def decrypt(text, key, rcs):
res = text[:]
lin_matrix = invert(mds_matrix(t, 0))
key_matrix = mds_matrix(t, 1)
keys = [key] + ([None] * rounds)
for r in range(rounds):
keys[r + 1] = [ mpc.in_prod(key_matrix[i], keys[r]) + rcs[(r * t) + i] for i in range(t) ]
keys.reverse()
###
for i in range(t):
res[i] -= keys[0][i]
###
for r in range(1, full2 + 1):
res = [ mpc.in_prod(lin_matrix[i], res) for i in range(t) ]
for i in range(t):
res[i] = res[i] ** s
res[i] -= keys[r][i]
###
for r in range(full2 + 1, full2 + partial + 1):
res = [ mpc.in_prod(lin_matrix[i], res) for i in range(t) ]
res[0] = res[0] ** s
for i in range(t):
res[i] -= keys[r][i]
###
for r in range(full2 + partial + 1, full2 + partial + full1 + 1):
res = [ mpc.in_prod(lin_matrix[i], res) for i in range(t) ]
for i in range(t):
res[i] = res[i] ** s
res[i] -= keys[r][i]
###
return res
def encrypt(text, key, rcs):
assert len(text) == t
assert len(key) == t
assert len(rcs) == t * rounds
res = text[:]
lin_matrix = mds_matrix(t, 0)
key_matrix = mds_matrix(t, 1)
keys = [key] + ([None] * rounds)
for r in range(rounds):
keys[r + 1] = [ mpc.in_prod(key_matrix[i], keys[r]) + rcs[(r * t) + i] for i in range(t) ]
###
for r in range(full1):
for i in range(t):
res[i] += keys[r][i]
res[i] = res[i] ** 3
res = [ mpc.in_prod(lin_matrix[i], res) for i in range(t) ]
###
for r in range(full1, full1 + partial):
for i in range(t):
res[i] += keys[r][i]
res[0] = res[0] ** 3
res = [ mpc.in_prod(lin_matrix[i], res) for i in range(t) ]
###
for r in range(full1 + partial, full1 + partial + full2):
for i in range(t):
res[i] += keys[r][i]
res[i] = res[i] ** 3
res = [ mpc.in_prod(lin_matrix[i], res) for i in range(t) ]
###
for i in range(t):
res[i] += keys[rounds][i]
###
return res
async def main():
# initialize mpc, define secure int type
LEN = 100000
await mpc.start()
secint = mpc.SecInt(128)
# party 0 samples the inputs locally...
if mpc.pid == 0:
vec1 = [np.random.randint(1, 1000) for _ in range(LEN)]
vec2 = [np.random.randint(1, 1000) for _ in range(LEN)]
# ...and secret-shares them with the others
result_type = [secint()] * LEN
sec_vec1 = mpc.input([secint(v)
for v in vec1] if mpc.pid == 0 else result_type,
senders=0)
sec_vec2 = mpc.input([secint(v)
for v in vec2] if mpc.pid == 0 else result_type,
senders=0)
# compute inner product
ip = mpc.in_prod(sec_vec1, sec_vec2)
# output result (to everybody)
result = await mpc.output(ip)
print("result:", result)
if mpc.pid == 0:
assert (result == np.dot(vec1, vec2))
await mpc.shutdown()
def __lt__(
self, other
): # NB: __lt__() is basic comparison as in Python's list.sort()
c = mpc.in_prod([self.n, -self.d], [other.d, other.n]) < 0
c = mpc.if_else(self.pos, c, 0)
c = mpc.if_else(other.pos, c, 1)
return c
def arg_le_rat(x0, x1):
(n0, d0) = x0
(n1, d1) = x1
a = mpc.in_prod([n0, d0], [d1, -n1]) >= 0
h = mpc.scalar_mul(a, [n1 - n0, d1 - d0])
m = (h[0] + n0, h[1] + d0)
return a, m
def encrypt(m, roundkeys, linmatrices, roundconstants):
m = mpc.vector_add(m, roundkeys[0])
for r in range(rounds):
m = substitute(m)
m = [mpc.in_prod(linmatrices[r][i], m) for i in range(blocksize)]
m = mpc.vector_add(m, roundconstants[r])
m = mpc.vector_add(m, roundkeys[r + 1])
return m
def GI(x):
"""Gini impurity for contingency table x."""
y = [args.alpha * s + 1
for s in map(mpc.sum, x)] # NB: alternatively, use s + (s == 0)
D = mpc.prod(y)
G = mpc.in_prod(list(map(mpc.in_prod, x, x)), list(map(lambda x: 1 / x,
y)))
return [D * G, D] # numerator, denominator
def decrypt(m, roundkeys, invlinmatrices, roundconstants):
for r in range(rounds, 0, -1):
m = mpc.vector_add(m, roundkeys[r])
m = mpc.vector_add(m, roundconstants[r - 1])
m = [
mpc.in_prod(invlinmatrices[r - 1][i], m) for i in range(blocksize)
]
m = invsubstitute(m)
return mpc.vector_add(m, roundkeys[0])
def random_permutation(n, sectype):
"""Random permutation of [sectype(i) for i in range(n)]. """
p = [sectype(i) for i in range(n)]
for i in range(n - 1):
x_r = random_unit_vector(n - i, sectype)
p_r = mpc.in_prod(p[i:], x_r)
d_r = mpc.scalar_mul(p[i] - p_r, x_r)
p[i] = p_r
for j in range(n - i):
p[i + j] += d_r[j]
return p
def random_permutation(n): # returns list of n secint elements
p = [secint(i) for i in range(n)] # initialize p to identity permutation
for i in range(n - 1):
x_r = random_unit_vector(
n - i) # x_r = [0]*(r-i) + [1] + [0]*(n-1-r), i <= r < n
p_r = mpc.in_prod(p[i:], x_r) # p_r = p[r]
d_r = mpc.scalar_mul(
p[i] - p_r, x_r) # d_r = [0]*(r-i) + [p[i] - p[r]] + [0]*(n-1-r)
p[i] = p_r # p[i] = p[r]
for j in range(n - i):
p[i + j] += d_r[j] # p[r] = p[r} + p[i] - p[r] = p[i]
return p
def test_empty_input(self):
secint = mpc.SecInt()
self.assertEqual(mpc.run(mpc.gather([])), [])
self.assertEqual(mpc.run(mpc.output([])), [])
self.assertEqual(mpc._reshare([]), [])
self.assertEqual(mpc.convert([], None), [])
self.assertEqual(mpc.sum([]), 0)
self.assertEqual(mpc.prod([]), 1)
self.assertEqual(mpc.in_prod([], []), 0)
self.assertEqual(mpc.vector_add([], []), [])
self.assertEqual(mpc.vector_sub([], []), [])
self.assertEqual(mpc.scalar_mul(secint(0), []), [])
self.assertEqual(mpc.schur_prod([], []), [])
self.assertEqual(mpc.from_bits([]), 0)
async def main():
# Use 32-bit (default) secure integers:
secint = mpc.SecInt()
# Each party locally generates LOAD random entries of type secint:
my_entries_for_vec_x = [secint(randint(-1000, 1000)) for _ in range(LOAD)]
my_entries_for_vec_y = [secint(randint(-1000, 1000)) for _ in range(LOAD)]
# Start MPyC runtime to let all parties connect:
await mpc.start()
# The entries for vectors x and y are secret-shared between all parties:
vec_x = flatten(mpc.input(my_entries_for_vec_x))
vec_y = flatten(mpc.input(my_entries_for_vec_y))
# Secure dot products are supported natively and *very* efficiently:
c = mpc.in_prod(vec_x, vec_y)
# Open the secret-shared value c and let all parties print the result:
print('Dot product:', await mpc.output(c))
# Shutdown MPyC runtime to close all connections:
await mpc.shutdown()
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('-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(
f'Setting certificate file to default = {certificate_filename}')
else:
certificate_filename = args.options[0]
T = load_tableau(args.data)
m = len(T) - 1
n = len(T[0]) - 1
l = mpc.options.bit_length
secfxp = mpc.SecFxp(l)
for i in range(m + 1):
for j in range(n + 1):
T[i][j] = secfxp(T[i][j])
basis = [secfxp(i + n) for i in range(m)]
cobasis = [secfxp(j) for j in range(n)]
await mpc.start()
iteration = 0
logging.info(f'{iteration} Termination?...')
p_col_index, minimum = argmin_int(T[-1][:-1])
while await mpc.output(minimum < 0):
iteration += 1
logging.info(f'{iteration} Determining pivot...')
p_col = index_matrix_prod(p_col_index + [secfxp(0)], T, True)
constraints = [(T[i][-1] + (p_col[i] <= 0), p_col[i])
for i in range(m)]
p_row_index, _ = argmin_rat(constraints)
pivot = mpc.in_prod(p_row_index, p_col)
logging.info(f'{iteration} Updating tableau...')
h = mpc.scalar_mul(1 / pivot, mpc.vector_sub(p_row_index + [0], p_col))
p_row = index_matrix_prod(p_row_index, T[:-1])
v = mpc.vector_add(p_row, p_col_index + [0])
for i in range(m + 1):
T[i] = mpc.vector_add(T[i], mpc.scalar_mul(h[i], v))
# 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(f'{iteration} Termination?...')
p_col_index, minimum = argmin_int(T[-1][:-1])
logging.info('Termination...')
mx = await mpc.output(T[-1][-1])
print(' max(f) =', mx)
logging.info('Computing solution...')
solution = [secfxp(0) for _ in range(n)]
for i in range(m):
x = mpc.unit_vector(basis[i], m + n)[:n]
y = mpc.scalar_mul(T[i][-1], x)
solution = mpc.vector_add(solution, y)
solution = await mpc.output(solution)
logging.info('Computing dual solution...')
dual_solution = [secfxp(0) for _ in range(m)]
for j in range(n):
x = mpc.unit_vector(cobasis[j], m + n)[n:]
y = mpc.scalar_mul(T[-1][j], x)
dual_solution = mpc.vector_add(dual_solution, y)
dual_solution = await mpc.output(dual_solution)
await mpc.shutdown()
logging.info(f'Writing output to {certificate_filename}')
tab = '\t'
with open(os.path.join('data', 'lp', certificate_filename), 'w') as f:
f.write(f'# tableau =\n{args.data}\n')
f.write(f'# bit-length =\n{mpc.options.bit_length}\n')
f.write(f'# security parameter =\n{mpc.options.sec_param}\n')
f.write(f'# threshold =\n{mpc.threshold}\n')
f.write(f'# solution =\n{tab.join(x.__repr__() for x in solution)}\n')
f.write(
f'# dual solution =\n{tab.join(x.__repr__() for x in dual_solution)}\n'
)
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 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])
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])
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(mpc.args)
if not args.options:
certificate_filename = "c" + str(mpc.id) + ".cert"
logging.info('Setting certificate file to default = %s',
certificate_filename)
else:
certificate_filename = args.options[0]
T = load_tableau(args.data)
m = len(T) - 1
n = len(T[0]) - 1
l = mpc.options.bit_length
secfxp = mpc.SecFxp(l)
for i in range(len(T)):
for j in range(len(T[0])):
T[i][j] = secfxp(T[i][j])
basis = [secfxp(i + n) for i in range(m)]
cobasis = [secfxp(j) for j in range(n)]
mpc.start()
iteration = 0
logging.info('%d Termination?...', iteration)
p_col_index, minimum = argmin_int(T[-1][:-1])
while mpc.run(mpc.output(minimum < 0)):
iteration += 1
logging.info('%d Determining pivot...', iteration)
p_col = index_matrix_prod(p_col_index + [secfxp(0)], T, True)
constraints = [(T[i][-1] + (p_col[i] <= 0), p_col[i])
for i in range(m)]
p_row_index, _ = argmin_rat(constraints)
pivot = mpc.in_prod(p_row_index, p_col)
pivot1 = 1 / pivot
mpc.run(mpc.barrier())
logging.info('%d Updating tableau...', iteration)
h = mpc.scalar_mul(pivot1, [(p_row_index[i] if i < m else 0) - p_col[i]
for i in range(m + 1)])
p_row = index_matrix_prod(p_row_index, T[:-1])
v = mpc.vector_add(p_row, p_col_index + [0])
for i in range(m + 1):
T[i] = mpc.vector_add(T[i], mpc.scalar_mul(h[i], v))
#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 = mpc.run(mpc.output(T[-1][-1]))
print(' max(f) =', mx)
logging.info('Computing solution...')
solution = [secfxp(0) for _ in range(n)]
for i in range(m):
x = unit_vector(basis[i], m + n)[:n]
y = mpc.scalar_mul(T[i][-1], x)
solution = mpc.vector_add(solution, y)
solution = mpc.run(mpc.output(solution))
logging.info('Computing dual solution...')
dual_solution = [secfxp(0) for _ in range(m)]
for j in range(n):
x = unit_vector(cobasis[j], m + n)[n:]
y = mpc.scalar_mul(T[-1][j], x)
dual_solution = mpc.vector_add(dual_solution, y)
dual_solution = mpc.run(mpc.output(dual_solution))
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.security_parameter) + '\n')
f.write('# threshold = \n' + str(mpc.threshold) + '\n')
f.write('# solution = \n')
f.write('\t'.join(x.__repr__() for x in solution) + '\n')
f.write('# dual solution = \n')
f.write('\t'.join(x.__repr__() for x in dual_solution) + '\n')
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()
def __lt__(
self, other
): # NB: __lt__() is basic comparison as in Python's list.sort()
return mpc.in_prod([self.n, -self.d], [other.d, other.n]) < 0
def keyschedule(key, keymatrices):
return [[mpc.in_prod(keymatrices[r][i], key) for i in range(keysize)]
for r in range(rounds + 1)]
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 arg_le_rat(x0, x1):
n0, d0 = x0
n1, d1 = x1
a = mpc.in_prod([n0, d0], [d1, -n1]) >= 0
m = mpc.if_else(a, [n1, d1], [n0, d0])
return a, m
