def scratch(puz, sk, m):
assert len(m) == 20
d, puzid = puz
leaves, tree = sk
root = tree[-1][0]
# Draw a random nonce
nonce = random_string(k / 8)
# Select Q1 branches
h1 = sha1_fixed(rzfill(puzid + root + nonce, 64))
qinds = select_hash(h1, Q1, TREE1_HEIGHT - 1)
leaves1 = [leaves[i] for i in qinds]
branches1 = [merkle_select(tree, i) for i in qinds]
# Merkle-Damgard hash
# leaf [branch] ... leaf [branch]
state = h1
for leaf, branch in zip(leaves1, branches1):
lb = [leaf] + branch
for j in range(CIRCUITS_PER_BRANCH):
lbh = lb[j * HASHES_PER_CIRCUIT : (j + 1) * HASHES_PER_CIRCUIT]
state = sha1_fixed(rzfill(state + "".join(lbh), ENC_BLOCKS_PER_CIRCUIT * 64))
h2 = state
# Check if winner!
if not long(binascii.hexlify(h2), base=16) < 2 ** (k - d):
return
# print 'h2', binascii.hexlify(h2)
# Use H(h2|m) to select 4*Q2 more leaves
hm = h2
q2inds = []
iters = int(ceil(float(4 * Q2) / (k / (TREE1_HEIGHT - 1))))
for i in range(iters):
hm = hash(hm + m)
# print 'hm', binascii.hexlify(hm)
q2inds += select_hash(hm, (k / (TREE1_HEIGHT - 1)), TREE1_HEIGHT - 1)
q2inds = q2inds[: Q2 * 4]
# print "[scratch] qinds:", qinds, "q2inds:", q2inds
# Choose the first Q2 (we have all of them)
chosen = list(q2inds)
random.shuffle(chosen)
chosen = set(q2inds[:Q2])
chosen = [q for q in q2inds if q in chosen]
leaves2 = [leaves[i] for i in chosen]
branches2 = [merkle_select(tree, i) for i in chosen]
ticket = root, nonce, zip(leaves1 + leaves2, branches1 + branches2), chosen
return ticket
def verify_ticket(puz, ticket, m):
# Parse ticket as root, nonce, branches
d, puzid = puz
root, nonce, leavesbranches, zinds = ticket
# Check that root selects a set of q branches
h1 = sha1_fixed(rzfill(puzid + root + nonce, 64))
qinds = select_hash(h1, Q1, TREE1_HEIGHT - 1)
# Compute hashtree digest over all the data in branches
assert len(leavesbranches) == Q1 + Q2
assert len(qinds) + len(zinds) == Q1 + Q2
for ind, (leaf, branch) in zip(tuple(qinds) + tuple(zinds), leavesbranches):
assert len(branch) == TREE1_HEIGHT - 1
assert merkle_check(hash(leaf), branch, root, ind)
# Merkle Damgard hash over all leaves and branches
state = h1
for leaf, branch in leavesbranches[:Q1]:
lb = [leaf] + branch
for j in range(CIRCUITS_PER_BRANCH):
lbh = lb[j * HASHES_PER_CIRCUIT : (j + 1) * HASHES_PER_CIRCUIT]
state = sha1_fixed(rzfill(state + "".join(lbh), ENC_BLOCKS_PER_CIRCUIT * 64))
h2 = state
assert long(binascii.hexlify(h2), 16) < 2 ** (k - d)
# Check that zinds are a Q2 subset of the 4Q2 chosen ones
hm = h2
iters = int(ceil(float(4 * Q2) / (k / (TREE1_HEIGHT - 1))))
q2inds = []
for i in range(iters):
hm = hash(hm + m)
q2inds += select_hash(hm, (k / (TREE1_HEIGHT - 1)), TREE1_HEIGHT - 1)
q2inds = q2inds[: 4 * Q2]
# print 'q2inds', q2inds
assert len(zinds) == Q2
# assert zinds == q2inds[:Q2]
assert is_subset(zinds, q2inds)
return True
def vc_verify_ticket_full(puz, ticket, m, witnesses):
d, puzid = puz
ciphertext_sets, hmacs, public_value, hmacG = ticket
assert len(witnesses) == N_CIRCUITS + 1
for b in range(Q1 + Q2):
for i in range(CIRCUITS_PER_BRANCH):
ciphertexts = ciphertext_sets[b * CIRCUITS_PER_BRANCH + i]
assert len(ciphertexts) == HASHES_PER_CIRCUIT * 20
cblocks = sha1_fixed(rzfill(ciphertexts, ENC_BLOCKS_PER_CIRCUIT * 64))
bi = (b << 16) + i
bi_s = long_to_string(bi, 4)
v_input = hash(
(hmacs[b * CIRCUITS_PER_BRANCH + i] + hmacs[b * CIRCUITS_PER_BRANCH + i + 1] + cblocks + bi_s + hmacG)
)
assert vc_check_circuit_1(v_input, witnesses[b * CIRCUITS_PER_BRANCH + i])
puzstr = long_to_string(d, 4) + puz[1]
v_input = hash(hmacs[0] + hmacs[-1] + m + puzstr + elgamal.group_element_to_string(public_value))
assert vc_check_circuit_final(v_input, witnesses[-1])
def write_inputs(output_dir, puz, vcticket, witnesses):
import os
import scratch_pb2
output_dir = output_dir + "B_c%02d_h%02d_q1%02d_q2%02d" % (HASHES_PER_CIRCUIT, TREE1_HEIGHT, Q1, Q2)
try:
os.makedirs(output_dir)
except OSError:
pass # directory already exists
class CircuitInput(object):
def __init__(self, f):
self.f = f
self.wirecount = 0
def write(self, s):
assert len(s) % 4 == 0, "Only writing multiples of 32 bits"
for i in range(len(s) / 4):
b = s[i * 4 : (i + 1) * 4]
ss = binascii.hexlify(b)
self.f.write("%d %s\n" % (self.wirecount, ss))
# print 'wrote:', self.wirecount
self.wirecount += 1
def close(self):
self.f.write("%d 1\n" % (self.wirecount,))
d, puzid = puz
ciphertext_sets, hmacs, public_value, hmacG = vcticket
for i, witness in enumerate(witnesses[:-1]):
# Inner witness
(
root,
bi_s,
lbhere,
hmacG_key,
old_hmac,
new_hmac,
cblocks,
ciphertexts,
old_state,
old_hmac_key,
old_merkle_state,
new_state,
hmac_key,
enc_key,
inds_s,
) = witness
# Local indices
b = string_to_long(bi_s) >> 16
z = (string_to_long(bi_s)) & 0xFFFF
# Verifier input
v_input = hash((hmacs[i] + hmacs[i + 1] + cblocks + bi_s + hmacG))
print "inner witness[%d]: v_input:%s old_hmac:%s new_hmac:%s" % (
i,
binascii.hexlify(v_input),
binascii.hexlify(old_hmac),
binascii.hexlify(new_hmac),
)
# Encryptions
ciphertexts = ciphertext_sets[i]
cblocks = sha1_fixed(rzfill(ciphertexts, 64 * ENC_BLOCKS_PER_CIRCUIT))
# Write the wire inputs file
with open(os.path.join(output_dir, "wire_input_%02d.in" % i), "w") as f:
cf = CircuitInput(f)
# Verifier's input
cf.write(v_input)
# Prover's inputs
cf.write(root)
cf.write(enc_key)
assert len(inds_s) == 48
cf.write(inds_s)
cf.write(bi_s)
cf.write(rzfill("".join(lbhere), 20 * (HASHES_PER_CIRCUIT)))
print binascii.hexlify(rzfill("".join(lbhere), 20 * (HASHES_PER_CIRCUIT)))
cf.write(old_hmac)
cf.write(new_hmac)
cf.write(hmacG)
cf.write(old_merkle_state)
cf.write(hmacG_key)
cf.write(cblocks)
cf.write(old_state)
cf.write(old_hmac_key)
cf.write(new_state)
cf.write(hmac_key)
cf.close()
print "hmacG", binascii.hexlify(hmacG)
# Final Witness
for _ in [1]:
(
root,
nonce,
hmacG,
hmacG_key,
first_hmac_key,
h2,
inds_s,
last_hmac_key,
hmac0,
hmacN,
m,
puzstr,
public_value,
secret_exponent,
secret_value,
) = witnesses[-1]
gu = elgamal.g_raised_to(secret_exponent)
hu = elgamal.h_raised_to(secret_exponent)
assert public_value == gu
assert secret_value == hu
enc_key = sha1_fixed(elgamal.group_element_to_string(secret_value))
# Check the verifier input
v_input = hash(hmac0 + hmacN + m + puzstr + elgamal.group_element_to_string(gu))
# Write the wire inputs file
with open(os.path.join(output_dir, "wire_input_final.in"), "w") as f:
cf = CircuitInput(f)
# Verifier's input
# cf.write(v_input)
assert len(v_input) == 20
# Prover's inputs
cf.write(hmacG)
cf.write(hmac0)
cf.write(hmacN)
cf.write(m)
assert len(m) == 20
cf.write(puzstr)
assert len(puzstr) == 24
cf.write(root)
cf.write(nonce)
cf.write(hmacG_key)
cf.write(first_hmac_key)
cf.write(h2)
assert len(inds_s) == 48
cf.write(inds_s)
cf.write(last_hmac_key)
print "root", binascii.hexlify(root)
print "nonce", binascii.hexlify(nonce)
print "hmac0", binascii.hexlify(hmac0)
print "hmacN", binascii.hexlify(hmacN)
# cf.write(elgamal.group_element_to_string(gu))
# assert len(elgamal.group_element_to_string(gu)) == 128
cf.write(elgamal.group_element_to_string(hu))
assert len(elgamal.group_element_to_string(hu)) == 128
bitstring = bin(secret_exponent)[2:]
bitstring = "0" * (512 - len(bitstring)) + bitstring
for bit in map(int, bitstring[::-1]):
cf.write(long_to_string(bit, 4))
cf.close()
def vc_check_circuit_final(v_input, witness):
(
root,
nonce,
hmacG,
hmacG_key,
first_hmac_key,
h2,
inds_s,
last_hmac_key,
hmac0,
hmacN,
m,
puzstr,
public_value,
secret_exponent,
secret_value,
) = witness
d = string_to_long(puzstr[:4])
puzid = puzstr[4:]
# Recompute h1 and check indices
h1 = sha1_fixed(rzfill(puzid + root + nonce, 64))
q1inds = select_hash(h1, Q1, TREE1_HEIGHT - 1)
# Recompute the entire inds hash
hm = hash(h2 + m)
q2inds = []
iters = int(ceil(float(4 * Q2) / (k / (TREE1_HEIGHT - 1))))
for i in range(iters):
hm = hash(hm + m)
q2inds += select_hash(hm, (k / (TREE1_HEIGHT - 1)), TREE1_HEIGHT - 1)
inds = []
for j in range(Q1 + Q2):
inds.append(string_to_long(inds_s[j * 2 : (j + 1) * 2]))
inds = tuple(inds)
assert inds[:Q1] == q1inds
# TODO: check that Q2 is a subset of q2inds
assert len(inds[Q1 : Q1 + Q2]) == Q2
# Check the diffie hellman value for enc_key and secret_value
gu = elgamal.g_raised_to(secret_exponent)
hu = elgamal.h_raised_to(secret_exponent)
assert secret_value == hu
enc_key = sha1_fixed(elgamal.group_element_to_string(secret_value))
print "h1", binascii.hexlify(h1)
# Check v_input
assert hmac0 == sha1_fixed(rzfill(first_hmac_key + h1 + "\0" * 20, 64))
assert hmacN == sha1_fixed(rzfill(last_hmac_key + h2 + root, 64))
assert hmacG == hash(hmacG_key + root + enc_key + inds_s)
# Check the verifier input
assert v_input == hash(hmac0 + hmacN + m + puzstr + elgamal.group_element_to_string(gu))
# Check winning condition
assert long(binascii.hexlify(h2), 16) < 2 ** (k - d)
return True
def vc_check_circuit_1(v_input, witness):
# Parse witness
(
root,
bi_s,
lbhere,
hmacG_key,
old_hmac,
new_hmac,
cblocks,
ciphertexts,
old_state,
old_hmac_key,
old_merkle_state,
new_state,
hmac_key,
enc_key,
inds_s,
) = witness
b = string_to_long(bi_s) >> 16
i = string_to_long(bi_s) & 0xFFFF
# Recompute the global HMAC
hmacG = hash(hmacG_key + root + enc_key + inds_s)
# Open verifier input
assert hash((old_hmac + new_hmac + cblocks + bi_s + hmacG)) == v_input
# Check opening of state commitment
old_hmac_check = sha1_fixed(rzfill(old_hmac_key + old_state + old_merkle_state, 64))
assert old_hmac_check == old_hmac
# Check the encryption of branches
stream = rzfill("".join(lbhere), HASHES_PER_CIRCUIT * 20)
ciphertexts = shacal_encrypt(stream, b * HASHES_PER_CIRCUIT * CIRCUITS_PER_BRANCH + i * HASHES_PER_CIRCUIT, enc_key)
assert cblocks == sha1_fixed(rzfill(ciphertexts, 64 * ENC_BLOCKS_PER_CIRCUIT))
# Check the updated hash state
stream = rzfill(old_state + "".join(lbhere), ENC_BLOCKS_PER_CIRCUIT * 64)
if b < Q1:
new_state_check = sha1_fixed(stream)
else:
new_state_check = old_state
assert new_state == new_state_check
# Check the incremental merkle state
ind = string_to_long(inds_s[2 * b : 2 * (b + 1)])
if i > 0:
ind_copy = ind >> (i * HASHES_PER_CIRCUIT - 1)
else:
ind_copy = ind
merkle_state = old_merkle_state
for j in range(HASHES_PER_CIRCUIT):
if i * HASHES_PER_CIRCUIT + j >= TREE1_HEIGHT:
continue
sibling = lbhere[j]
if i == 0 and j == 0:
merkle_state = hash(sibling) # It's actually the leaf
else:
if not ind_copy % 2: # left node select, sibling to the right
merkle_state = hash(merkle_state + sibling)
else:
merkle_state = hash(sibling + merkle_state)
ind_copy >>= 1
if i * HASHES_PER_CIRCUIT + j == TREE1_HEIGHT - 1:
assert merkle_state == root
# Check opening of the new hmac commitment
hmac = sha1_fixed(rzfill(hmac_key + new_state + merkle_state, 64))
assert hmac == new_hmac
return True
def transform(puz, ticket, m, hmac_keys, secret_exponent):
d, puzid = puz
root, nonce, leavesbranches, chosen = ticket
secret_value = elgamal.h_raised_to(secret_exponent)
public_value = elgamal.g_raised_to(secret_exponent)
enc_key = sha1_fixed(elgamal.group_element_to_string(secret_value))
# A) Need to encrypt the root, nonce, leaves, and branches, in chunks
# B) Need to make HMAC commitments to the internal state
# C) Need to break the leavesQ1/branchesQ1 into chunks to be verified
# Build an iterator over the randomness rather than counting for now
assert len(hmac_keys) == 2 + N_CIRCUITS
# These need to be coalesced into group elements!
ciphertexts = []
assert len(leavesbranches) == Q1 + Q2
h1 = sha1_fixed(rzfill(puzid + root + nonce, 64))
inds = select_hash(h1, Q1, TREE1_HEIGHT - 1) + tuple(chosen)
assert len(inds) == Q1 + Q2
inds_s = rzfill("".join(long_to_string(ind, 2) for ind in inds), 48)
# The first randomness is used as IV for the hashchain over leaves
state = h1
# Ciphertext accumulators, as well as the set of ciphertexts
cipher_accs = []
ciphertext_sets = []
# Commitments to local state
hmacs = []
# Initialize hmacs with root, empty state/inds
hmac = sha1_fixed(rzfill(hmac_keys[0] + h1 + "\0" * 20, 64))
hmacs.append(hmac)
# Commitments to glob
hmacG = hash((hmac_keys[-1] + root + enc_key + inds_s))
# Witnesses
witnesses = []
merkle_state = "\0" * 20
# First prepare the encryptions
for b in range(Q1 + Q2):
leaf, branch = leavesbranches[b]
leafbranch = [leaf] + branch
ind = inds[b]
for i in range(CIRCUITS_PER_BRANCH):
# qhere is the number of branches to process here
lbhere = leafbranch[HASHES_PER_CIRCUIT * i : HASHES_PER_CIRCUIT * (i + 1)]
stream = rzfill(state + "".join(lbhere), ENC_BLOCKS_PER_CIRCUIT * 64)
# Update the state
old_state = state
if b < Q1:
state = sha1_fixed(stream)
# Encrypt using SHACAL, then pad to multiple of 512 bits
stream = rzfill("".join(lbhere), HASHES_PER_CIRCUIT * 20)
ciphertexts = shacal_encrypt(
stream, b * HASHES_PER_CIRCUIT * CIRCUITS_PER_BRANCH + i * HASHES_PER_CIRCUIT, enc_key
)
assert len(ciphertexts) == HASHES_PER_CIRCUIT * 20
ciphertext_sets.append(ciphertexts)
# Now we need to hash over the ciphertexts used in this circuit
cipher_accs.append(sha1_fixed(rzfill(ciphertexts, ENC_BLOCKS_PER_CIRCUIT * 64)))
# Finally we need to prepare the auxiliary merkle tree information
if i > 0:
ind_copy = ind >> (i * HASHES_PER_CIRCUIT - 1)
else:
ind_copy = ind
old_merkle_state = merkle_state
for j in range(HASHES_PER_CIRCUIT):
if i * HASHES_PER_CIRCUIT + j >= TREE1_HEIGHT:
continue
sibling = lbhere[j]
if i == 0 and j == 0:
merkle_state = hash(sibling) # It's actually the leaf
else:
if not ind_copy % 2: # left node select, sibling to the right
merkle_state = hash(merkle_state + sibling)
else:
merkle_state = hash(sibling + merkle_state)
ind_copy >>= 1
if i * HASHES_PER_CIRCUIT + j == TREE1_HEIGHT - 1:
assert merkle_state == root
# Finally, we must collect the root, state, index accumulator, into
# an hmac commitment
hmac = sha1_fixed(rzfill(hmac_keys[b * CIRCUITS_PER_BRANCH + i + 1] + state + merkle_state, 64))
hmacs.append(hmac)
witness = (
root,
long_to_string((b << 16) + i, 4),
lbhere,
hmac_keys[-1],
hmacs[-2],
hmacs[-1],
cipher_accs[-1],
ciphertexts,
old_state,
hmac_keys[b * CIRCUITS_PER_BRANCH + i],
old_merkle_state,
state,
hmac_keys[b * CIRCUITS_PER_BRANCH + i + 1],
enc_key,
inds_s,
)
witnesses.append(witness)
# Verifier information
verifier_data = ciphertext_sets, hmacs, public_value, hmacG
# Witness information
puzstr = long_to_string(d, 4) + puzid
last_witness = (
root,
nonce,
hmacG,
hmac_keys[-1],
hmac_keys[0],
state,
inds_s,
hmac_keys[-2],
hmacs[0],
hmacs[-1],
m,
puzstr,
public_value,
secret_exponent,
secret_value,
)
witnesses.append(last_witness)
return verifier_data, witnesses