add first cut of GF(2^8)..

shamirss.py

@@ -0,0 +1,117 @@
+import unittest
+import random
+
+def _makered(x, y):
+	'''Make reduction table entry.
+
+	given x * 2^8, reduce it assuming polynomial y.
+	'''
+
+	x = x << 8
+
+	for i in range(3, -1, -1):
+		if x & (1 << (i + 8)):
+			x ^= (0x100 + y) << i
+
+	assert x < 256
+
+	return x
+
+class GF2p8:
+	@staticmethod
+	def _primativemul(a, b):
+		masks = [ 0, 0xff ]
+
+		r = 0
+
+		for i in range(0, 8):
+			mask = a & 1
+			r ^= (masks[mask] & b) << i
+			a = a >> 1
+
+		return r
+
+	# polynomial 0x187
+	_reduce = { x: _makered(x, 0x87) for x in range(0, 16) }
+
+	def __init__(self, v):
+		if v >= 256:
+			raise ValueError('%d is not a member of GF(2^8)' % v)
+
+		self._v = v
+
+	def __add__(self, o):
+		if isinstance(o, int):
+			return self + self.__class__(o)
+
+		return self.__class__(self._v ^ o._v)
+
+	def __radd__(self, o):
+		return self.__add__(o)
+
+	def __rmul__(self, o):
+		return self.__mul__(o)
+
+	def __sub__(self, o):
+		return self.__class__(self._v ^ o._v)
+
+	def __mul__(self, o):
+
+		if isinstance(o, int):
+			o = self.__class__(o)
+
+		m = o._v
+
+		# multiply
+		r = self._primativemul(self._v, m)
+
+		# reduce
+		r ^= self._reduce[r >> 12] << 4
+		r ^= self._reduce[(r >> 8) & 0xf ]
+
+		r &= 0xff
+
+		return self.__class__(r)
+
+	def __eq__(self, o):
+		if isinstance(o, int):
+			return self._v == o
+
+		return self._v == o._v
+
+	def __repr__(self):
+		return '%s(%d)' % (self.__class__.__name__, self._v)
+
+class TestShamirSS(unittest.TestCase):
+	def test_gf28(self):
+		for i in range(10):
+			a = GF2p8(random.randint(0, 255))
+			b = GF2p8(random.randint(0, 255))
+			c = GF2p8(random.randint(0, 255))
+
+			self.assertEqual(a * 0, 0)
+
+			# Identity
+			self.assertEqual(a + 0, a)
+			self.assertEqual(a * 1, a)
+			self.assertEqual(0 + a, a)
+			self.assertEqual(1 * a, a)
+
+			# Associativity
+			self.assertEqual((a + b) + c, a + (b + c))
+			self.assertEqual((a * b) * c, a * (b * c))
+
+			# Communitative
+			self.assertEqual(a + b, b + a)
+			self.assertEqual(a * b, b * a)
+
+			# Distributive
+			self.assertEqual(a * (b + c), a * b + a * c)
+			self.assertEqual((b + c) * a, b * a + c * a)
+
+			# Basic mul
+			self.assertEqual(GF2p8(0x80) * 2, 0x87)
+			self.assertEqual(GF2p8(0x80) * 6, (0x80 * 6) ^ (0x187 << 1))
+			self.assertEqual(GF2p8(0x80) * 8, (0x80 * 8) ^ (0x187 << 2) ^ (0x187 << 1) ^ 0x187)
+
+			self.assertEqual(a + b - b, a)