diff --git a/src/shamira/tests/test_gf256.py b/src/shamira/tests/test_gf256.py
--- a/src/shamira/tests/test_gf256.py
+++ b/src/shamira/tests/test_gf256.py
@@ -22,6 +22,26 @@ class TestGF256(TestCase):
 			for b in range(256):
 				self.assertEqual(_gfmul(a, b), gfmul(a, b))
 
+	def test_gfpow(self):
+		self.assertEqual(gfpow(0, 0), 1)
+
+		for i in range(1, 256):
+			self.assertEqual(gfpow(i, 0), 1)
+			self.assertEqual(gfpow(i, 1), i)
+			self.assertEqual(gfpow(0, i), 0)
+			self.assertEqual(gfpow(1, i), 1)
+			self.assertEqual(gfpow(i, 256), i)
+			self.assertEqual(gfpow(i, 2), gfmul(i, i))
+
+		random.seed(1918)
+		for i in range(256):
+			j = random.randint(2, 255)
+			k = random.randint(3, 255)
+			y = 1
+			for m in range(k):
+				y = gfmul(y, j)
+			self.assertEqual(gfpow(j, k), y)
+
 	def test_evaluate(self):
 		for x in range(256):
 			(a0, a1, a2, a3) = (x, x>>1, x>>2, x>>3)