From c4d90bf4ea0c5b7a016028ed994de19638d3113b Mon Sep 17 00:00:00 2001 From: Determinant Date: Tue, 17 Nov 2020 20:04:09 -0500 Subject: support saving as a keystore file --- frozen_deps/Cryptodome/Protocol/SecretSharing.py | 278 +++++++++++++++++++++++ 1 file changed, 278 insertions(+) create mode 100644 frozen_deps/Cryptodome/Protocol/SecretSharing.py (limited to 'frozen_deps/Cryptodome/Protocol/SecretSharing.py') diff --git a/frozen_deps/Cryptodome/Protocol/SecretSharing.py b/frozen_deps/Cryptodome/Protocol/SecretSharing.py new file mode 100644 index 0000000..6fdc9b4 --- /dev/null +++ b/frozen_deps/Cryptodome/Protocol/SecretSharing.py @@ -0,0 +1,278 @@ +# +# SecretSharing.py : distribute a secret amongst a group of participants +# +# =================================================================== +# +# Copyright (c) 2014, Legrandin +# All rights reserved. +# +# Redistribution and use in source and binary forms, with or without +# modification, are permitted provided that the following conditions +# are met: +# +# 1. Redistributions of source code must retain the above copyright +# notice, this list of conditions and the following disclaimer. +# 2. Redistributions in binary form must reproduce the above copyright +# notice, this list of conditions and the following disclaimer in +# the documentation and/or other materials provided with the +# distribution. +# +# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS +# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE +# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, +# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, +# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER +# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +# POSSIBILITY OF SUCH DAMAGE. +# =================================================================== + +from Cryptodome.Util.py3compat import is_native_int +from Cryptodome.Util import number +from Cryptodome.Util.number import long_to_bytes, bytes_to_long +from Cryptodome.Random import get_random_bytes as rng + + +def _mult_gf2(f1, f2): + """Multiply two polynomials in GF(2)""" + + # Ensure f2 is the smallest + if f2 > f1: + f1, f2 = f2, f1 + z = 0 + while f2: + if f2 & 1: + z ^= f1 + f1 <<= 1 + f2 >>= 1 + return z + + +def _div_gf2(a, b): + """ + Compute division of polynomials over GF(2). + Given a and b, it finds two polynomials q and r such that: + + a = b*q + r with deg(r)= d: + s = 1 << (deg(r) - d) + q ^= s + r ^= _mult_gf2(b, s) + return (q, r) + + +class _Element(object): + """Element of GF(2^128) field""" + + # The irreducible polynomial defining this field is 1+x+x^2+x^7+x^128 + irr_poly = 1 + 2 + 4 + 128 + 2 ** 128 + + def __init__(self, encoded_value): + """Initialize the element to a certain value. + + The value passed as parameter is internally encoded as + a 128-bit integer, where each bit represents a polynomial + coefficient. The LSB is the constant coefficient. + """ + + if is_native_int(encoded_value): + self._value = encoded_value + elif len(encoded_value) == 16: + self._value = bytes_to_long(encoded_value) + else: + raise ValueError("The encoded value must be an integer or a 16 byte string") + + def __eq__(self, other): + return self._value == other._value + + def __int__(self): + """Return the field element, encoded as a 128-bit integer.""" + return self._value + + def encode(self): + """Return the field element, encoded as a 16 byte string.""" + return long_to_bytes(self._value, 16) + + def __mul__(self, factor): + + f1 = self._value + f2 = factor._value + + # Make sure that f2 is the smallest, to speed up the loop + if f2 > f1: + f1, f2 = f2, f1 + + if self.irr_poly in (f1, f2): + return _Element(0) + + mask1 = 2 ** 128 + v, z = f1, 0 + while f2: + # if f2 ^ 1: z ^= v + mask2 = int(bin(f2 & 1)[2:] * 128, base=2) + z = (mask2 & (z ^ v)) | ((mask1 - mask2 - 1) & z) + v <<= 1 + # if v & mask1: v ^= self.irr_poly + mask3 = int(bin((v >> 128) & 1)[2:] * 128, base=2) + v = (mask3 & (v ^ self.irr_poly)) | ((mask1 - mask3 - 1) & v) + f2 >>= 1 + return _Element(z) + + def __add__(self, term): + return _Element(self._value ^ term._value) + + def inverse(self): + """Return the inverse of this element in GF(2^128).""" + + # We use the Extended GCD algorithm + # http://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor + + if self._value == 0: + raise ValueError("Inversion of zero") + + r0, r1 = self._value, self.irr_poly + s0, s1 = 1, 0 + while r1 > 0: + q = _div_gf2(r0, r1)[0] + r0, r1 = r1, r0 ^ _mult_gf2(q, r1) + s0, s1 = s1, s0 ^ _mult_gf2(q, s1) + return _Element(s0) + + def __pow__(self, exponent): + result = _Element(self._value) + for _ in range(exponent - 1): + result = result * self + return result + + +class Shamir(object): + """Shamir's secret sharing scheme. + + A secret is split into ``n`` shares, and it is sufficient to collect + ``k`` of them to reconstruct the secret. + """ + + @staticmethod + def split(k, n, secret, ssss=False): + """Split a secret into ``n`` shares. + + The secret can be reconstructed later using just ``k`` shares + out of the original ``n``. + Each share must be kept confidential to the person it was + assigned to. + + Each share is associated to an index (starting from 1). + + Args: + k (integer): + The sufficient number of shares to reconstruct the secret (``k < n``). + n (integer): + The number of shares that this method will create. + secret (byte string): + A byte string of 16 bytes (e.g. the AES 128 key). + ssss (bool): + If ``True``, the shares can be used with the ``ssss`` utility. + Default: ``False``. + + Return (tuples): + ``n`` tuples. A tuple is meant for each participant and it contains two items: + + 1. the unique index (an integer) + 2. the share (a byte string, 16 bytes) + """ + + # + # We create a polynomial with random coefficients in GF(2^128): + # + # p(x) = \sum_{i=0}^{k-1} c_i * x^i + # + # c_0 is the encoded secret + # + + coeffs = [_Element(rng(16)) for i in range(k - 1)] + coeffs.append(_Element(secret)) + + # Each share is y_i = p(x_i) where x_i is the public index + # associated to each of the n users. + + def make_share(user, coeffs, ssss): + idx = _Element(user) + share = _Element(0) + for coeff in coeffs: + share = idx * share + coeff + if ssss: + share += _Element(user) ** len(coeffs) + return share.encode() + + return [(i, make_share(i, coeffs, ssss)) for i in range(1, n + 1)] + + @staticmethod + def combine(shares, ssss=False): + """Recombine a secret, if enough shares are presented. + + Args: + shares (tuples): + The *k* tuples, each containin the index (an integer) and + the share (a byte string, 16 bytes long) that were assigned to + a participant. + ssss (bool): + If ``True``, the shares were produced by the ``ssss`` utility. + Default: ``False``. + + Return: + The original secret, as a byte string (16 bytes long). + """ + + # + # Given k points (x,y), the interpolation polynomial of degree k-1 is: + # + # L(x) = \sum_{j=0}^{k-1} y_i * l_j(x) + # + # where: + # + # l_j(x) = \prod_{ \overset{0 \le m \le k-1}{m \ne j} } + # \frac{x - x_m}{x_j - x_m} + # + # However, in this case we are purely interested in the constant + # coefficient of L(x). + # + + k = len(shares) + + gf_shares = [] + for x in shares: + idx = _Element(x[0]) + value = _Element(x[1]) + if any(y[0] == idx for y in gf_shares): + raise ValueError("Duplicate share") + if ssss: + value += idx ** k + gf_shares.append((idx, value)) + + result = _Element(0) + for j in range(k): + x_j, y_j = gf_shares[j] + + numerator = _Element(1) + denominator = _Element(1) + + for m in range(k): + x_m = gf_shares[m][0] + if m != j: + numerator *= x_m + denominator *= x_j + x_m + result += y_j * numerator * denominator.inverse() + return result.encode() -- cgit v1.2.3-70-g09d2