Get started with threshold encryption

eos/core/bigint/python.py

@@ -27,6 +27,9 @@ class BigInt(EosObject):
 		
 		self.impl = int(a, b) if isinstance(a, str) else int(a)
 	
+	def __repr__(self):
+		return '<BigInt {}>'.format(str(self))
+	
 	def __pow__(self, other, modulo=None):
 		if not isinstance(other, BigInt):
 			other = BigInt(other)

eos/psr/bitstream.py

@@ -70,6 +70,16 @@ class BitStream(EosObject):
 		self.nbits += nbits
 		self.remaining += nbits
 	
+	def read_bigint(self):
+		length = self.read(32)
+		length = length.__int__()
+		return self.read(length)
+	
+	def write_bigint(self, value):
+		self.write(BigInt(value.nbits()), 32) # TODO: Arbitrary lengths
+		self.write(value)
+		return self
+	
 	def read_string(self):
 		length = self.read(32)
 		length = length.__int__() # JS attempts to call this twice if we do it in one line
@@ -98,6 +108,8 @@ class BitStream(EosObject):
 		else:
 			for i in range(len(strg)):
 				self.write(BigInt(strg.charCodeAt(i)), 7)
+		
+		return self
 	
 	# Make the size of this BitStream a multiple of the block_size
 	def multiple_of(self, block_size, pad_at_end=False):

eos/psr/crypto.py

@@ -140,3 +140,36 @@ class SEGCiphertext(EGCiphertext):
 		c = SHA256().update_bigint(gs, self.gamma, self.delta).hash_as_bigint()
 		
 		return self.c == c
+
+class Polynomial(EmbeddedObject):
+	coefficients = EmbeddedObjectListField(BigInt) # x^0, x^1, ... x^n
+	modulus = EmbeddedObjectField(BigInt)
+	
+	def value(self, x):
+		if not isinstance(x, BigInt):
+			x = BigInt(x)
+		
+		result = ZERO
+		for i in range(len(self.coefficients)):
+			#result = (result + ((self.coefficients[i] * pow(x, i, self.modulus)) % self.modulus)) % self.modulus
+			result = result + (self.coefficients[i] * pow(x, i))
+		return result
+
+class PedersenVSSPrivateKey(EmbeddedObject):
+	public_key = EmbeddedObjectField(SEGPublicKey)
+	
+	x = EmbeddedObjectField(BigInt) # secret
+	
+	def get_modified_secret(self):
+		mod_s = self.x
+		for j in range(1, threshold + 1): # 1 to threshold
+	
+	def decrypt(self, ciphertext):
+		if (
+			ciphertext.gamma <= ZERO or ciphertext.gamma >= self.public_key.group.p or
+			ciphertext.delta <= ZERO or ciphertext.delta >= self.public_key.group.p
+			):
+			raise Exception('Ciphertext is malformed')
+		
+		gamma_inv = pow(ciphertext.gamma, self.public_key.group.p - ONE - self.x, self.public_key.group.p)
+		return gamma_inv

eos/psr/secretsharing.py

@@ -0,0 +1,93 @@
+#   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_element()
+			self.f.coefficients.append(coeff)
+			#self.F.append(PedersenVSSCommitment(val=coeff, rand=self.sk.public_key.group.random_element()))
+			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_element())
+		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 other.pk.encrypt(self.f.value(other_idx + 1) % self.setup.group.p)
+		return BitStream().write_bigint(self.f.value(other_idx + 1)).multiple_of(other.pk.group.p.nbits(), True).map(other.pk.encrypt, other.pk.group.p.nbits())
+	
+	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

eos/psr/tests.py

@@ -22,6 +22,7 @@ from eos.psr.bitstream import *
 from eos.psr.crypto import *
 from eos.psr.election import *
 from eos.psr.mixnet import *
+from eos.psr.secretsharing import *
 from eos.psr.workflow import *
 
 class EGTestCase(EosTestCase):
@@ -297,3 +298,83 @@ class ElectionTestCase(EosTestCase):
 		# Release result
 		self.do_task_assert(election, 'eos.base.workflow.TaskReleaseResults', None)
 		election.save()
+
+class AAAPVSSTestCase(EosTestCase):
+	@py_only
+	def test_basic(self):
+		setup = PedersenVSSSetup()
+		setup.group = DEFAULT_GROUP
+		setup.threshold = 3 # 3 of 5
+		
+		for _ in range(5):
+			participant = PedersenVSSParticipant(setup)
+			participant.sk = EGPrivateKey.generate()
+			participant.pk = participant.sk.public_key
+			setup.participants.append(participant)
+		
+		# Step 1
+		
+		for participant in setup.participants:
+			participant.commit_pk_share()
+		
+		# IRL: Send hi=F[0] commitments around
+		
+		# Send shares around
+		for i in range(len(setup.participants)):
+			participant = setup.participants[i]
+			for j in range(len(setup.participants)):
+				other = setup.participants[j]
+				share = participant.get_share_for(j)
+				#share_dec = other.sk.decrypt(share)
+				share_dec = BitStream.unmap(share, other.sk.decrypt, other.sk.public_key.group.p.nbits()).read_bigint()
+				other.shares_received.append(share_dec)
+		
+		# Step 2
+		
+		# IRL: Decommit hi=F[0], send F around
+		
+		# Verify shares
+		for i in range(len(setup.participants)):
+			participant = setup.participants[i]
+			for j in range(len(setup.participants)):
+				other = setup.participants[j]
+				
+				# Verify share received by other from participant
+				share_dec = other.shares_received[i]
+				g_share_dec_expected = ONE
+				for k in range(0, setup.threshold):
+					g_share_dec_expected = (g_share_dec_expected * pow(participant.F[k], pow(j + 1, k), setup.group.p)) % setup.group.p
+				if pow(setup.group.g, share_dec, setup.group.p) != g_share_dec_expected:
+					import pdb; pdb.set_trace()
+					raise Exception('Share not consistent with commitments')
+		
+		# Compute threshold public key
+		pk = setup.compute_public_key()
+		
+		# Compute secret key shares
+		for participant in setup.participants:
+			participant.compute_secret_key()
+		
+		# Encrypt data
+		
+		pt = pk.group.random_element()
+		ct = pk.encrypt(pt)
+		
+		# Decrypt data
+		
+		decryption_shares = []
+		
+		# Pick any threshold
+		__pragma__('skip')
+		import random
+		__pragma__('noskip')
+		threshold_participants = list(range(len(setup.participants)))
+		random.shuffle(threshold_participants)
+		threshold_participants = threshold_participants[:setup.threshold]
+		
+		for i in setup.threshold:
+			share = setup.participants[i].threshold_sk.decrypt(ct)
+			decryption_shares.append((i, share))
+		
+		m = setup.combine_decryptions(decryption_shares)
+		self.assertEqualJSON(pt, m)