implement better algorithm for power calculation...

shamirss.py

@@ -227,16 +227,39 @@ class GF2p8:
 		if x == -1 and self._invcache:
 			return self.__class__(self._invcache[self._v])
 
-		if x < 0:
-			x += 255
+		# we loop after 255, so no need to do extra work
+		x %= 255
 
-		v = self.__class__(1)
+		# Note: not constant time, also, not optimial algorithm
 
-		# TODO - make faster via caching and squaring
-		for i in range(x):
-			v *= self
+		# The art of computer programming vol 2. § 4.6.3 Algorithm A
+		# https://archive.org/details/artofcomputerpro0000knut/page/400/mode/2up
 
-		return v
+		# A1
+		n = x
+		y = self.__class__(1)
+		z = self
+
+		while n:
+			# A2
+			n, isodd = divmod(n, 2)
+
+			if not isodd:
+				# A5
+				z *= z
+				continue
+
+			# A3
+			y *= z
+
+			# A4
+			if not n:
+				break
+
+			# A5
+			z *= z
+
+		return y
 
 	def powerseries(self, cnt):
 		'''Generate [ self ** 0, self ** 1, ..., self ** cnt ].'''
@@ -340,11 +363,20 @@ class TestShamirSS(unittest.TestCase):
 		a = GF2p8(random.randint(0, 255))
 
 		v = GF2p8(1)
-		for i in range(10):
+		for i in range(260):
 			self.assertEqual(a ** i, v)
 
 			v = v * a
 
+		for i in range(10):
+			neg = random.randint(-600, -1)
+
+			p = neg
+			while p < 0:
+				p += 255
+
+			self.assertEqual(a ** neg, a ** p)
+
 		for i in range(10):
 			a = GF2p8(random.randint(0, 255))