# GNU GPLv3, see LICENSE
# easier to print, single file, reconstruct-only version of the code
# encoding fixed to Base32
# Python 3.6
# full version available at https://bitbucket.org/Scharlach/shamira

"""Arithmetic operations on Galois Field 2**8. See https://en.wikipedia.org/wiki/Finite_field_arithmetic"""


def gfmul(a, b):
	"""Basic multiplication. Russian peasant algorithm."""
	res = 0
	while a and b:
		if b&1: res ^= a
		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: ((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.partition(".")
		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"))

	args = parser.parse_args()
	args.func(args)


def _reconstruct(args):
	try: print(reconstruct(*args.share))
	except SException as e: print(e)


if __name__=="__main__":
	run()