async def random_unit_vector(n): # returns list of n secint elements
await mpc.returnType(secint, n) # set return type of this MPyC coroutine
if n == 1:
return [secint(1)]
b = mpc.random_bit(secint) # pick one random bit if n>=2
x = random_unit_vector((n + 1) // 2) # recursive call with m=(n+1)//2
if n % 2 == 0:
y = mpc.scalar_mul(b, x) # y = [0]*m or y = x
return y + mpc.vector_sub(x, y) # [0]*m + x or x + [0]*m
elif await mpc.eq_public(b * x[0], 1): # reject if b=1 and x[0]=1
return random_unit_vector(n) # start over
else:
y = mpc.scalar_mul(b, x[1:]) # y = [0]*m or y = x[1:]
return x[:1] + y + mpc.vector_sub(
x[1:], y) # [x[0]] + ([0]*m + x[1:] or [0]*m + x[1:])
async def random_unit_vector(n, sectype):
"""Random permutation of [sectype(1)] + [sectype(0) for i in range(n-1)]."""
await mpc.returnType((sectype, True), n)
if n == 1:
return [sectype(1)]
b = mpc.random_bit(sectype)
x = random_unit_vector((n + 1) // 2, sectype)
if n % 2 == 0:
y = mpc.scalar_mul(b, x)
return y + mpc.vector_sub(x, y)
elif await mpc.eq_public(b * x[0], 1):
return random_unit_vector(n, sectype)
else:
y = mpc.scalar_mul(b, x[1:])
return x[:1] + y + mpc.vector_sub(x[1:], y)
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():
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()
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()
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 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('-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'
)
