Update ecc.py

README.md

@@ -77,7 +77,8 @@ warning: format of factorization is now dict like {p1: e1, p2: e2, ...}
 *   .find\_points\_in\_range(start, end) - list of points in range of x coordinate
 *   .find\_points\_rand(count) - list of count random points
 *   .add(p1, p2) - p1 + p2 on elliptic curve
-*   .power(p, n) - n✕P or (P + P + ... + P) n times
+*   .negate(p) - -p on elliptic curve
+*   .power(p, n) - n✕P or (P + P + ... + P) n times. If n < 0, firstly negate P to get (-P) and then take (-n)✕(-P)
 *   .generate(n) - n✕G
 *   .get\_order(p, limit) - slow method, trying to determine order of p; limit is max order to try
 

libnum/ecc.py

@@ -131,13 +131,22 @@ def add(self, p1, p2):
         y = (l * (x1 - x) - y1) % self.module  # yes, it's that new x
         return (x, y)
 
+    def negate(self, p):
+        """
+        Negation of a point or a new point Q = -P where P + Q = O
+        """
+        return (p[0], -p[1] % self.module)     
+
     def power(self, p, n):
         """
         n✕P or (P + P + ... + P) n times
+        If n < 0, firstly negate P to get -P and then take (-n)✕(-P)
         """
+        if n < 0:
+            return self.power(self.negate(p), -n)
         if n == 0 or self.is_null(p):
             return NULL_POINT
-
+             
         res = NULL_POINT
         while n:
             if n & 1: