Changeset - f90dd9a4f5a4
Parent rev.
Child rev.
[Not reviewed]
default
0 4 0
Laman - 4 years ago 2020-12-07 21:53:15

integrated fft evaluation into core functions
4 files changed with 36 insertions and 10 deletions:
src/shamira/core.py
11
5
src/shamira/fft.py
21
1
src/shamira/tests/test_fft.py
2
2
src/shamira/tests/test_shamira.py
2
2
0 comments (0 inline, 0 general)
src/shamira/core.py
➞
Show inline comments
 
# GNU GPLv3, see LICENSE
 

			




	
	
	
		
 
import os

			




	
	
	
		
 
import re

			




	
	
	
		
 
import base64

			




	
	
	
		
 
import binascii

			




	
	
	
		
 

			




	
	
	
		
 
from . import gf256

			




	
	
	
		
 
from . import fft

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
class SException(Exception): pass

			




	
	
	
		
 
class InvalidParams(SException): pass

			




	
	
	
		
 
class DetectionException(SException): pass

			




	
	
	
		
 
class DecodingException(SException): pass

			




	
	
	
		
 
class MalformedShare(SException): pass

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
def compute_x(n):

			




	
	
	
		
 
	return fft.precompute_x(fft.ceil_size(n))[:n]

			




	
	
	
		
 

			




	
	
	
		
 

			




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

			




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

			




	
	
	
		
 
	return points

			




	
	
	
		
 
	# 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)]

			




	
	
	
		
 
	return fft.evaluate(coefs, 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), ...]"""

			




	
	
	
		
 
	xs = compute_x(n)

			




	
	
	
		
 
	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)]

			




	
	
	
		
 
	return [(xi, bytes([s[i] for s in shares])) for (i, xi) in enumerate(xs)]

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
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])

			




        

    


    
    

    

        

                

                    src/shamira/fft.py
                

                

                  
                      
                        

                      ➞

                      
                        
                  

                  
                      
                  
                      
                  
                      
                  
                      
                  
                  
                

                

                    Show inline comments
                    
                

        

        

            



	
	
	
		
 
import math

			




	
	
	
		
 
import cmath

			




	
	
	
		
 
import itertools

			




	
	
	
		
 

			




	
	
	
		
 
from .gf256 import gfmul, gfpow

			




	
	
	
		
 

			




	
	
	
		
 
# values of n-th square roots

			




	
	
	
		
 
# divisors of 255 and their factors in natural numbers

			




	
	
	
		
 
DIVISORS = [3, 5, 15, 17, 51, 85, 255]

			




	
	
	
		
 
FACTORS = {3: [3], 5: [5], 15: [3, 5], 17: [17], 51: [3, 17], 85: [5, 17], 255: [3, 5, 17]}

			




	
	
	
		
 
# values of n-th square roots in GF256

			




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

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
def ceil_size(n):

			




	
	
	
		
 
	assert n <= DIVISORS[-1]

			




	
	
	
		
 
	for (i, ni) in enumerate(DIVISORS):

			




	
	
	
		
 
		if ni >= n:

			




	
	
	
		
 
			break

			




	
	
	
		
 

			




	
	
	
		
 
	return ni

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
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

			




	
	
		
 
@@ -64,12 +76,20 @@ def prime_fft(p, divisors, basic_dft=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

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
def evaluate(coefs, n):

			




	
	
	
		
 
	ni = ceil_size(n)

			




	
	
	
		
 
	extended_coefs = coefs + [0]*(ni-len(coefs))

			




	
	
	
		
 
	ys = prime_fft(extended_coefs, FACTORS[ni])

			




	
	
	
		
 

			




	
	
	
		
 
	return ys[:n]

			




        

    


    
    

    

        

                

                    src/shamira/tests/test_fft.py
                

                

                  
                      
                        

                      ➞

                      
                        
                  

                  
                      
                  
                      
                  
                      
                  
                      
                  
                  
                

                

                    Show inline comments
                    
                

        

        

            



	
	
	
		
 
# GNU GPLv3, see LICENSE

			




	
	
	
		
 

			




	
	
	
		
 
import random

			




	
	
	
		
 
import functools

			




	
	
	
		
 
import operator

			




	
	
	
		
 
from unittest import TestCase

			




	
	
	
		
 

			




	
	
	
		
 
from ..gf256 import evaluate

			




	
	
	
		
 
from .. import gf256

			




	
	
	
		
 
from ..fft import *

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
def batch_evaluate(coefs, xs):

			




	
	
	
		
 
	return [evaluate(coefs, x) for x in xs]

			




	
	
	
		
 
	return [gf256.evaluate(coefs, x) for x in 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]),

			




        

    


    
    

    

        

                

                    src/shamira/tests/test_shamira.py
                

                

                  
                      
                        

                      ➞

                      
                        
                  

                  
                      
                  
                      
                  
                      
                  
                      
                  
                  
                

                

                    Show inline comments
                    
                

        

        

            



	
	
	
		
 
# GNU GPLv3, see LICENSE

			




	
	
	
		
 
import os

			




	
	
	
		
 
import random

			




	
	
	
		
 
from unittest import TestCase

			




	
	
	
		
 

			




	
	
	
		
 
from .. import *

			




	
	
	
		
 
from .. import gf256

			




	
	
	
		
 
from ..core import encode, decode,detect_encoding, _share_byte

			




	
	
	
		
 
from ..core import encode, decode, detect_encoding, _share_byte, compute_x

			




	
	
	
		
 

			




	
	
	
		
 

			




	
	
	
		
 
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)

			




	
	
	
		
 
		xs = list(range(1, 4))

			




	
	
	
		
 
		xs = compute_x(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)]:

			




        

    



    


    



    



      

      





    
    0 comments (0 inline, 0 general)
    





    


  

  







  


    




    








    
        Server instance: Sirius-556
    
    
        This site is powered by
            Kallithea 0.7.0,
        which is
        © 2010–2023 by various authors & licensed under GPLv3.
            – Support