major fix, was generating shares for k-1 instead of k...

also use 0 as a coeff, the original paper uses 0.

for powerseries, my docs were correct, but the implementation
wrong...  partly because I used zip which works on mismatched
lengths..

shamirss.py

@@ -33,6 +33,12 @@ import unittest.mock
 
 random = secrets.SystemRandom()
 
+__all__ = [
+	'create_shares',
+	'recover_data',
+	'GF2p8',
+]
+
 def _makered(x, y):
 	'''Make reduction table entry.
 
@@ -63,10 +69,12 @@ def create_shares(data, k, nshares):
 
 	data = bytes(data)
 
+	#print(repr(data), repr(k), repr(nshares))
+
 	powers = (None, ) + tuple(GF2p8(x).powerseries(k - 1) for x in
 	    range(1, nshares + 1))
 
-	coeffs = [ [ x ] + [ random.randint(1, 255) for y in
+	coeffs = [ [ x ] + [ random.randint(0, 255) for y in
 	    range(k - 1) ] for idx, x in enumerate(data) ]
 
 	return [ (x, bytes([ int(evalpoly(coeffs[idx],
@@ -166,9 +174,9 @@ class GF2p8:
 	def powerseries(self, cnt):
 		'''Generate [ self ** 0, self ** 1, ..., self ** cnt ].'''
 
-		r = [ 1 ]
+		r = [ self.__class__(1) ]
 
-		for i in range(1, cnt):
+		for i in range(1, cnt + 1):
 			r.append(r[-1] * self)
 
 		return r
@@ -191,6 +199,8 @@ class TestShamirSS(unittest.TestCase):
 
 		powers = a.powerseries(5)
 
+		self.assertTrue(all(isinstance(x, GF2p8) for x in powers))
+
 		vals = [ GF2p8(random.randint(0, 255)) for x in range(5) ]
 
 		r = evalpoly(vals, powers)
@@ -205,9 +215,13 @@ class TestShamirSS(unittest.TestCase):
 		self.assertRaises(TypeError, create_shares, '', 1, 1)
 
 		val = bytes([ random.randint(0, 255) for x in range(100) ])
+		#val = b'this is a test of english text.'
+		#val = b'1234'
 
 		a = create_shares(val, 2, 3)
 
+		self.assertNotIn(val, set(x[1] for x in a))
+
 		# that it has the number of shares
 		self.assertEqual(len(a), 3)
 
@@ -248,7 +262,7 @@ class TestShamirSS(unittest.TestCase):
 			a = GF2p8(random.randint(0, 255))
 
 			powers = a.powerseries(10)
-			for j in range(10):
+			for j in range(11):
 				self.assertEqual(powers[j], a ** j)
 
 	def test_gf2p8_errors(self):