# HG changeset patch
# User Laman
# Date 2020-12-07 21:53:15
# Node ID f90dd9a4f5a43ce3bd9757f46a96d01749786c2c
# Parent  25c5d4c877c607964497908cd9aab3a9b516fdf4

integrated fft evaluation into core functions

diff --git a/src/shamira/core.py b/src/shamira/core.py
--- a/src/shamira/core.py
+++ b/src/shamira/core.py
@@ -6,6 +6,7 @@ import base64
 import binascii
 
 from . import gf256
+from . import fft
 
 
 class SException(Exception): pass
@@ -15,13 +16,17 @@ class DecodingException(SException): pas
 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):
@@ -31,8 +36,9 @@ def generate_raw(secret, k, n):
 	: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):
diff --git a/src/shamira/fft.py b/src/shamira/fft.py
--- a/src/shamira/fft.py
+++ b/src/shamira/fft.py
@@ -4,10 +4,22 @@ 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."""
@@ -73,3 +85,11 @@ def prime_fft(p, divisors, basic_dft=dft
 		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]
diff --git a/src/shamira/tests/test_fft.py b/src/shamira/tests/test_fft.py
--- a/src/shamira/tests/test_fft.py
+++ b/src/shamira/tests/test_fft.py
@@ -5,12 +5,12 @@ 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):
diff --git a/src/shamira/tests/test_shamira.py b/src/shamira/tests/test_shamira.py
--- a/src/shamira/tests/test_shamira.py
+++ b/src/shamira/tests/test_shamira.py
@@ -5,7 +5,7 @@ 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):
@@ -29,7 +29,7 @@ class TestShamira(TestCase):
 			_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"))