Eos/eos/psr/secretsharing.py

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2017-10-05 19:12:02 +11:00
# Eos - Verifiable elections
# Copyright © 2017 RunasSudo (Yingtong Li)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
from eos.core.bigint import *
from eos.core.objects import *
from eos.core.hashing import *
from eos.psr.crypto import *
from eos.psr.bitstream import *
class PedersenVSSSetup:
def __init__(self):
self.group = None
self.participants = []
self.threshold = 0
self.public_key = None
def compute_public_key(self):
h = ONE
for participant in self.participants:
h = (h * participant.h.val) % self.group.p
self.public_key = SEGPublicKey(group=self.group, X=h)
return self.public_key
def combine_decryption(self, decryption_shares):
gamma_inv = ONE
for i, share in decryption_shares:
lagrange_num = ONE
lagrange_den = ONE
for j, _ in decryption_shares:
lagrange_num = lagrange_num * BigInt(j)
lagrange_den = lagrange_den * BigInt(j - i)
if lagrange_num % lagrange_den != 0:
raise Exception('Cannot raise to fractional exponent')
gamma_inv = gamma_inv * pow(share, lagrange_num / lagrange_den, self.group.p)
class PedersenVSSCommitment(EmbeddedObject):
val = EmbeddedObjectField(BigInt)
rand = EmbeddedObjectField(BigInt)
class PedersenVSSParticipant():
def __init__(self, setup):
self.setup = setup
self.pk = None
self.shares_received = []
self.F = []
self.h = None
self.h_commitment = None
self.sk = None # non-threshold
self.threshold_sk = None
self.f = Polynomial(modulus=self.setup.group.p)
def commit_pk_share(self):
# Generate random polynomial
for _ in range(0, self.setup.threshold): # 0 to k-1
coeff = self.setup.group.random_Zq_element()
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self.f.coefficients.append(coeff)
self.F.append(pow(self.setup.group.g, coeff, self.setup.group.p))
self.h = PedersenVSSCommitment(val=self.F[0], rand=self.setup.group.random_Zq_element())
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self.h_commitment = SHA256().update_obj(self.h).hash_as_bigint()
return self.h_commitment
def get_share_for(self, other_idx):
other = self.setup.participants[other_idx]
return BitStream().write_bigint(self.f.value(other_idx + 1)).multiple_of(other.pk.nbits(), True).map(other.pk.encrypt, other.pk.nbits())
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def compute_secret_key(self):
x = ZERO
for share in self.shares_received:
x = (x + share) % self.setup.group.p
self.threshold_sk = PedersenVSSPrivateKey(public_key=self.setup.public_key, x=x)
return self.threshold_sk