if a&0x80: a = 0xff&(a<<1)^0x1b

		else: a <<= 1

		b >>= 1

	return res

g = 3  # generator

E = [None]*256  # exponentials

L = [None]*256  # logarithms

acc = 1

for i in range(256):

	E[i] = acc

	L[acc] = i

	acc = gfmul(acc, g)

L[1] = 0

inv = [E[255-L[i]] if i!=0 else None for i in range(256)]  # multiplicative inverse

def get_constant_coef(*points):

	"""Compute constant polynomial coefficient given the points.

	See https://en.wikipedia.org/wiki/Shamir's_Secret_Sharing#Computationally_Efficient_Approach"""

	k = len(points)

	res = 0

	for i in range(k):

		(x, y) = points[i]

		prod = 1

		for j in range(k):

			if i==j: continue

			(xj, yj) = points[j]

			prod = gfmul(prod, (gfmul(xj, inv[xj^x])))

		res ^= gfmul(y, prod)

	return res

###

import base64

import binascii

class SException(Exception): pass

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 returns garbage."""

	secret_len = len(shares[0][1])

	res = [None]*secret_len

	for i in range(secret_len):

		points = [(x, s[i]) for (x, s) in shares]

		res[i] = (get_constant_coef(*points))

	return bytes(res)

def reconstruct(*shares):

	"""Wraps reconstruct_raw.

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

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

	bs = reconstruct_raw(*(decode(s) for s in shares))

	try:

		return bs.decode(encoding="utf-8")

	except UnicodeDecodeError:

		raise SException('Failed to decode bytes to utf-8. Either you supplied invalid shares, or you missed the "raw" flag. Offending value: "{0}"'.format(bs))

def decode(share):

	try:

		(*_, i, share_str) = share.split(".")

		i = int(i)

		if not 1<=i<=255:

			raise SException("Malformed share: Failed 1<=k<=255, k={0}".format(i))

		share_bytes = base64.b32decode(share_str)

		return (i, share_bytes)

	except (ValueError, binascii.Error):

		raise SException('Malformed share: share="{0}"'.format(share))

###

from argparse import ArgumentParser

def run():

	parser = ArgumentParser()

	subparsers = parser.add_subparsers()

	joiner = subparsers.add_parser("join")

	joiner.add_argument("share", nargs="+", help="shares to be joined")

	joiner.set_defaults(func=_reconstruct)

	parser.set_defaults(func=lambda: parser.error("missing command"))

# GNU GPLv3, see LICENSE

import os

import re

import base64

import binascii

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))

	# we might be concerned with zero coefficients degenerating our polynomial, but there's no reason - we still need k shares to determine it is the case

	coefs = [int(secret_b)]+[int(b) for b in os.urandom(k-1)]

	points = [gf256.evaluate(coefs, i) for i in range(1, n+1)]

	return points

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]

	return [(i+1, bytes([s[i] for s in shares])) for i in range(n)]

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."""

	secret_len = len(shares[0][1])

	res = [None]*secret_len

	for i in range(secret_len):

		points = [(x, s[i]) for (x, s) in shares]

		res[i] = (gf256.get_constant_coef(*points))

	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.

	:param raw: (bool) whether to return bytes (True) or str (False)

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

	if not encoding:

		encoding = detect_encoding(shares)

	bs = reconstruct_raw(*(decode(s, encoding) for s in shares))

	try:

		return bs if raw else bs.decode(encoding="utf-8")

	except UnicodeDecodeError:

		raise DecodingException('Failed to decode bytes to utf-8. Either you supplied invalid shares, or you missed the "raw" flag. Offending value: {0}'.format(bs))