def commit(h, m, n, d):
if len(h) != m * n + d + 1:
raise ArithmeticError
if m < 1 or n < 1 or d < 0 or d >= m:
raise IndexError
b = [dumb25519.random_scalar()
for j in range(n)] + [dumb25519.Scalar(0)] # blinding terms
M = [] # blinded coefficient matrix; initially we define using columns
# the first column is unique
M.append([h[i] for i in range(d)] + [h[d] - b[0]] +
[dumb25519.Scalar(0) for i in range(m - d)])
# the rest of the columns (this is why there is an extra blinding term)
for j in range(n):
M.append([b[j]] +
[h[i] for i in range(j * m + d + 1, (j + 1) * m + d)] +
[h[(j + 1) * m + d] - b[j + 1]])
# test that each matrix entry is a Scalar
for i in range(n + 1):
for j in range(m + 1):
if not isinstance(M[i][j], dumb25519.Scalar):
raise TypeError
# commit to each row
r = [dumb25519.random_scalar() for i in range(m + 1)] # masks
H = [] # commitments
for i in range(m + 1):
H.append(dumb25519.pedersen_commit([col[i] for col in M], r[i]))
return H, [M, b, r]
def test_batch_2_m_1_n_4(self):
M = 1
N = 4
data = [[Scalar(random.randint(0,2**N-1)),random_scalar()] for i in range(M)]
proof1 = pybullet.prove(data,N)
data = [[Scalar(random.randint(0,2**N-1)),random_scalar()] for i in range(M)]
proof2 = pybullet.prove(data,N)
pybullet.verify([proof1,proof2],N)
def test_scalar_vector_mul_scalar(self):
l = 3
v = ScalarVector([random_scalar() for i in range(l)])
s = random_scalar()
w = v*s
self.assertEqual(len(w),l)
for i in range(l):
self.assertEqual(w[i],v[i]*s)
def test_scalar_vector_sub(self):
l = 3
v = ScalarVector([random_scalar() for i in range(l)])
w = ScalarVector([random_scalar() for i in range(l)])
x = v-w
self.assertEqual(len(x),l)
for i in range(l):
self.assertEqual(x[i],v[i]-w[i])
def test_scalar_vector_hadamard(self):
l = 3
v = ScalarVector([random_scalar() for i in range(l)])
w = ScalarVector([random_scalar() for i in range(l)])
x = v*w
self.assertEqual(len(x),l)
for i in range(l):
self.assertEqual(x[i],v[i]*w[i])
def test_inner_product(self):
l = 3
v = ScalarVector([random_scalar() for i in range(l)])
w = ScalarVector([random_scalar() for i in range(l)])
x = v**w
r = Scalar(0)
for i in range(l):
r += v[i]*w[i]
self.assertEqual(r,x)
def test_invalid_batch_2_m_1_2_n_4(self):
M = 1
N = 4
data = [[Scalar(random.randint(0,2**N-1)),random_scalar()] for i in range(M)]
proof1 = pybullet.prove(data,N)
M = 2
data = [[Scalar(random.randint(2**N,2**(N+1)-1)),random_scalar()] for i in range(M)]
proof2 = pybullet.prove(data,N)
with self.assertRaises(ArithmeticError):
pybullet.verify([proof1,proof2],N)
def gen_account(public_key,a):
r = dumb25519.random_scalar()
co = G*a + H*r
ek = dumb25519.random_scalar()
s = dumb25519.hash_to_scalar(str(public_key.tpk)+str(public_key.spk)+str(public_key.X)+str(ek))
pk = public_key.X + H*s
_ek = ecies.encrypt(public_key.tpk,str(pk)+str(co),str(ek))
_a = ecies.encrypt(public_key.spk,str(pk)+str(co),str(a))
_r = ecies.encrypt(public_key.spk,str(pk)+str(co),str(r))
return Account(pk,co,_ek,_a,_r),DepositKey(a,r)
def test_scalar_vector_slice(self):
l = 3
scalars = [random_scalar() for i in range(2*l)]
v = ScalarVector(scalars)
w = v[:l]
self.assertEqual(len(w),l)
self.assertEqual(w.scalars,scalars[:l])
def test_point_vector_mul_scalar(self):
l = 3
V = PointVector([random_point() for i in range(l)])
s = random_scalar()
W = V*s
self.assertEqual(len(W),l)
for i in range(l):
self.assertEqual(W[i],V[i]*s)
def encrypt(m,A):
k = Scalar(0)
while k == Scalar(0):
k = random_scalar()
output = Ciphertext()
output.K = G*k
output.M = m + hash_to_scalar(A*k)
return output
def test_batch_inversion(self):
l = 8
v = ScalarVector([random_scalar() for i in range(l)])
v.append(Scalar(1))
v.append(Scalar(dumb25519.l - 1))
w = v.invert()
for i in range(len(v)):
self.assertEqual(v[i] * w[i], Scalar(1))
def test_invalid_value(self):
M = 1
N = 4
data = [[
Scalar(random.randint(2**N, 2**(N + 1) - 1)),
random_scalar()
]]
with self.assertRaises(ArithmeticError):
pybullet.verify([pybullet.prove(data, N)], N)
def test_point_vector_mul_scalar_vector(self):
l = 3
V = PointVector([random_point() for i in range(l)])
v = ScalarVector([random_scalar() for i in range(l)])
W = V*v
R = dumb25519.Z
for i in range(l):
R += V[i]*v[i]
self.assertEqual(W,R)
def spend(withdrawal_keys, deposit_keys, tx, mu):
witness = prepare_witness(withdrawal_keys, deposit_keys)
witness_list = [
witness.d_ijk, witness.x_i, witness.a_in, witness.a_ij, witness.r_in,
witness.r_out
] # this is so we can flatten for commitment
t = dumb25519.random_scalar()
C = dumb25519.pedersen_commit(dumb25519.flatten(witness_list), t)
s = dumb25519.hash_to_scalar(str(C) + str(tx) + str(mu))
def encrypt(public_key, tag, message):
if not isinstance(public_key, dumb25519.Point):
raise TypeError
r = dumb25519.random_scalar()
R = G * r
P = public_key * r
hashes = hashlib.sha256(str(P) + str(tag)).hexdigest()
sym_key = hashes[:len(hashes) / 2]
mac_key = hashes[len(hashes) / 2:]
e = binascii.hexlify(
AES.new(sym_key, AES.MODE_CFB, '0' * 16).encrypt(str(message)))
sigma = hashlib.sha256(mac_key +
hashlib.sha256(mac_key +
e).hexdigest()).hexdigest()
return Ciphertext(R, e, sigma)
def prove(data,N):
clear_cache()
M = len(data)
# curve points
G = dumb25519.G
H = hash_to_point('pybullet H')
Gi = PointVector([hash_to_point('pybullet Gi ' + str(i)) for i in range(M*N)])
Hi = PointVector([hash_to_point('pybullet Hi ' + str(i)) for i in range(M*N)])
# set amount commitments
V = PointVector([])
aL = ScalarVector([])
for v,gamma in data:
V.append((H*v + G*gamma)*inv8)
mash(V[-1])
aL.extend(scalar_to_bits(v,N))
# set bit arrays
aR = ScalarVector([])
for bit in aL.scalars:
aR.append(bit-Scalar(1))
alpha = random_scalar()
A = (Gi*aL + Hi*aR + G*alpha)*inv8
sL = ScalarVector([random_scalar()]*(M*N))
sR = ScalarVector([random_scalar()]*(M*N))
rho = random_scalar()
S = (Gi*sL + Hi*sR + G*rho)*inv8
# get challenges
mash(A)
mash(S)
y = cache
y_inv = y.invert()
mash('')
z = cache
# polynomial coefficients
l0 = aL - ScalarVector([z]*(M*N))
l1 = sL
# ugly sum
zeros_twos = []
for i in range (M*N):
zeros_twos.append(Scalar(0))
for j in range(1,M+1):
temp = Scalar(0)
if i >= (j-1)*N and i < j*N:
temp = Scalar(2)**(i-(j-1)*N)
zeros_twos[-1] += temp*(z**(1+j))
# more polynomial coefficients
r0 = aR + ScalarVector([z]*(M*N))
r0 = r0*exp_scalar(y,M*N)
r0 += ScalarVector(zeros_twos)
r1 = exp_scalar(y,M*N)*sR
# build the polynomials
t0 = l0**r0
t1 = l0**r1 + l1**r0
t2 = l1**r1
tau1 = random_scalar()
tau2 = random_scalar()
T1 = (H*t1 + G*tau1)*inv8
T2 = (H*t2 + G*tau2)*inv8
mash(T1)
mash(T2)
x = cache # challenge
taux = tau1*x + tau2*(x**2)
for j in range(1,M+1):
gamma = data[j-1][1]
taux += z**(1+j)*gamma
mu = x*rho+alpha
l = l0 + l1*x
r = r0 + r1*x
t = l**r
mash(taux)
mash(mu)
mash(t)
x_ip = cache # challenge
L = PointVector([])
R = PointVector([])
# initial inner product inputs
data_ip = [Gi,PointVector([Hi[i]*(y_inv**i) for i in range(len(Hi))]),H*x_ip,l,r,None,None]
while True:
data_ip = inner_product(data_ip)
# we have reached the end of the recursion
if len(data_ip) == 2:
return [V,A,S,T1,T2,taux,mu,L,R,data_ip[0],data_ip[1],t]
# we are not done yet
L.append(data_ip[-2])
R.append(data_ip[-1])
def verify(proofs,N):
# determine the length of the longest proof
max_MN = 2**max([len(proof[7]) for proof in proofs])
# curve points
Z = dumb25519.Z
G = dumb25519.G
H = hash_to_point('pybullet H')
Gi = PointVector([hash_to_point('pybullet Gi ' + str(i)) for i in range(max_MN)])
Hi = PointVector([hash_to_point('pybullet Hi ' + str(i)) for i in range(max_MN)])
# set up weighted aggregates
y0 = Scalar(0)
y1 = Scalar(0)
z1 = Scalar(0)
z3 = Scalar(0)
z4 = [Scalar(0)]*max_MN
z5 = [Scalar(0)]*max_MN
scalars = ScalarVector([]) # for final check
points = PointVector([]) # for final check
# run through each proof
for proof in proofs:
clear_cache()
V,A,S,T1,T2,taux,mu,L,R,a,b,t = proof
# get size information
M = 2**len(L)/N
# weighting factors for batching
weight_y = random_scalar()
weight_z = random_scalar()
if weight_y == Scalar(0) or weight_z == Scalar(0):
raise ArithmeticError
# reconstruct all challenges
for v in V:
mash(v)
mash(A)
mash(S)
if cache == Scalar(0):
raise ArithmeticError
y = cache
y_inv = y.invert()
mash('')
if cache == Scalar(0):
raise ArithmeticError
z = cache
mash(T1)
mash(T2)
if cache == Scalar(0):
raise ArithmeticError
x = cache
mash(taux)
mash(mu)
mash(t)
if cache == Scalar(0):
raise ArithmeticError
x_ip = cache
y0 += taux*weight_y
k = (z-z**2)*sum_scalar(y,M*N)
for j in range(1,M+1):
k -= (z**(j+2))*sum_scalar(Scalar(2),N)
y1 += (t-k)*weight_y
for j in range(M):
scalars.append(z**(j+2)*weight_y)
points.append(V[j]*Scalar(8))
scalars.append(x*weight_y)
points.append(T1*Scalar(8))
scalars.append(x**2*weight_y)
points.append(T2*Scalar(8))
scalars.append(weight_z)
points.append(A*Scalar(8))
scalars.append(x*weight_z)
points.append(S*Scalar(8))
# inner product
W = ScalarVector([])
for i in range(len(L)):
mash(L[i])
mash(R[i])
if cache == Scalar(0):
raise ArithmeticError
W.append(cache)
W_inv = W.invert()
for i in range(M*N):
index = i
g = a
h = b*((y_inv)**i)
for j in range(len(L)-1,-1,-1):
J = len(W)-j-1
base_power = 2**j
if index/base_power == 0:
g *= W_inv[J]
h *= W[J]
else:
g *= W[J]
h *= W_inv[J]
index -= base_power
g += z
h -= (z*(y**i) + (z**(2+i/N))*(Scalar(2)**(i%N)))*((y_inv)**i)
z4[i] += g*weight_z
z5[i] += h*weight_z
z1 += mu*weight_z
for i in range(len(L)):
scalars.append(W[i]**2*weight_z)
points.append(L[i]*Scalar(8))
scalars.append(W_inv[i]**2*weight_z)
points.append(R[i]*Scalar(8))
z3 += (t-a*b)*x_ip*weight_z
# now check all proofs together
scalars.append(-y0-z1)
points.append(G)
scalars.append(-y1+z3)
points.append(H)
for i in range(max_MN):
scalars.append(-z4[i])
points.append(Gi[i])
scalars.append(-z5[i])
points.append(Hi[i])
if not dumb25519.multiexp(scalars,points) == Z:
raise ArithmeticError('Bad z check!')
return True
def verify(proofs,N):
# determine the length of the longest proof
max_MN = 2**max([len(proof.L) for proof in proofs])
# curve points
Z = dumb25519.Z
Gi = PointVector([hash_to_point('pybullet Gi ' + str(i)) for i in range(max_MN)])
Hi = PointVector([hash_to_point('pybullet Hi ' + str(i)) for i in range(max_MN)])
# set up weighted aggregates
y0 = Scalar(0)
y1 = Scalar(0)
z1 = Scalar(0)
z3 = Scalar(0)
z4 = [Scalar(0)]*max_MN
z5 = [Scalar(0)]*max_MN
scalars = ScalarVector([]) # for final check
points = PointVector([]) # for final check
# run through each proof
for proof in proofs:
tr = transcript.Transcript('Bulletproof')
V = proof.V
A = proof.A
S = proof.S
T1 = proof.T1
T2 = proof.T2
taux = proof.taux
mu = proof.mu
L = proof.L
R = proof.R
a = proof.a
b = proof.b
t = proof.t
# get size information
M = 2**len(L)/N
# weighting factors for batching
weight_y = random_scalar()
weight_z = random_scalar()
if weight_y == Scalar(0) or weight_z == Scalar(0):
raise ArithmeticError
# reconstruct challenges
for v in V:
tr.update(v)
tr.update(A)
tr.update(S)
y = tr.challenge()
if y == Scalar(0):
raise ArithmeticError
y_inv = y.invert()
z = tr.challenge()
if z == Scalar(0):
raise ArithmeticError
tr.update(T1)
tr.update(T2)
x = tr.challenge()
if x == Scalar(0):
raise ArithmeticError
tr.update(taux)
tr.update(mu)
tr.update(t)
x_ip = tr.challenge()
if x_ip == Scalar(0):
raise ArithmeticError
y0 += taux*weight_y
k = (z-z**2)*sum_scalar(y,M*N)
for j in range(1,M+1):
k -= (z**(j+2))*sum_scalar(Scalar(2),N)
y1 += (t-k)*weight_y
for j in range(M):
scalars.append(z**(j+2)*weight_y)
points.append(V[j]*Scalar(8))
scalars.append(x*weight_y)
points.append(T1*Scalar(8))
scalars.append(x**2*weight_y)
points.append(T2*Scalar(8))
scalars.append(weight_z)
points.append(A*Scalar(8))
scalars.append(x*weight_z)
points.append(S*Scalar(8))
# inner product
W = ScalarVector([])
for i in range(len(L)):
tr.update(L[i])
tr.update(R[i])
W.append(tr.challenge())
if W[i] == Scalar(0):
raise ArithmeticError
W_inv = W.invert()
for i in range(M*N):
index = i
g = a
h = b*((y_inv)**i)
for j in range(len(L)-1,-1,-1):
J = len(W)-j-1
base_power = 2**j
if index/base_power == 0:
g *= W_inv[J]
h *= W[J]
else:
g *= W[J]
h *= W_inv[J]
index -= base_power
g += z
h -= (z*(y**i) + (z**(2+i/N))*(Scalar(2)**(i%N)))*((y_inv)**i)
z4[i] += g*weight_z
z5[i] += h*weight_z
z1 += mu*weight_z
for i in range(len(L)):
scalars.append(W[i]**2*weight_z)
points.append(L[i]*Scalar(8))
scalars.append(W_inv[i]**2*weight_z)
points.append(R[i]*Scalar(8))
z3 += (t-a*b)*x_ip*weight_z
# now check all proofs together
scalars.append(-y0-z1)
points.append(Gc)
scalars.append(-y1+z3)
points.append(Hc)
for i in range(max_MN):
scalars.append(-z4[i])
points.append(Gi[i])
scalars.append(-z5[i])
points.append(Hi[i])
if not dumb25519.multiexp(scalars,points) == Z:
raise ArithmeticError('Bad verification!')
return True
def prove(data,N):
tr = transcript.Transcript('Bulletproof')
M = len(data)
# curve points
Gi = PointVector([hash_to_point('pybullet Gi ' + str(i)) for i in range(M*N)])
Hi = PointVector([hash_to_point('pybullet Hi ' + str(i)) for i in range(M*N)])
# set amount commitments
V = PointVector([])
aL = ScalarVector([])
for v,gamma in data:
V.append(com(v,gamma)*inv8)
tr.update(V[-1])
aL.extend(scalar_to_bits(v,N))
# set bit arrays
aR = ScalarVector([])
for bit in aL.scalars:
aR.append(bit-Scalar(1))
alpha = random_scalar()
A = (Gi**aL + Hi**aR + Gc*alpha)*inv8
sL = ScalarVector([random_scalar()]*(M*N))
sR = ScalarVector([random_scalar()]*(M*N))
rho = random_scalar()
S = (Gi**sL + Hi**sR + Gc*rho)*inv8
# get challenges
tr.update(A)
tr.update(S)
y = tr.challenge()
z = tr.challenge()
y_inv = y.invert()
# polynomial coefficients
l0 = aL - ScalarVector([z]*(M*N))
l1 = sL
# for polynomial coefficients
zeros_twos = []
z_cache = z**2
for j in range(M):
for i in range(N):
zeros_twos.append(z_cache*2**i)
z_cache *= z
# more polynomial coefficients
r0 = aR + ScalarVector([z]*(M*N))
r0 = r0*exp_scalar(y,M*N)
r0 += ScalarVector(zeros_twos)
r1 = exp_scalar(y,M*N)*sR
# build the polynomials
t0 = l0**r0
t1 = l0**r1 + l1**r0
t2 = l1**r1
tau1 = random_scalar()
tau2 = random_scalar()
T1 = com(t1,tau1)*inv8
T2 = com(t2,tau2)*inv8
tr.update(T1)
tr.update(T2)
x = tr.challenge()
taux = tau1*x + tau2*(x**2)
for j in range(1,M+1):
gamma = data[j-1][1]
taux += z**(1+j)*gamma
mu = x*rho+alpha
l = l0 + l1*x
r = r0 + r1*x
t = l**r
tr.update(taux)
tr.update(mu)
tr.update(t)
x_ip = tr.challenge()
# initial inner product inputs
data = InnerProductRound(Gi,PointVector([Hi[i]*(y_inv**i) for i in range(len(Hi))]),Hc*x_ip,l,r,tr)
while True:
inner_product(data)
# we have reached the end of the recursion
if data.done:
return Bulletproof(V,A,S,T1,T2,taux,mu,data.L,data.R,data.a,data.b,t)
def gen_private_key():
return dumb25519.random_scalar()
def prove(x):
if not x < max_x:
raise ValueError('Discrete log is too large!')
if not x >= 0:
raise ValueError('Discrete log must not be negative!')
b = nary(x, 2)
# generate blinders that sum to zero
r = dumb25519.ScalarVector([])
r_sum = dumb25519.Scalar(0)
s = dumb448.ScalarVector([])
s_sum = dumb448.Scalar(0)
for i in range(len(b) - 1):
r.append(dumb25519.random_scalar())
r_sum += dumb25519.Scalar(2)**i * r[-1]
s.append(dumb448.random_scalar())
s_sum += dumb448.Scalar(2)**i * s[-1]
temp_2inv_25519 = (dumb25519.Scalar(2)**(len(b) - 1)).invert()
temp_2inv_448 = (dumb448.Scalar(2)**(len(b) - 1)).invert()
r.append(-temp_2inv_25519 * r_sum)
s.append(-temp_2inv_448 * s_sum)
# sanity check on blinder sums
temp_r = dumb25519.Scalar(0)
temp_s = dumb448.Scalar(0)
for i in range(len(b)):
temp_r += dumb25519.Scalar(2)**i * r[i]
temp_s += dumb448.Scalar(2)**i * s[i]
if not temp_r == dumb25519.Scalar(0) or not temp_s == dumb448.Scalar(0):
raise ArithmeticError('Blinder sum check failed!')
# generators
G = dumb25519.G
G1 = dumb25519.hash_to_point('G1')
H = dumb448.hash_to_point('H')
H1 = dumb448.hash_to_point('H1')
# commitments to bits of x
C_G = dumb25519.PointVector([])
C_H = dumb448.PointVector([])
for i in range(len(b)):
C_G.append(dumb25519.Scalar(b[i]) * G1 + r[i] * G)
C_H.append(dumb448.Scalar(b[i]) * H1 + s[i] * H)
# sanity check on commitment sums
temp_C_G = dumb25519.Z
temp_C_H = dumb448.Z
for i in range(len(b)):
temp_C_G += dumb25519.Scalar(2)**i * C_G[i]
temp_C_H += dumb448.Scalar(2)**i * C_H[i]
if not temp_C_G == dumb25519.Scalar(
x) * G1 or not temp_C_H == dumb448.Scalar(x) * H1:
raise ArithmeticError('Bit construction check failed!')
# proof elements
e0_G = dumb25519.ScalarVector([])
e0_H = dumb448.ScalarVector([])
a0 = dumb25519.ScalarVector([])
a1 = dumb25519.ScalarVector([])
b0 = dumb448.ScalarVector([])
b1 = dumb448.ScalarVector([])
# construct the proof
for i in range(len(b)):
# the current bit is 0
if b[i] == 0:
j = dumb25519.random_scalar()
k = dumb448.random_scalar()
e1_G = dumb25519.hash_to_scalar(C_G[i], C_H[i], j * G, k * H)
e1_H = dumb448.hash_to_scalar(C_G[i], C_H[i], j * G, k * H)
a0.append(dumb25519.random_scalar())
b0.append(dumb448.random_scalar())
e0_G.append(
dumb25519.hash_to_scalar(C_G[i], C_H[i],
a0[i] * G - e1_G * (C_G[i] - G1),
b0[i] * H - e1_H * (C_H[i] - H1)))
e0_H.append(
dumb448.hash_to_scalar(C_G[i], C_H[i],
a0[i] * G - e1_G * (C_G[i] - G1),
b0[i] * H - e1_H * (C_H[i] - H1)))
a1.append(j + e0_G[i] * r[i])
b1.append(k + e0_H[i] * s[i])
# the current bit is 1
elif b[i] == 1:
j = dumb25519.random_scalar()
k = dumb448.random_scalar()
e0_G.append(dumb25519.hash_to_scalar(C_G[i], C_H[i], j * G, k * H))
e0_H.append(dumb448.hash_to_scalar(C_G[i], C_H[i], j * G, k * H))
a1.append(dumb25519.random_scalar())
b1.append(dumb448.random_scalar())
e1_G = dumb25519.hash_to_scalar(C_G[i], C_H[i],
a1[i] * G - e0_G[i] * C_G[i],
b1[i] * H - e0_H[i] * C_H[i])
e1_H = dumb448.hash_to_scalar(C_G[i], C_H[i],
a1[i] * G - e0_G[i] * C_G[i],
b1[i] * H - e0_H[i] * C_H[i])
a0.append(j + e1_G * r[i])
b0.append(k + e1_H * s[i])
# somehow the bit is something else
else:
raise ArithmeticError('Bit decomposition must be 0 or 1!')
return Proof(
dumb25519.Scalar(x) * G1,
dumb448.Scalar(x) * H1, C_G, C_H, e0_G, e0_H, a0, a1, b0, b1)
def verify(proofs,N):
# determine the length of the longest proof
max_MN = 2**max([len(proof[7]) for proof in proofs])
# curve points
Z = dumb25519.Z
G = dumb25519.G
H = dumb25519.H
Gi = PointVector([hash_to_point('pybullet Gi ' + str(i)) for i in range(max_MN)])
Hi = PointVector([hash_to_point('pybullet Hi ' + str(i)) for i in range(max_MN)])
# verify that all points are in the correct subgroup
for item in dumb25519.flatten(proofs):
if not isinstance(item,Point):
continue
if not item*Scalar(dumb25519.l) == Z:
raise ArithmeticError
# set up weighted aggregates
y0 = Scalar(0)
y1 = Scalar(0)
Y2 = Z
Y3 = Z
Y4 = Z
Z0 = Z
z1 = Scalar(0)
Z2 = Z
z3 = Scalar(0)
z4 = [Scalar(0)]*max_MN
z5 = [Scalar(0)]*max_MN
# run through each proof
for proof in proofs:
clear_cache()
V,A,S,T1,T2,taux,mu,L,R,a,b,t = proof
# get size information
M = 2**len(L)/N
# weighting factor for batching
w = random_scalar()
# reconstruct all challenges
for v in V:
mash(v)
mash(A)
mash(S)
y = cache
mash('')
z = cache
mash(T1)
mash(T2)
x = cache
mash(taux)
mash(mu)
mash(t)
x_ip = cache
y0 += taux*w
k = (z-z**2)*sum_scalar(y,M*N)
for j in range(1,M+1):
k -= (z**(j+2))*sum_scalar(Scalar(2),N)
y1 += (t-k)*w
Temp = Z
for j in range(M):
Temp += V[j]*(z**(j+2)*Scalar(8))
Y2 += Temp*w
Y3 += T1*(x*w*Scalar(8))
Y4 += T2*((x**2)*w*Scalar(8))
Z0 += (A*Scalar(8)+S*(x*Scalar(8)))*w
# inner product
W = []
for i in range(len(L)):
mash(L[i])
mash(R[i])
W.append(cache)
for i in range(M*N):
index = i
g = a
h = b*((y.invert())**i)
for j in range(len(L)-1,-1,-1):
J = len(W)-j-1
base_power = 2**j
if index/base_power == 0:
g *= W[J].invert()
h *= W[J]
else:
g *= W[J]
h *= W[J].invert()
index -= base_power
g += z
h -= (z*(y**i) + (z**(2+i/N))*(Scalar(2)**(i%N)))*((y.invert())**i)
z4[i] += g*w
z5[i] += h*w
z1 += mu*w
Multiexp = []
for i in range(len(L)):
Multiexp.append([L[i],Scalar(8)*(W[i]**2)])
Multiexp.append([R[i],Scalar(8)*(W[i].invert()**2)])
Z2 += dumb25519.multiexp(Multiexp)*w
z3 += (t-a*b)*x_ip*w
# now check all proofs together
if not G*y0 + H*y1 - Y2 - Y3 - Y4 == Z:
raise ArithmeticError('Bad y check!')
Multiexp = [[Z0,Scalar(1)],[G,-z1],[Z2,Scalar(1)],[H,z3]]
for i in range(max_MN):
Multiexp.append([Gi[i],-z4[i]])
Multiexp.append([Hi[i],-z5[i]])
if not dumb25519.multiexp(Multiexp) == Z:
raise ArithmeticError('Bad z check!')
return True
def test_random(self):
random_scalar()
random_point()
def gen_private_key():
return PrivateKey(ecies.gen_private_key(),ecies.gen_private_key(),dumb25519.random_scalar())
def test_8_random(self):
data = [[random_point(),random_scalar()] for i in range(8)]
result = Z
for datum in data:
result += datum[0]*datum[1]
self.assertEqual(dumb25519.multiexp(data),result)
def test_prove_verify_m_2_n_4(self):
M = 2
N = 4
data = [[Scalar(random.randint(0,2**N-1)),random_scalar()] for i in range(M)]
pybullet.verify([pybullet.prove(data,N)],N)