def test_bsecfld(self):
secfld = mpc.SecFld(char=2, min_order=2**8)
a = secfld(57)
b = secfld(67)
self.assertEqual(int(mpc.run(mpc.output(mpc.input(a, 0)))), 57)
self.assertEqual(int(mpc.run(mpc.output(+a - -a))), 0)
self.assertEqual(int(mpc.run(mpc.output(a * b))), 137)
self.assertEqual(int(mpc.run(mpc.output(a * b / a))), 67)
self.assertEqual(int(mpc.run(mpc.output(a**254 * a))), 1)
self.assertEqual(int(mpc.run(mpc.output(a & b))), 1)
self.assertEqual(int(mpc.run(mpc.output(a | b))), 123)
self.assertEqual(int(mpc.run(mpc.output(a ^ b))), 122)
self.assertEqual(int(mpc.run(mpc.output(~a))), 198)
c = mpc.run(mpc.output(mpc.to_bits(secfld(0))))
self.assertEqual(c, [0, 0, 0, 0, 0, 0, 0, 0])
c = mpc.run(mpc.output(mpc.to_bits(secfld(1))))
self.assertEqual(c, [1, 0, 0, 0, 0, 0, 0, 0])
c = mpc.run(mpc.output(mpc.to_bits(secfld(255))))
self.assertEqual(c, [1, 1, 1, 1, 1, 1, 1, 1])
c = mpc.run(mpc.output(mpc.to_bits(secfld(255), 1)))
self.assertEqual(c, [1])
c = mpc.run(mpc.output(mpc.to_bits(secfld(255), 4)))
self.assertEqual(c, [1, 1, 1, 1])
self.assertEqual(mpc.run(mpc.output(mpc.matrix_sub([[a]], [[a]])[0])),
[0])
self.assertEqual(
mpc.run(mpc.output(mpc.matrix_prod([c], [[a] * 4], True)[0])), [0])
self.assertEqual(
mpc.run(mpc.output(mpc.matrix_prod([[a] * 4], [c], True)[0])), [0])
def sbox(x):
"""AES S-Box."""
y = mpc.to_bits(x**254)
z = mpc.matrix_prod([y], A, True)[0]
w = mpc.vector_add(z, B)
v = mpc.from_bits(w)
return v
def sbox1(v):
"""AES inverse S-Box."""
w = mpc.to_bits(v)
z = mpc.vector_add(w, B)
y = mpc.matrix_prod([z], A1, True)[0]
x = mpc.from_bits(y)**254
return x
async def linear_solve(A, B):
secfld = type(A[0][0])
d, e = len(A), len(B[0])
await mpc.returnType(secfld, d * e + 1)
R, detR = random_matrix_determinant(secfld, d)
RA = mpc.matrix_prod(R, A)
RA = await mpc.output([a for row in RA for a in row])
RA = np.reshape(RA, (d, d))
RB = mpc.matrix_prod(R, B)
RB = await mpc.gather(RB) # NB: RB is secret-shared
invA_B, detRA = bareiss(secfld.field, np.concatenate((RA, RB), axis=1))
detA = detRA / detR
adjA_B = [secfld(a) * detA for row in invA_B for a in row]
return adjA_B + [detA]
async def main():
parser = argparse.ArgumentParser()
parser.add_argument('-k',
'--order',
type=int,
metavar='K',
help='order K of hash chain, length n=2**K')
parser.add_argument('--recursive',
action='store_true',
help='use recursive pebbler')
parser.add_argument('--no-one-way',
action='store_true',
default=False,
help='use dummy one-way function')
parser.add_argument('--no-random-seed',
action='store_true',
default=False,
help='use fixed seed')
parser.set_defaults(order=1)
args = parser.parse_args()
await mpc.start()
if args.recursive:
Pebbler = P
else:
Pebbler = p
IV = [[aes.secfld(3)] * 4] * 4 # IV as 4x4 array of GF(256) elements
global f
if args.no_one_way:
D = aes.circulant_matrix([3, 0, 0, 0])
f = lambda x: mpc.matrix_prod(D, x)
else:
K = aes.key_expansion(IV)
f = lambda x: mpc.matrix_add(aes.encrypt(K, x), x)
if args.no_random_seed:
x0 = IV
else:
x0 = [[mpc.random.getrandbits(aes.secfld, 8) for _ in range(4)]
for _ in range(4)]
k = args.order
print(f'Hash chain of length {2**k}:')
r = 1
for v in Pebbler(k, x0):
if v is None: # initial stage
print(f'{r:4}', '-')
await mpc.throttler(0.1
) # raise barrier roughly every 10 AES calls
else: # output stage
await aes.xprint(f'{r:4} x{2**(k+1) - 1 - r:<4} =', v)
r += 1
await mpc.shutdown()
def decrypt(K, s):
"""AES decryption of s given key schedule K."""
Nr = len(K) - 1 # Nr is 10 or 14
for i in range(Nr, 0, -1):
s = mpc.matrix_add(s, K[i])
if i < Nr:
s = mpc.matrix_prod(C1, s)
s = [s[j][-j:] + s[j][:-j] for j in range(4)]
s = [[sbox1(x) for x in _] for _ in s]
s = mpc.matrix_add(s, K[0])
return s
def encrypt(K, s):
"""AES encryption of s given key schedule K."""
Nr = len(K) - 1 # Nr is 10 or 14
s = mpc.matrix_add(s, K[0])
for i in range(1, Nr + 1):
s = [[sbox(x) for x in _] for _ in s]
s = [s[j][j:] + s[j][:j] for j in range(4)]
if i < Nr:
s = mpc.matrix_prod(C, s)
s = mpc.matrix_add(s, K[i])
return s
def random_matrix_determinant(secfld, d):
d_2 = d * (d - 1) // 2
L = np.diagflat([secfld(1)] * d)
L[np.tril_indices(d, -1)] = mpc._randoms(secfld, d_2)
L[np.triu_indices(d, 1)] = [secfld(0)] * d_2
diag = mpc._randoms(secfld, d)
U = np.diagflat(diag)
U[np.tril_indices(d, -1)] = [secfld(0)] * d_2
U[np.triu_indices(d, 1)] = mpc._randoms(secfld, d_2)
R = mpc.matrix_prod(L.tolist(), U.tolist())
detR = mpc.prod(diag) # detR != 0 with overwhelming probability
return R, detR
async def schmidt_multilateration(locations, toas):
"""Schmidt's multilateration algorithm."""
# Transform sensor locations and ToA measurements
# into linear system A w = b, using Schmidt's method:
norm = [mpc.in_prod(p, p) for p in locations]
A, b = [], []
for i, j, k in itertools.combinations(range(len(locations)), 3):
Delta = [toas[j] - toas[k], toas[k] - toas[i], toas[i] - toas[j]]
XYZN = [
locations[i] + [norm[i]], locations[j] + [norm[j]],
locations[k] + [norm[k]]
]
r_x, r_y, r_z, r_n = mpc.matrix_prod([Delta], XYZN)[0]
A.append([2 * r_x, 2 * r_y, 2 * r_z])
b.append(mpc.prod(Delta) + r_n)
# Compute least-squares solution w satisfying A^T A w = A^T b:
AT, bT = list(map(list, zip(*A))), [b] # transpose of A and b
ATA = mpc.matrix_prod(AT, AT, tr=True) # A^T (A^T)^T = A^T A
ATb = mpc.matrix_prod(AT, bT, tr=True) # A^T (b^T)^T = A^T b
w_det = linear_solve(ATA, ATb)
x, y, z, det = await mpc.output(w_det)
w = x / det, y / det, z / det
return w
async def id3(T, R) -> asyncio.Future:
sizes = [mpc.in_prod(T, v) for v in S[C]]
i, mx = mpc.argmax(sizes)
sizeT = mpc.sum(sizes)
stop = (sizeT <= int(args.epsilon * len(T))) + (mx == sizeT)
if not (R and await mpc.is_zero_public(stop)):
i = await mpc.output(i)
logging.info(f'Leaf node label {i}')
tree = i
else:
T_R = [[mpc.schur_prod(T, v) for v in S[A]] for A in R]
gains = [GI(mpc.matrix_prod(T_A, S[C], True)) for T_A in T_R]
k = await mpc.output(mpc.argmax(gains, key=SecureFraction)[0])
T_Rk = T_R[k]
del T_R, gains # release memory
A = list(R)[k]
logging.info(f'Attribute node {A}')
if args.parallel_subtrees:
subtrees = await mpc.gather(
[id3(Tj, R.difference([A])) for Tj in T_Rk])
else:
subtrees = [await id3(Tj, R.difference([A])) for Tj in T_Rk]
tree = A, subtrees
return tree
async def main():
parser = argparse.ArgumentParser()
parser.add_argument(
'-i',
'--dataset',
type=int,
metavar='I',
help=('dataset 0=uvlp (default), 1=wiki, 2=tb2x2, 3=woody, '
'4=LPExample_R20, 5=sc50b, 6=kb2, 7=LPExample'))
parser.add_argument('-l',
'--bit-length',
type=int,
metavar='L',
help='override preset bit length for dataset')
parser.set_defaults(dataset=0, bit_length=0)
args = parser.parse_args()
settings = [('uvlp', 24, 37 / 3), ('wiki', 24, 20), ('tb2x2', 18, 10.5),
('woody', 36, 540), ('LPExample_R20', 52, 3.441176),
('sc50b', 52, 70), ('kb2', 96, 1749.9204734889486),
('LPExample', 96, 1188806595)]
name, bit_length, exact_max = settings[args.dataset]
if args.bit_length:
bit_length = args.bit_length
with open(os.path.join('data', 'lp', name + '.csv')) as file:
T = list(csv.reader(file))
m = len(T) - 1
n = len(T[0]) - 1
secfxp = mpc.SecFxp(bit_length)
print(
f'Using secure {bit_length}-bit fixed-point numbers: {secfxp.__name__}'
)
print(f'dataset: {name} with {m} constraints and {n} variables')
T[0][-1] = '0' # initialize optimal value
for i in range(m + 1):
for j in range(n + 1):
T[i][j] = secfxp(float(T[i][j]), integral=False)
c = T[0][:-1] # maximize c.x subject to A.x <= b, x >= 0
A = [T[i + 1][:-1] for i in range(m)]
b = [T[i + 1][-1] for i in range(m)]
await mpc.start()
cobasis = [secfxp(j) for j in range(n)]
basis = [secfxp(n + i) for i in range(m)]
iteration = 0
while True:
# find index of pivot column
p_col_index, minimum = argmin_int(T[0][:-1])
if await mpc.output(minimum >= 0):
break # maximum reached
# find index of pivot row
p_col = mpc.matrix_prod([p_col_index], T, True)[0]
constraints = [[T[i][-1], p_col[i], p_col[i] > 0.0001]
for i in range(1, m + 1)]
p_row_index, (_, pivot, _) = argmin_rat(constraints)
# reveal progress a bit
iteration += 1
mx = await mpc.output(T[0][-1])
p = await mpc.output(pivot)
logging.info(f'Iteration {iteration}: {mx} pivot={p}')
# swap basis entries
delta = mpc.in_prod(basis, p_row_index) - mpc.in_prod(
cobasis, p_col_index)
cobasis = mpc.vector_add(cobasis, mpc.scalar_mul(delta, p_col_index))
basis = mpc.vector_sub(basis, mpc.scalar_mul(delta, p_row_index))
# update tableau Tij = Tij - (Til - bool(i==k))/Tkl * (Tkj + bool(j==l))
p_col_index.append(secfxp(0))
p_row_index.insert(0, secfxp(0))
p_col = mpc.vector_sub(p_col, p_row_index)
p_col = mpc.scalar_mul(1 / pivot, p_col)
p_row = mpc.matrix_prod([p_row_index], T)[0]
p_row = mpc.vector_add(p_row, p_col_index)
T = mpc.gauss(T, secfxp(1), p_col, p_row)
mx = await mpc.output(T[0][-1])
rel_error = (mx - exact_max) / exact_max
print(f'max = {mx} (error {rel_error:.3%}) in {iteration} iterations')
logging.info('Solution x')
x = [secfxp(0) for _ in range(n)]
for i in range(m):
u = mpc.unit_vector(basis[i], m + n)[:n]
v = mpc.scalar_mul(T[i + 1][-1], u)
x = mpc.vector_add(x, v)
cx = mpc.in_prod(c, x)
Ax = mpc.matrix_prod([x], A, True)[0]
approx = lambda a: 1.01 * a + 0.0001
Ax_bounded_by_b = mpc.all(Ax[i] <= approx(b[i]) for i in range(m))
x_nonnegative = mpc.all(x[j] >= 0 for j in range(n))
logging.info('Dual solution y')
y = [secfxp(0) for _ in range(m)]
for j in range(n):
u = mpc.unit_vector(cobasis[j], m + n)[n:]
v = mpc.scalar_mul(T[0][j], u)
y = mpc.vector_sub(y, v)
yb = mpc.in_prod(y, b)
yA = mpc.matrix_prod([y], A)[0]
approx = lambda a: mpc.if_else(a < 0, 1 / 1.01, 1.01) * a + 0.0001
yA_bounded_by_c = mpc.all(yA[j] <= approx(c[j]) for j in range(n))
y_nonpositive = mpc.all(y[i] <= 0 for i in range(m))
cx_eq_yb = abs(cx - yb) <= 0.01 * abs(cx)
check = mpc.all([
cx_eq_yb, Ax_bounded_by_b, x_nonnegative, yA_bounded_by_c,
y_nonpositive
])
check = bool(await mpc.output(check))
print(
f'verification c.x == y.b, A.x <= b, x >= 0, y.A <= c, y <= 0: {check}'
)
x = await mpc.output(x)
print(f'solution = {x}')
await mpc.shutdown()
def tensormatrix_prod(x, W, b):
logging.info('- - - - - - - - fc - - - - - - -')
W, b = W.tolist(), b.tolist()
return [mpc.vector_add(mpc.matrix_prod([z.tolist()], W)[0], b) for z in x]
async def main():
parser = argparse.ArgumentParser()
parser.add_argument('-d', '--data', help='filename for tableau')
parser.add_argument('options', nargs='*')
parser.set_defaults(data='default')
args = parser.parse_args()
if not args.options:
certificate_filename = f'c{mpc.pid}.cert'
logging.info('Setting certificate file to default = %s',
certificate_filename)
else:
certificate_filename = args.options[0]
T = load_tableau(args.data)
l = mpc.options.bit_length
m = len(T) - 1
n = len(T[0]) - 1
secint = mpc.SecInt(l, n=m + n)
for i in range(m + 1):
for j in range(n + 1):
T[i][j] = secint(T[i][j])
Zp = secint.field
N = Zp.nth
w = Zp.root
w_powers = [Zp(1)]
for _ in range(N - 1):
w_powers.append(w_powers[-1] * w)
assert w_powers[-1] * w == 1
basis = [secint(w_powers[-(i + n)]) for i in range(m)]
cobasis = [secint(w_powers[-j]) for j in range(n)]
prev_pivot = secint(1)
await mpc.start()
iteration = 0
logging.info('%d Termination?...', iteration)
p_col_index, minimum = argmin_int(T[-1][:-1])
while await mpc.output(minimum < 0):
iteration += 1
logging.info('%d Determining pivot...', iteration)
p_col = mpc.matrix_prod([p_col_index], T, True)[0]
constraints = [(T[i][-1] + (p_col[i] <= 0), p_col[i])
for i in range(m)]
p_row_index, (_, pivot) = argmin_rat(constraints)
logging.info('%d Updating tableau...', iteration)
# T[i,j] = T[i,j]*p/p' - (C[i]/p' - p_row_index[i])*(R[j] + p * p_col_index[j])
p_row = mpc.matrix_prod([p_row_index], T)[0]
delta_row = mpc.scalar_mul(prev_pivot, p_col_index)
delta_row.append(secint(0))
p_row = mpc.vector_add(p_row, delta_row)
prev_p_inv = 1 / prev_pivot
p_col = mpc.scalar_mul(prev_p_inv, p_col)
p_col = mpc.vector_sub(p_col, p_row_index + [secint(0)])
T = mpc.gauss(T, pivot * prev_p_inv, p_col, p_row)
prev_pivot = pivot
# swap basis entries
delta = mpc.in_prod(basis, p_row_index) - mpc.in_prod(
cobasis, p_col_index)
p_row_index = mpc.scalar_mul(delta, p_row_index)
basis = mpc.vector_sub(basis, p_row_index)
p_col_index = mpc.scalar_mul(delta, p_col_index)
cobasis = mpc.vector_add(cobasis, p_col_index)
logging.info('%d Termination?...', iteration)
p_col_index, minimum = argmin_int(T[-1][:-1])
logging.info('Termination...')
mx = await mpc.output(T[-1][-1])
cd = await mpc.output(prev_pivot)
print(' max(f) = %d / %d = %f' %
(mx.value, cd.value, float(mx.value) / cd.value))
logging.info('Computing solution...')
sum_x_powers = [secint(0) for _ in range(N)]
for i in range(m):
x_powers = pow_list(T[i][-1] / N, basis[i], N)
sum_x_powers = mpc.vector_add(sum_x_powers, x_powers)
solution = [None] * n
for j in range(n):
coefs = [w_powers[(j * k) % N] for k in range(N)]
solution[j] = mpc.lin_comb(coefs, sum_x_powers)
solution = await mpc.output(solution)
logging.info('Computing dual solution...')
sum_x_powers = [secint(0) for _ in range(N)]
for j in range(n):
x_powers = pow_list(T[-1][j] / N, cobasis[j], N)
sum_x_powers = mpc.vector_add(sum_x_powers, x_powers)
dual_solution = [None] * m
for i in range(m):
coefs = [w_powers[((n + i) * k) % N] for k in range(N)]
dual_solution[i] = mpc.lin_comb(coefs, sum_x_powers)
dual_solution = await mpc.output(dual_solution)
await mpc.shutdown()
logging.info('Writing output to %s.', certificate_filename)
with open(os.path.join('data', 'lp', certificate_filename), 'w') as f:
f.write('# tableau = \n' + args.data + '\n')
f.write('# bit-length = \n' + str(mpc.options.bit_length) + '\n')
f.write('# security parameter = \n' + str(mpc.options.sec_param) +
'\n')
f.write('# threshold = \n' + str(mpc.threshold) + '\n')
f.write('# common denominator = \n' + str(cd.value) + '\n')
f.write('# solution = \n')
f.write('\t'.join(str(x.value) for x in solution) + '\n')
f.write('# dual solution = \n')
f.write('\t'.join(str(x.value) for x in dual_solution) + '\n')
def test_secfxp(self):
secfxp = mpc.SecFxp()
c = mpc.to_bits(secfxp(0),
0) # mpc.output() only works for nonempty lists
self.assertEqual(c, [])
c = mpc.run(mpc.output(mpc.to_bits(secfxp(0))))
self.assertEqual(c, [0.0] * 32)
c = mpc.run(mpc.output(mpc.to_bits(secfxp(1))))
self.assertEqual(c, [0.0] * 16 + [1.0] + [0.0] * 15)
c = mpc.run(mpc.output(mpc.to_bits(secfxp(0.5))))
self.assertEqual(c, [0.0] * 15 + [1.0] + [0.0] * 16)
c = mpc.run(mpc.output(mpc.to_bits(secfxp(8113))))
self.assertEqual(c, [0.0] * 16 + [
float(b) for b in [1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0]
])
c = mpc.run(mpc.output(mpc.to_bits(secfxp(2**15 - 1))))
self.assertEqual(c, [float(b) for b in [0] * 16 + [1] * 15 + [0]])
c = mpc.run(mpc.output(mpc.to_bits(secfxp(-1))))
self.assertEqual(c, [float(b) for b in [0] * 16 + [1] * 16])
c = mpc.run(mpc.output(mpc.to_bits(secfxp(-2**15))))
self.assertEqual(c, [float(b) for b in [0] * 31 + [1]])
for f in [8, 16, 32, 64]:
secfxp = mpc.SecFxp(2 * f)
c = mpc.run(mpc.output(secfxp(1) + secfxp(1)))
self.assertEqual(c.frac_length, f)
self.assertEqual(c, 2)
c = mpc.run(mpc.output(secfxp(2**-f) + secfxp(1)))
if f != 64: # NB: 1 + 2**-64 == 1 in Python
self.assertEqual(c, 1 + 2**-f)
self.assertEqual(mpc.run(mpc.output(secfxp(0.5) * secfxp(2.0))), 1)
self.assertEqual(mpc.run(mpc.output(secfxp(2.0) * secfxp(0.5))), 1)
s = [10.7, -3.4, 0.1, -0.11]
self.assertEqual(mpc.run(mpc.output(list(map(secfxp, s)))), s)
s = [10.5, -3.25, 0.125, -0.125]
a, b, c, d = list(map(secfxp, s))
t = [v * v for v in s]
self.assertEqual(mpc.run(mpc.output([a * a, b * b, c * c, d * d])),
t)
x = [a, b, c, d]
self.assertEqual(mpc.run(mpc.output(mpc.schur_prod(x, x))), t)
self.assertEqual(mpc.run(mpc.output(mpc.schur_prod(x, x[:]))), t)
t = sum(t)
self.assertEqual(mpc.run(mpc.output(mpc.in_prod(x, x))), t)
self.assertEqual(mpc.run(mpc.output(mpc.in_prod(x, x[:]))), t)
self.assertEqual(
mpc.run(mpc.output(mpc.matrix_prod([x], [x], True)[0])), [t])
t = [_ for a, b, c, d in [s] for _ in [a + b, a * b, a - b]]
self.assertEqual(mpc.run(mpc.output([a + b, a * b, a - b])), t)
t = [
_ for a, b, c, d in [s]
for _ in [(a + b)**2, (a + b)**2 + 3 * c]
]
self.assertEqual(
mpc.run(mpc.output([(a + b)**2, (a + b)**2 + 3 * c])), t)
t = [int(_) for a, b, c, d in [s] for _ in [a < b, b < c, c < d]]
self.assertEqual(mpc.run(mpc.output([a < b, b < c, c < d])), t)
t = int(s[0] < s[1] and s[1] < s[2])
self.assertEqual(mpc.run(mpc.output((a < b) & (b < c))), t)
t = int(s[0] < s[1] or s[1] < s[2])
self.assertEqual(mpc.run(mpc.output((a < b) | (b < c))), t)
t = (int(s[0] < s[1]) ^ int(s[1] < s[2]))
self.assertEqual(mpc.run(mpc.output((a < b) ^ (b < c))), t)
t = (int(not s[0] < s[1]) ^ int(s[1] < s[2]))
self.assertEqual(mpc.run(mpc.output(~(a < b) ^ b < c)), t)
t = [int(s[0] > 1), int(10 * s[1] < 5), int(10 * s[0] == 5)]
self.assertEqual(
mpc.run(mpc.output([a > 1, 10 * b < 5, 10 * a == 5])), t)
s[3] = -0.120
d = secfxp(s[3])
t = s[3] / 0.25
self.assertAlmostEqual(mpc.run(mpc.output(d / 0.25)).signed(),
t,
delta=1)
t = s[3] / s[2] + s[0]
self.assertAlmostEqual(mpc.run(mpc.output(d / c + a)).signed(),
t,
delta=1)
t = round(t * (1 << f))
self.assertAlmostEqual(mpc.run(mpc.output(d / c + a)), t, delta=1)
t = ((s[0] + s[1])**2 + 3 * s[2]) / s[2]
self.assertAlmostEqual(mpc.run(mpc.output(
((a + b)**2 + 3 * c) / c)).signed(),
t,
delta=2)
t = 1 / s[3]
self.assertAlmostEqual((mpc.run(mpc.output(1 / d))).signed(),
t,
delta=1)
t = s[2] / s[3]
self.assertAlmostEqual(mpc.run(mpc.output(c / d)).signed(),
t,
delta=1)
t = -s[3] / s[2]
t = round(t * (1 << f))
self.assertAlmostEqual(mpc.run(mpc.output(-d / c)), t, delta=1)
t = s[2] / s[3]
t = round(t * (1 << f))
self.assertAlmostEqual(mpc.run(mpc.output(d / c)), t, delta=1)
self.assertEqual(mpc.run(mpc.output(mpc.sgn(+a))), int(s[0] > 0))
self.assertEqual(mpc.run(mpc.output(mpc.sgn(-a))), -int(s[0] > 0))
self.assertEqual(mpc.run(mpc.output(mpc.sgn(secfxp(0)))), 0)
self.assertEqual(mpc.run(mpc.output(abs(secfxp(-1.5)))), 1.5)
self.assertEqual(mpc.run(mpc.output(mpc.min(a, b, c, d))), min(s))
self.assertEqual(mpc.run(mpc.output(mpc.min(a, 0))), min(s[0], 0))
self.assertEqual(mpc.run(mpc.output(mpc.min(0, b))), min(0, s[1]))
self.assertEqual(mpc.run(mpc.output(mpc.max(a, b, c, d))), max(s))
self.assertEqual(mpc.run(mpc.output(mpc.max(a, 0))), max(s[0], 0))
self.assertEqual(mpc.run(mpc.output(mpc.max(0, b))), max(0, s[1]))
self.assertEqual(
mpc.run(mpc.output(list(mpc.min_max(a, b, c, d)))),
[min(s), max(s)])
self.assertEqual(mpc.run(mpc.output(secfxp(5) % 2)), 1)
self.assertEqual(mpc.run(mpc.output(secfxp(1) % 2**(1 - f))), 0)
self.assertEqual(mpc.run(mpc.output(secfxp(2**-f) % 2**(1 - f))),
2**-f)
self.assertEqual(
mpc.run(mpc.output(secfxp(2 * 2**-f) % 2**(1 - f))), 0)
self.assertEqual(mpc.run(mpc.output(secfxp(1) // 2**(1 - f))),
2**(f - 1))
self.assertEqual(mpc.run(mpc.output(secfxp(27.0) % 7.0)), 6.0)
self.assertEqual(mpc.run(mpc.output(secfxp(-27.0) // 7.0)), -4.0)
self.assertEqual(
mpc.run(mpc.output(list(divmod(secfxp(27.0), 6.0)))),
[4.0, 3.0])
self.assertEqual(mpc.run(mpc.output(secfxp(21.5) % 7.5)), 6.5)
self.assertEqual(mpc.run(mpc.output(secfxp(-21.5) // 7.5)), -3.0)
self.assertEqual(
mpc.run(mpc.output(list(divmod(secfxp(21.5), 0.5)))),
[43.0, 0.0])
async def main():
global secint
parser = argparse.ArgumentParser()
parser.add_argument('-b',
'--batch-size',
type=int,
metavar='B',
help='number of images to classify')
parser.add_argument(
'-o',
'--offset',
type=int,
metavar='O',
help='offset for batch (otherwise random in [0,10000-B])')
parser.add_argument(
'-d',
'--d-k-star',
type=int,
metavar='D',
help='k=D=0,1,2 for Legendre-based comparison using d_k^*')
parser.add_argument('--no-legendre',
action='store_true',
help='disable Legendre-based comparison')
parser.add_argument('--no-vectorization',
action='store_true',
help='disable vectorization of comparisons')
parser.set_defaults(batch_size=1, offset=-1, d_k_star=1)
args = parser.parse_args()
batch_size = args.batch_size
offset = args.offset
if args.no_legendre:
secint = mpc.SecInt(14) # using vectorized MPyC integer comparison
else:
if args.d_k_star == 0:
secint = mpc.SecInt(
14, p=3546374752298322551) # Legendre-0 range [-134, 134]
bsgn = bsgn_0
vector_bsgn = vector_bsgn_0
elif args.d_k_star == 1:
secint = mpc.SecInt(
14, p=9409569905028393239) # Legendre-1 range [-383, 383]
bsgn = bsgn_1
vector_bsgn = vector_bsgn_1
else:
secint = mpc.SecInt(
14, p=15569949805843283171) # Legendre-2 range [-594, 594]
bsgn = bsgn_2
vector_bsgn = vector_bsgn_2
one_by_one = args.no_vectorization
await mpc.start()
if offset < 0:
offset = random.randrange(10001 - batch_size) if mpc.pid == 0 else None
offset = await mpc.transfer(offset, senders=0)
logging.info('--------------- INPUT -------------')
print(
f'Type = {secint.__name__}, range = ({offset}, {offset + batch_size})')
# read batch_size labels and images at given offset
df = gzip.open(os.path.join('data', 'cnn', 't10k-labels-idx1-ubyte.gz'))
d = df.read()[8 + offset:8 + offset + batch_size]
labels = list(map(int, d))
print('Labels:', labels)
df = gzip.open(os.path.join('data', 'cnn', 't10k-images-idx3-ubyte.gz'))
d = df.read()[16 + offset * 28**2:16 + (offset + batch_size) * 28**2]
L = np.array(list(d)).reshape(batch_size, 28**2)
if batch_size == 1:
x = np.array(L[0]).reshape(28, 28)
print(
np.array2string(np.vectorize(lambda a: int(bool((a / 255))))(x),
separator=''))
L = np.vectorize(lambda a: secint(int(a)))(L).tolist()
logging.info('--------------- LAYER 1 -------------')
logging.info('- - - - - - - - fc - - - - - - -')
L = mpc.matrix_prod(L, load_W('fc1'))
L = mpc.matrix_add(L, [load_b('fc1')] * len(L))
logging.info('- - - - - - - - bsgn - - - - - - -')
if one_by_one:
L = np.vectorize(lambda a: (a >= 0) * 2 - 1)(L).tolist()
else:
L = [vector_sge(_) for _ in L]
await mpc.barrier()
logging.info('--------------- LAYER 2 -------------')
logging.info('- - - - - - - - fc - - - - - - -')
L = mpc.matrix_prod(L, load_W('fc2'))
L = mpc.matrix_add(L, [load_b('fc2')] * len(L))
await mpc.barrier()
logging.info('- - - - - - - - bsgn - - - - - - -')
if args.no_legendre:
secint.bit_length = 10
if one_by_one:
activate = np.vectorize(lambda a: (a >= 0) * 2 - 1)
L = activate(L).tolist()
else:
L = [vector_sge(_) for _ in L]
else:
if one_by_one:
activate = np.vectorize(bsgn)
L = activate(L).tolist()
else:
L = [vector_bsgn(_) for _ in L]
await mpc.barrier()
logging.info('--------------- LAYER 3 -------------')
logging.info('- - - - - - - - fc - - - - - - -')
L = mpc.matrix_prod(L, load_W('fc3'))
L = mpc.matrix_add(L, [load_b('fc3')] * len(L))
await mpc.barrier()
logging.info('- - - - - - - - bsgn - - - - - - -')
if args.no_legendre:
secint.bit_length = 10
if one_by_one:
activate = np.vectorize(lambda a: (a >= 0) * 2 - 1)
L = activate(L).tolist()
else:
L = [vector_sge(_) for _ in L]
else:
if one_by_one:
activate = np.vectorize(bsgn)
L = activate(L).tolist()
else:
L = [vector_bsgn(_) for _ in L]
await mpc.barrier()
logging.info('--------------- LAYER 4 -------------')
logging.info('- - - - - - - - fc - - - - - - -')
L = mpc.matrix_prod(L, load_W('fc4'))
L = mpc.matrix_add(L, [load_b('fc4')] * len(L))
await mpc.barrier()
logging.info('--------------- OUTPUT -------------')
if args.no_legendre:
secint.bit_length = 14
for i in range(batch_size):
prediction = await mpc.output(mpc.argmax(L[i])[0])
error = '******* ERROR *******' if prediction != labels[i] else ''
print(
f'Image #{offset+i} with label {labels[i]}: {prediction} predicted. {error}'
)
print(await mpc.output(L[i]))
await mpc.shutdown()
def test_secfxp(self):
secfxp = mpc.SecFxp()
self.assertEqual(
mpc.run(mpc.output(mpc.input(secfxp(7.75), senders=0))), 7.75)
c = mpc.to_bits(secfxp(0),
0) # mpc.output() only works for nonempty lists
self.assertEqual(c, [])
c = mpc.run(mpc.output(mpc.to_bits(secfxp(0))))
self.assertEqual(c, [0.0] * 32)
c = mpc.run(mpc.output(mpc.to_bits(secfxp(1))))
self.assertEqual(c, [0.0] * 16 + [1.0] + [0.0] * 15)
c = mpc.run(mpc.output(mpc.to_bits(secfxp(0.5))))
self.assertEqual(c, [0.0] * 15 + [1.0] + [0.0] * 16)
c = mpc.run(mpc.output(mpc.to_bits(secfxp(8113))))
self.assertEqual(c, [0.0] * 16 +
[1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0])
c = mpc.run(mpc.output(mpc.to_bits(secfxp(2**15 - 1))))
self.assertEqual(c, [0] * 16 + [1] * 15 + [0])
c = mpc.run(mpc.output(mpc.to_bits(secfxp(-1))))
self.assertEqual(c, [0] * 16 + [1] * 16)
c = mpc.run(mpc.output(mpc.to_bits(secfxp(-2**15))))
self.assertEqual(c, [0] * 31 + [1])
for f in [8, 16, 32, 64]:
secfxp = mpc.SecFxp(2 * f)
c = mpc.run(mpc.output(secfxp(1) + secfxp(1)))
self.assertEqual(c, 2)
c = mpc.run(mpc.output(secfxp(2**-f) + secfxp(1)))
if f != 64: # NB: 1 + 2**-64 == 1 in Python
self.assertEqual(c, 1 + 2**-f)
self.assertEqual(mpc.run(mpc.output(secfxp(0.5) * secfxp(2.0))), 1)
self.assertEqual(mpc.run(mpc.output(secfxp(2.0) * secfxp(0.5))), 1)
c = mpc.run(
mpc.output(
secfxp(2**(f // 2 - 1) - 0.5) *
secfxp(-2**(f // 2) + 0.5)))
self.assertEqual(c, -2**(f - 1) + 1.5 * 2**(f // 2 - 1) - 0.25)
s = [10.75, -3.375, 0.125, -0.125]
self.assertEqual(mpc.run(mpc.output(list(map(secfxp, s)))), s)
s = [10.5, -3.25, 0.125, -0.125]
a, b, c, d = list(map(secfxp, s))
t = [v * v for v in s]
self.assertEqual(mpc.run(mpc.output([a * a, b * b, c * c, d * d])),
t)
x = [a, b, c, d]
self.assertEqual(mpc.run(mpc.output(mpc.schur_prod(x, x))), t)
self.assertEqual(mpc.run(mpc.output(mpc.schur_prod(x, x[:]))), t)
t = sum(t)
self.assertEqual(mpc.run(mpc.output(mpc.in_prod(x, x))), t)
self.assertEqual(mpc.run(mpc.output(mpc.in_prod(x, x[:]))), t)
self.assertEqual(
mpc.run(mpc.output(mpc.matrix_prod([x], [x], True)[0])), [t])
u = mpc.unit_vector(secfxp(3), 4)
self.assertEqual(
mpc.run(mpc.output(mpc.matrix_prod([x], [u], True)[0])),
[s[3]])
self.assertEqual(
mpc.run(mpc.output(mpc.matrix_prod([u], [x], True)[0])),
[s[3]])
self.assertEqual(
mpc.run(mpc.output(mpc.gauss([[a]], b, [a], [b])[0])), [0])
t = [_ for a, b, c, d in [s] for _ in [a + b, a * b, a - b]]
self.assertEqual(mpc.run(mpc.output([a + b, a * b, a - b])), t)
t = [
_ for a, b, c, d in [s]
for _ in [(a + b)**2, (a + b)**2 + 3 * c]
]
self.assertEqual(
mpc.run(mpc.output([(a + b)**2, (a + b)**2 + 3 * c])), t)
t = [_ for a, b, c, d in [s] for _ in [a < b, b < c, c < d]]
self.assertEqual(mpc.run(mpc.output([a < b, b < c, c < d])), t)
t = s[0] < s[1] and s[1] < s[2]
self.assertEqual(mpc.run(mpc.output((a < b) & (b < c))), t)
t = s[0] < s[1] or s[1] < s[2]
self.assertEqual(mpc.run(mpc.output((a < b) | (b < c))), t)
t = (int(s[0] < s[1]) ^ int(s[1] < s[2]))
self.assertEqual(mpc.run(mpc.output((a < b) ^ (b < c))), t)
t = (int(not s[0] < s[1]) ^ int(s[1] < s[2]))
self.assertEqual(mpc.run(mpc.output(~(a < b) ^ b < c)), t)
t = [s[0] > 1, 10 * s[1] < 5, 10 * s[0] == 5]
self.assertEqual(
mpc.run(mpc.output([a > 1, 10 * b < 5, 10 * a == 5])), t)
s[3] = -0.120
d = secfxp(s[3])
t = s[3] / 0.25
self.assertAlmostEqual(mpc.run(mpc.output(d / 0.25)),
t,
delta=2**(1 - f))
t = round(s[3] / s[2] + s[0])
self.assertEqual(round(mpc.run(mpc.output(d / c + a))), t)
t = ((s[0] + s[1])**2 + 3 * s[2]) / s[2]
self.assertAlmostEqual(mpc.run(mpc.output(
((a + b)**2 + 3 * c) / c)),
t,
delta=2**(8 - f))
t = 1 / s[3]
self.assertAlmostEqual(mpc.run(mpc.output(1 / d)),
t,
delta=2**(6 - f))
t = s[2] / s[3]
self.assertAlmostEqual(mpc.run(mpc.output(c / d)),
t,
delta=2**(3 - f))
t = -s[3] / s[2]
self.assertAlmostEqual(mpc.run(mpc.output(-d / c)),
t,
delta=2**(3 - f))
self.assertEqual(mpc.run(mpc.output(mpc.sgn(+a))), s[0] > 0)
self.assertEqual(mpc.run(mpc.output(mpc.sgn(-a))), -(s[0] > 0))
self.assertEqual(mpc.run(mpc.output(mpc.sgn(secfxp(0)))), 0)
self.assertEqual(mpc.run(mpc.output(abs(secfxp(-1.5)))), 1.5)
self.assertEqual(mpc.run(mpc.output(mpc.min(a, b, c, d))), min(s))
self.assertEqual(mpc.run(mpc.output(mpc.min(a, 0))), min(s[0], 0))
self.assertEqual(mpc.run(mpc.output(mpc.min(0, b))), min(0, s[1]))
self.assertEqual(mpc.run(mpc.output(mpc.max(a, b, c, d))), max(s))
self.assertEqual(mpc.run(mpc.output(mpc.max(a, 0))), max(s[0], 0))
self.assertEqual(mpc.run(mpc.output(mpc.max(0, b))), max(0, s[1]))
self.assertEqual(
mpc.run(mpc.output(list(mpc.min_max(a, b, c, d)))),
[min(s), max(s)])
self.assertEqual(mpc.run(mpc.output(mpc.argmin([a, b, c, d])[0])),
1)
self.assertEqual(
mpc.run(mpc.output(mpc.argmin([a, b], key=operator.neg)[1])),
max(s))
self.assertEqual(mpc.run(mpc.output(mpc.argmax([a, b, c, d])[0])),
0)
self.assertEqual(
mpc.run(mpc.output(mpc.argmax([a, b], key=operator.neg)[1])),
min(s))
self.assertEqual(mpc.run(mpc.output(secfxp(5) % 2)), 1)
self.assertEqual(mpc.run(mpc.output(secfxp(1) % 2**(1 - f))), 0)
self.assertEqual(mpc.run(mpc.output(secfxp(2**-f) % 2**(1 - f))),
2**-f)
self.assertEqual(
mpc.run(mpc.output(secfxp(2 * 2**-f) % 2**(1 - f))), 0)
self.assertEqual(mpc.run(mpc.output(secfxp(1) // 2**(1 - f))),
2**(f - 1))
self.assertEqual(mpc.run(mpc.output(secfxp(27.0) % 7.0)), 6.0)
self.assertEqual(mpc.run(mpc.output(secfxp(-27.0) // 7.0)), -4.0)
self.assertEqual(
mpc.run(mpc.output(list(divmod(secfxp(27.0), 6.0)))),
[4.0, 3.0])
self.assertEqual(mpc.run(mpc.output(secfxp(21.5) % 7.5)), 6.5)
self.assertEqual(mpc.run(mpc.output(secfxp(-21.5) // 7.5)), -3.0)
self.assertEqual(
mpc.run(mpc.output(list(divmod(secfxp(21.5), 0.5)))),
[43.0, 0.0])
async def main():
parser = argparse.ArgumentParser()
parser.add_argument(
'-i',
'--dataset',
type=int,
metavar='I',
help=('dataset 0=uvlp (default), 1=wiki, 2=tb2x2, 3=woody, '
'4=LPExample_R20, 5=sc50b, 6=kb2, 7=LPExample'))
parser.add_argument('-l',
'--bit-length',
type=int,
metavar='L',
help='override preset bit length for dataset')
parser.set_defaults(dataset=0, bit_length=0)
args = parser.parse_args()
settings = [('uvlp', 8, 1, 2), ('wiki', 6, 1, 2), ('tb2x2', 6, 1, 2),
('woody', 8, 1, 3), ('LPExample_R20', 70, 1, 5),
('sc50b', 104, 10, 55), ('kb2', 536, 100000, 106),
('LPExample', 110, 1, 178)]
name, bit_length, scale, n_iter = settings[args.dataset]
if args.bit_length:
bit_length = args.bit_length
with open(os.path.join('data', 'lp', name + '.csv')) as file:
T = list(csv.reader(file))
m = len(T) - 1
n = len(T[0]) - 1
secint = mpc.SecInt(bit_length, n=m +
n) # force existence of Nth root of unity, N>=m+n
print(f'Using secure {bit_length}-bit integers: {secint.__name__}')
print(
f'dataset: {name} with {m} constraints and {n} variables (scale factor {scale})'
)
T[0][-1] = '0' # initialize optimal value
for i in range(m + 1):
g = 0
for j in range(n + 1):
T[i][j] = int(scale * float(T[i][j])) # scale to integer
g = math.gcd(g, T[i][j])
g = max(g, 1) if i else 1 # skip cost row
for j in range(n + 1):
T[i][j] = secint(T[i][j] // g)
c = T[0][:-1] # maximize c.x subject to A.x <= b, x >= 0
A = [T[i + 1][:-1] for i in range(m)]
b = [T[i + 1][-1] for i in range(m)]
Zp = secint.field
N = Zp.nth
w = Zp.root # w is an Nth root of unity in Zp, where N >= m + n
w_powers = [Zp(1)]
for _ in range(N - 1):
w_powers.append(w_powers[-1] * w)
assert w_powers[-1] * w == 1
await mpc.start()
cobasis = [secint(w_powers[-j]) for j in range(n)]
basis = [secint(w_powers[-(i + n)]) for i in range(m)]
previous_pivot = secint(1)
iteration = 0
while True:
# find index of pivot column
p_col_index, minimum = argmin_int(T[0][:-1])
if await mpc.output(minimum >= 0):
break # maximum reached
# find index of pivot row
p_col = mpc.matrix_prod([p_col_index], T, True)[0]
constraints = [[T[i][-1] + (p_col[i] <= 0), p_col[i]]
for i in range(1, m + 1)]
p_row_index, (_, pivot) = argmin_rat(constraints)
# reveal progress a bit
iteration += 1
mx = await mpc.output(T[0][-1])
cd = await mpc.output(previous_pivot)
p = await mpc.output(pivot) # NB: no await in f-strings in Python 3.6
logging.info(
f'Iteration {iteration}/{n_iter}: {mx / cd} pivot={p / cd}')
# swap basis entries
delta = mpc.in_prod(basis, p_row_index) - mpc.in_prod(
cobasis, p_col_index)
cobasis = mpc.vector_add(cobasis, mpc.scalar_mul(delta, p_col_index))
basis = mpc.vector_sub(basis, mpc.scalar_mul(delta, p_row_index))
# update tableau Tij = Tij*Tkl/Tkl' - (Til/Tkl' - bool(i==k)) * (Tkj + bool(j==l)*Tkl')
p_col_index.append(secint(0))
p_row_index.insert(0, secint(0))
pp_inv = 1 / previous_pivot
p_col = mpc.scalar_mul(pp_inv, p_col)
p_col = mpc.vector_sub(p_col, p_row_index)
p_row = mpc.matrix_prod([p_row_index], T)[0]
p_row = mpc.vector_add(p_row,
mpc.scalar_mul(previous_pivot, p_col_index))
T = mpc.gauss(T, pivot * pp_inv, p_col, p_row)
previous_pivot = pivot
mx = await mpc.output(T[0][-1])
cd = await mpc.output(previous_pivot
) # common denominator for all entries of T
print(
f'max = {mx} / {cd} / {scale} = {mx / cd / scale} in {iteration} iterations'
)
logging.info('Solution x')
sum_x_powers = [secint(0) for _ in range(N)]
for i in range(m):
x_powers = pow_list(T[i + 1][-1] / N, basis[i], N)
sum_x_powers = mpc.vector_add(sum_x_powers, x_powers)
x = [None] * n
for j in range(n):
coefs = [w_powers[(j * k) % N] for k in range(N)]
x[j] = mpc.in_prod(coefs, sum_x_powers)
cx = mpc.in_prod(c, x)
Ax = mpc.matrix_prod([x], A, True)[0]
Ax_bounded_by_b = mpc.all(Ax[i] <= b[i] * cd for i in range(m))
x_nonnegative = mpc.all(x[j] >= 0 for j in range(n))
logging.info('Dual solution y')
sum_x_powers = [secint(0) for _ in range(N)]
for j in range(n):
x_powers = pow_list(T[0][j] / N, cobasis[j], N)
sum_x_powers = mpc.vector_add(sum_x_powers, x_powers)
y = [None] * m
for i in range(m):
coefs = [w_powers[((n + i) * k) % N] for k in range(N)]
y[i] = mpc.in_prod(coefs, sum_x_powers)
y[i] = -y[i]
yb = mpc.in_prod(y, b)
yA = mpc.matrix_prod([y], A)[0]
yA_bounded_by_c = mpc.all(yA[j] <= c[j] * cd for j in range(n))
y_nonpositive = mpc.all(y[i] <= 0 for i in range(m))
cx_eq_yb = cx == yb
check = mpc.all([
cx_eq_yb, Ax_bounded_by_b, x_nonnegative, yA_bounded_by_c,
y_nonpositive
])
check = bool(await mpc.output(check))
print(
f'verification c.x == y.b, A.x <= b, x >= 0, y.A <= c, y <= 0: {check}'
)
x = await mpc.output(x)
print(f'solution = {[a / cd for a in x]}')
await mpc.shutdown()
