# GNU GPLv3, see LICENSE

import os

import re

import base64

import binascii

from . import gf256

class SException(Exception): pass

class InvalidParams(SException): pass

class DetectionException(SException): pass

class DecodingException(SException): pass

class MalformedShare(SException): pass

def _share_byte(secret_b, k, n):

	if not k<=n<255:

		raise InvalidParams("Failed k<=n<255, k={0}, n={1}".format(k, n))

def generate_raw(secret, k, n):

	"""Splits secret into shares.

	:param secret: (bytes)

	:param k: number of shares necessary for secret recovery. 1 <= k <= n

	:param n: (int) number of shares generated. 1 <= n < 255

	:return: [(i, (bytes) share), ...]"""

	shares = [_share_byte(b, k, n) for b in secret]

def reconstruct_raw(*shares):

	"""Tries to recover the secret from its shares.

	:param shares: (((int) i, (bytes) share), ...)

	:return: (bytes) reconstructed secret. Too few shares return garbage."""

	if len({x for (x, _) in shares}) < len(shares):

		raise MalformedShare("Found a non-unique share. Please check your inputs.")

	(xs, payloads) = zip(*shares)

	secret_len = len(payloads[0])

	res = [None]*secret_len

	weights = gf256.compute_weights(xs)

	for i in range(secret_len):

		ys = [s[i] for s in payloads]

		res[i] = (gf256.get_constant_coef(weights, ys))

	return bytes(res)

def generate(secret, k, n, encoding="b32", label="", omit_k_n=False):

	"""Wraps generate_raw().

	:param secret: (str or bytes)

	:param k: number of shares necessary for secret recovery

	:param n: number of shares generated

	:param encoding: {hex, b32, b64} desired output encoding. Hexadecimal, Base32 or Base64.

	:param label: (str) any label to prefix the shares with

	:param omit_k_n: (boolean) suppress the default shares prefix

	:return: [(str) share, ...]"""

	if isinstance(secret,str):

		secret = secret.encode("utf-8")

	shares = generate_raw(secret, k, n)

	prefix = ""

	if label:

		prefix = label + "."

	if not omit_k_n:

		prefix += "{0}.{1}.".format(k, n)

	return [prefix + encode(s, encoding) for s in shares]

def reconstruct(*shares, encoding="", raw=False):

	"""Wraps reconstruct_raw.

	:param shares: ((str) share, ...)

	:param encoding: {hex, b32, b64, ""} encoding of share strings. If not provided or empty, the function tries to guess it.

import math

import cmath

import itertools

from .gf256 import gfmul, gfpow

SQUARE_ROOTS = {3: 189, 5: 12, 15: 225, 17: 53, 51: 51, 85: 15, 255: 3}

def precompute_x(n):

	"""Return a geometric sequence [1, w, w**2, ..., w**(n-1)], where w**n==1.

	This can be done only for certain values of n."""

	assert n in SQUARE_ROOTS, n

	w = SQUARE_ROOTS[n]  # primitive N-th square root of 1

	return list(itertools.accumulate([1]+[w]*(n-1), gfmul))

def complex_dft(p):

	"""Quadratic formula from the definition. The basic case in complex numbers."""

	N = len(p)

	w = cmath.exp(-2*math.pi*1j/N)  # primitive N-th square root of 1

	y = [0]*N

	for k in range(N):

		xk = w**k

		for n in range(N):

			y[k] += p[n] * xk**n

	return y

def dft(p):

	"""Quadratic formula from the definition. In GF256."""

	N = len(p)

	x = precompute_x(N)

	y = [0]*N

	for k in range(N):

		for n in range(N):

			y[k] ^= gfmul(p[n], gfpow(x[k], n))

	return y

def compute_inverse(N1, N2):

	for i in range(N2):

		if N1*i % N2 == 1:

			return i

	raise ValueError("Failed to find an inverse to {0} mod {1}.".format(N1, N2))

def prime_fft(p, divisors, basic_dft=dft):

	"""https://en.wikipedia.org/wiki/Prime-factor_FFT_algorithm"""

	if len(divisors) == 1:

		return basic_dft(p)

	N = len(p)

	N1 = divisors[0]

	N2 = N//N1

	N1_inv = compute_inverse(N1, N2)

	N2_inv = compute_inverse(N2, N1)

	ys = []

	for n1 in range(N1):  # compute rows

		p_ = [p[(n2*N1+n1*N2) % N] for n2 in range(N2)]

		ys.append(prime_fft(p_, divisors[1:], basic_dft))

	for k2 in range(N2):  # compute cols

		p_ = [row[k2] for row in ys]

		y_ = basic_dft(p_)

		for (yi, row) in zip(y_, ys):  # update col

			row[k2] = yi

	# remap and output

	res = [0]*N

	for k1 in range(N1):

		for k2 in range(N2):

			res[(k1*N2*N2_inv+k2*N1*N1_inv) % N] = ys[k1][k2]

	return res

# GNU GPLv3, see LICENSE

import random

import functools

import operator

from unittest import TestCase

from ..fft import *

def batch_evaluate(coefs, xs):

class TestFFT(TestCase):

	def test_complex_dft(self):

		self.assertEqual(complex_dft([0]), [0+0j])

		self.assertEqual(complex_dft([1]), [1+0j])

		self.assertEqual(complex_dft([2]), [2+0j])

		all(self.assertAlmostEqual(a, b) for (a, b) in zip(complex_dft([3, 1]), [4+0j, 2+0j]))

		all(self.assertAlmostEqual(a, b) for (a, b) in zip(complex_dft([3, 1, 4]), [8+0j, 0.5+2.59807621j, 0.5-2.59807621j]))

		all(self.assertAlmostEqual(a, b) for (a, b) in zip(complex_dft([3, 1, 4, 1]), [9+0j, -1+0j, 5+0j, -1+0j]))

		all(self.assertAlmostEqual(a, b) for (a, b) in zip(

			complex_dft([3, 1, 4, 1, 5]),

			[14+0j, 0.80901699+2.04087031j, -0.30901699+5.20431056j, -0.30901699-5.20431056j, 0.80901699-2.04087031j]

		))

	def test_complex_prime_fft(self):

		random.seed(1918)

		for divisors in [[3], [2, 3], [3, 5], [3, 5, 17], [2, 3, 5, 7, 11]]:

			n = functools.reduce(operator.mul, divisors)

			coefficients = [random.randint(-128, 127) for i in range(n)]

			a = prime_fft(coefficients, divisors, complex_dft)

			b = complex_dft(coefficients)

			all(self.assertAlmostEqual(ai, bi) for (ai, bi) in zip(a, b))

	def test_finite_dft(self):

		random.seed(1918)

		x = {i: precompute_x(i) for i in [3, 5, 15, 17]}  # all sets of xs

		for n in [3, 5, 15, 17]:

			coefficients = [random.randint(0, 255) for i in range(n)]

			self.assertEqual(

				dft(coefficients),

				batch_evaluate(coefficients[::-1], x[n])

			)

	def test_finite_prime_fft(self):

		random.seed(1918)

		for divisors in [[3], [3, 5], [3, 17], [5, 17], [3, 5, 17]]:

			n = functools.reduce(operator.mul, divisors)

			coefficients = [random.randint(0, 255) for i in range(n)]

			a = prime_fft(coefficients, divisors)

			b = dft(coefficients)

			all(self.assertAlmostEqual(ai, bi) for (ai, bi) in zip(a, b))

# GNU GPLv3, see LICENSE

import os

import random

from unittest import TestCase

from .. import *

from .. import gf256

class TestShamira(TestCase):

	_urandom = os.urandom

	@classmethod

	def setUpClass(cls):

		random.seed(17)

		os.urandom = lambda n: bytes(random.randint(0, 255) for i in range(n))

	@classmethod

	def tearDownClass(cls):

		os.urandom = cls._urandom

	def test_share_byte(self):

		with self.assertRaises(InvalidParams):  # too few shares

			_share_byte(b"a", 5, 4)

		with self.assertRaises(InvalidParams):  # too many shares

			_share_byte(b"a", 5, 255)

		with self.assertRaises(ValueError):  # not castable to int

			_share_byte("x", 2, 3)

		ys = _share_byte(ord(b"a"), 2, 3)

		weights = gf256.compute_weights(xs)

		self.assertEqual(gf256.get_constant_coef(weights, ys), ord(b"a"))

		weights = gf256.compute_weights(xs[:2])

		self.assertEqual(gf256.get_constant_coef(weights, ys[:2]), ord(b"a"))

		weights = gf256.compute_weights(xs[:1])

		self.assertNotEqual(gf256.get_constant_coef(weights, ys[:1]), ord(b"a"))  # underdetermined => random

	def test_generate_reconstruct_raw(self):

		for (k, n) in [(2, 3), (254, 254)]:

			shares = generate_raw(b"abcd", k, n)

			random.shuffle(shares)

			self.assertEqual(reconstruct_raw(*shares[:k]), b"abcd")

			self.assertNotEqual(reconstruct_raw(*shares[:k-1]), b"abcd")

	def test_generate_reconstruct(self):

		for encoding in ["hex", "b32", "b64"]:

			for secret in [b"abcd", "abcde", "ěščřžý"]:

				for (k, n) in [(2, 3), (254, 254)]:

					raw = isinstance(secret, bytes)

					with self.subTest(enc=encoding, r=raw, sec=secret, k=k, n=n):

						shares = generate(secret, k, n, encoding)

						random.shuffle(shares)

						self.assertEqual(reconstruct(*shares[:k], encoding=encoding, raw=raw), secret)

						self.assertEqual(reconstruct(*shares[:k], raw=raw), secret)

						s = secret if raw else secret.encode("utf-8")

						self.assertNotEqual(reconstruct(*shares[:k-1], encoding=encoding, raw=True), s)

		shares = generate(b"\xfeaa", 2, 3)

		with self.assertRaises(DecodingException):

			reconstruct(*shares)

	def test_encode(self):

		share = (2, b"\x00\x01\x02")

		for (encoding, encoded_str) in [("hex", '000102'), ("b32", 'AAAQE==='), ("b64", 'AAEC')]:

			with self.subTest(enc=encoding):

				self.assertEqual(encode(share, encoding), "2."+encoded_str)

	def test_decode(self):

		with self.assertRaises(MalformedShare):

			decode("AAA")

			decode("1.")

			decode(".AAA")

			decode("1AAA")

			decode("1.0001020f", "hex")

			decode("1.000102030", "hex")

			decode("1.AAAQEAY")