def test_hashing(self):
hash_to_point('The Human Fund: Money For People')
hash_to_scalar('The Human Fund: Money For People')
hash_to_point(str(G))
hash_to_scalar(str(G))
hash_to_point(str(8675309))
hash_to_scalar(str(8675309))
with self.assertRaises(TypeError):
hash_to_point(8675309)
with self.assertRaises(TypeError):
hash_to_scalar(8675309)
with self.assertRaises(TypeError):
hash_to_point(G)
with self.assertRaises(TypeError):
hash_to_scalar(G)
def verify(proof):
xG = proof.xG
xH = proof.xH
C_G = proof.C_G
C_H = proof.C_H
e0_G = proof.e0_G
e0_H = proof.e0_H
a0 = proof.a0
a1 = proof.a1
b0 = proof.b0
b1 = proof.b1
# generators
G = dumb25519.G
G1 = dumb25519.hash_to_point('G1')
H = dumb448.hash_to_point('H')
H1 = dumb448.hash_to_point('H1')
# reconstruct hashes using commitments
xG_prime = dumb25519.Z
xH_prime = dumb448.Z
for i in range(len(C_G)):
xG_prime += dumb25519.Scalar(2)**i * C_G[i]
xH_prime += dumb448.Scalar(2)**i * C_H[i]
if not xG_prime == xG or not xH_prime == xH:
raise ArithmeticError('Commitments do not sum to hash value!')
for i in range(len(C_G)):
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])
e0_prime_G = 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_prime_H = 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))
if not e0_G[i] == e0_prime_G or not e0_H[i] == e0_prime_H:
raise ArithmeticError(
'Bitwise ring signature verification failed!')
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 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 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)
