Implement RPC mixnets
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@ -5,3 +5,6 @@
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__javascript__
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__pycache__
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refs
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\#*
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.#*
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@ -16,6 +16,7 @@
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from eos.core.bigint import *
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from eos.core.objects import *
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from eos.base.election import *
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class CyclicGroup(EmbeddedObject):
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p = EmbeddedObjectField(BigInt)
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@ -92,6 +93,15 @@ class EGCiphertext(EmbeddedObject):
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public_key = EmbeddedObjectField(EGPublicKey)
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gamma = EmbeddedObjectField(BigInt) # G^k
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delta = EmbeddedObjectField(BigInt) # M X^k
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def reencrypt(self, k=None):
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# Generate an encryption of one
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if k is None:
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k = BigInt.crypto_random(ONE, self.public_key.group.p - TWO)
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gamma = pow(self.public_key.group.g, k, self.public_key.group.p)
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delta = pow(self.public_key.X, k, self.public_key.group.p)
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return EGCiphertext(public_key=self.public_key, gamma=((self.gamma * gamma) % self.public_key.group.p), delta=((self.delta * delta) % self.public_key.group.p)), k
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# Signed ElGamal per Schnorr & Jakobssen
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class SEGPublicKey(EGPublicKey):
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@ -118,26 +128,84 @@ class SEGPublicKey(EGPublicKey):
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class SEGPrivateKey(EGPrivateKey):
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pk_class = SEGPublicKey
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def decrypt(self, ciphertext):
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if (
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ciphertext.gamma <= ZERO or ciphertext.gamma >= self.public_key.group.p or
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ciphertext.delta <= ZERO or ciphertext.delta >= self.public_key.group.p
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):
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raise Exception('Ciphertext is malformed')
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gs = (pow(self.public_key.group.g, ciphertext.z, self.public_key.group.p) * pow(ciphertext.gamma, self.public_key.group.p - ONE - ciphertext.c, self.public_key.group.p)) % self.public_key.group.p
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_, c = EosObject.to_sha256(str(gs), str(ciphertext.gamma), str(ciphertext.delta))
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if ciphertext.c != c:
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raise Exception('Signature is invalid')
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gamma_inv = pow(ciphertext.gamma, self.public_key.group.p - ONE - self.x, self.public_key.group.p)
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pt = (gamma_inv * ciphertext.delta) % self.public_key.group.p
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return pt - ONE
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class SEGCiphertext(EGCiphertext):
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public_key = EmbeddedObjectField(SEGPublicKey)
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c = EmbeddedObjectField(BigInt)
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z = EmbeddedObjectField(BigInt)
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def is_signature_valid(self):
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gs = (pow(self.public_key.group.g, self.z, self.public_key.group.p) * pow(self.gamma, self.public_key.group.p - ONE - self.c, self.public_key.group.p)) % self.public_key.group.p
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_, c = EosObject.to_sha256(str(gs), str(self.gamma), str(self.delta))
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return self.c == c
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class BlockEncryptedAnswer(EncryptedAnswer):
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blocks = EmbeddedObjectListField()
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def decrypt(self):
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# TODO
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raise Exception('NYI')
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class RPCMixnet:
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def __init__(self):
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self.params = []
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def random_permutation(self, n):
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permutation = list(range(n))
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# Fisher-Yates shuffle
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i = n
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while i != 0:
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rnd = BigInt.crypto_random(0, i - 1)
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rnd = rnd.__int__()
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i -= 1
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permutation[rnd], permutation[i] = permutation[i], permutation[rnd]
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return permutation
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def shuffle(self, encrypted_answers):
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shuffled_answers = [None] * len(encrypted_answers)
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permutations = self.random_permutation(len(encrypted_answers))
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permutations_and_reenc = []
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for i in range(len(encrypted_answers)):
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encrypted_answer = encrypted_answers[i]
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# Reencrypt the answer
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shuffled_blocks = []
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block_reencryptions = []
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for block in encrypted_answer.blocks:
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block2, reenc = block.reencrypt()
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shuffled_blocks.append(block2)
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block_reencryptions.append(reenc)
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# And shuffle it to the new position
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shuffled_answers[permutations[i]] = BlockEncryptedAnswer(blocks=shuffled_blocks)
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# Record the parameters
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permutations_and_reenc.append([permutations[i], block_reencryptions, block.public_key.group.random_element(), block.public_key.group.random_element()])
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commitments_left = []
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for i in range(len(permutations_and_reenc)):
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val = permutations_and_reenc[i]
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val_json = [val[0], [str(x) for x in val[1]], str(val[2])]
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commitments_left.append(EosObject.to_sha256(EosObject.to_json(val_json))[0])
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commitments_right = []
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for i in range(len(permutations_and_reenc)):
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# Find the answer that went to 'i'
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idx = next(idx for idx in range(len(permutations_and_reenc)) if permutations_and_reenc[idx][0] == i)
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val = permutations_and_reenc[idx]
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val_json = [idx, [str(x) for x in val[1]], str(val[3])]
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commitments_right.append(EosObject.to_sha256(EosObject.to_json(val_json))[0])
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self.params = permutations_and_reenc
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return shuffled_answers, commitments_left, commitments_right
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def challenge(self, i, is_left):
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if is_left:
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val = self.params[i]
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return [val[0], val[1], val[2]]
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else:
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idx = next(idx for idx in range(len(self.params)) if self.params[idx][0] == i)
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val = self.params[idx]
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return [idx, val[1], val[3]]
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@ -33,8 +33,13 @@ class SEGTestCase(EosTestCase):
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pt = DEFAULT_GROUP.random_element()
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sk = SEGPrivateKey.generate()
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ct = sk.public_key.encrypt(pt)
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self.assertTrue(ct.is_signature_valid())
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m = sk.decrypt(ct)
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self.assertEqualJSON(pt, m)
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ct2, _ = ct.reencrypt()
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m2 = sk.decrypt(ct2)
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self.assertEqualJSON(pt, m2)
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class BitStreamTestCase(EosTestCase):
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def test_bitstream(self):
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@ -106,3 +111,59 @@ class BlockEGTestCase(EosTestCase):
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m = bs2.read_string()
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obj2 = EosObject.deserialise_and_unwrap(EosObject.from_json(m))
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self.assertEqualJSON(obj, obj2)
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class MixnetTestCase(EosTestCase):
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@py_only
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def test_mixnet(self):
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# Generate key
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sk = SEGPrivateKey.generate()
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# Generate plaintexts
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pts = []
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for i in range(10):
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pts.append(sk.public_key.group.random_element())
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# Encrypt plaintexts
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answers = []
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for i in range(len(pts)):
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bs = BitStream(pts[i])
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bs.multiple_of(sk.public_key.group.p.nbits() - 1)
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ct = bs.map(sk.public_key.encrypt, sk.public_key.group.p.nbits() - 1)
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answers.append(BlockEncryptedAnswer(blocks=ct))
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# Set up mixnet
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mixnet = RPCMixnet()
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# Mix answers
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shuffled_answers, commitments_left, commitments_right = mixnet.shuffle(answers)
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# Decrypt shuffle
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msgs = []
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for i in range(len(shuffled_answers)):
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bs = BitStream.unmap(shuffled_answers[i].blocks, sk.decrypt, sk.public_key.group.p.nbits() - 1)
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m = bs.read()
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msgs.append(m)
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# Check decryption
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self.assertEqual(set(int(x) for x in pts), set(int(x) for x in msgs))
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# Check commitments
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def verify_shuffle(idx_left, idx_right, reencs):
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claimed_blocks = shuffled_answers[idx_right].blocks
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for j in range(len(answers[idx_left].blocks)):
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reencrypted_block, _ = answers[idx_left].blocks[j].reencrypt(reencs[j])
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self.assertEqual(claimed_blocks[j].gamma, reencrypted_block.gamma)
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self.assertEqual(claimed_blocks[j].delta, reencrypted_block.delta)
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for i in range(len(pts)):
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# Left
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perm, reencs, rand = mixnet.challenge(i, True)
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val_json = [perm, [str(x) for x in reencs], str(rand)]
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self.assertEqual(commitments_left[i], EosObject.to_sha256(EosObject.to_json(val_json))[0])
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verify_shuffle(i, perm, reencs)
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# Right
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perm, reencs, rand = mixnet.challenge(i, False)
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val_json = [perm, [str(x) for x in reencs], str(rand)]
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self.assertEqual(commitments_right[i], EosObject.to_sha256(EosObject.to_json(val_json))[0])
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verify_shuffle(perm, i, reencs)
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