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)