Shamira Changeset - f90dd9a4f5a4

Changeset - f90dd9a4f5a4

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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

src/shamira/fft.py

src/shamira/tests/test_fft.py

src/shamira/tests/test_shamira.py

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src/shamira/core.py

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@@ @@ -3,39 +3,45 @@ @@
 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), ...)

src/shamira/fft.py

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 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))
@@ @@ -70,6 +82,14 @@ def prime_fft(p, divisors, basic_dft=dft @@
 	# 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

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@@ @@ -2,18 +2,18 @@ @@
 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])

src/shamira/tests/test_shamira.py

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@@ @@ -2,13 +2,13 @@ @@
 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
@@ @@ -26,13 +26,13 @@ class TestShamira(TestCase): @@
 		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"))

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