(12345))