def test_gso_int_gram_enabled():
for int_type in int_types:
for m, n in dimensions:
A = make_integer_matrix(m, n, int_type=int_type)
for float_type in float_types:
M = GSO.Mat(copy(A), float_type=float_type)
assert M.int_gram_enabled is False
assert M.transform_enabled is False
M = GSO.Mat(copy(A), float_type=float_type, flags=GSO.INT_GRAM)
assert M.int_gram_enabled is True
assert M.transform_enabled is False
if m and n:
U = IntegerMatrix(m, m, int_type=int_type)
M = GSO.Mat(copy(A), U=U, float_type=float_type)
assert M.transform_enabled is True
assert M.inverse_transform_enabled is False
UinvT = IntegerMatrix(m, m, int_type=int_type)
M = GSO.Mat(copy(A),
U=U,
UinvT=UinvT,
float_type=float_type)
assert M.transform_enabled is True
assert M.inverse_transform_enabled is True
def ntru_plain_hybrid_basis(A, g, q, nsamples):
"""
Construct ntru basis for the MitM hybrid
"""
n = A.ncols
ell = n - g
B = IntegerMatrix(nsamples + ell, nsamples + ell)
for i in range(ell):
B[i, i] = 1
for j in range(nsamples):
B[i, j + ell] = A[i, j]
for i in range(nsamples):
B[i + ell, i + ell] = q
# print('B:')
# print(B)
Al = B.submatrix(0, ell, ell, ell + nsamples)
Ag = A.submatrix(ell, 0, nsamples, nsamples)
B = LLL.reduction(B)
return B, Al, Ag
def test_multisol():
A = make_integer_matrix()
m = GSO.Mat(A)
lll_obj = LLL.Reduction(m)
lll_obj()
solutions = []
solutions = Enumeration(m, nr_solutions=200).enumerate(0, 27, 48.5, 0)
assert len(solutions) == 126 / 2
for _, sol in solutions:
sol = IntegerMatrix.from_iterable(1, A.nrows,
map(lambda x: int(round(x)), sol))
sol = tuple((sol * A)[0])
dist = sum([x**2 for x in sol])
assert dist == 48
solutions = []
solutions = Enumeration(m, nr_solutions=126 / 2).enumerate(0, 27, 100., 0)
assert len(solutions) == 126 / 2
for _, sol in solutions:
sol = IntegerMatrix.from_iterable(1, A.nrows,
map(lambda x: int(round(x)), sol))
sol = tuple((sol * A)[0])
dist = sum([x**2 for x in sol])
assert dist == 48
def primal_lattice_basis(A, c, q, m=None):
"""
Construct primal lattice basis for LWE challenge
``(A,c)`` defined modulo ``q``.
:param A: LWE matrix
:param c: LWE vector
:param q: integer modulus
:param m: number of samples to use (``None`` means all)
"""
if m is None:
m = A.nrows
elif m > A.nrows:
raise ValueError("Only m=%d samples available." % A.nrows)
n = A.ncols
B = IntegerMatrix(m + n + 1, m + 1)
for i in range(m):
for j in range(n):
B[j, i] = A[i, j]
B[i + n, i] = q
B[-1, i] = c[i]
B[-1, -1] = 1
B = LLL.reduction(B)
assert (B[:n] == IntegerMatrix(n, m + 1))
B = B[n:]
return B
def load_matrix_file(filepath, randomize=False, seed=None):
"""
Load matrix from file, LLL reduce (and randomize).
:param filepath: Load matrix from this file
:param randomize: Randomize the basis
:param seed: Seed for randomization
:returns: lattice basis and BKZ object
"""
A = IntegerMatrix.from_file(filepath)
A = LLL.reduction(A)
A = IntegerMatrix.from_matrix(A, int_type="long")
M = GSO.Mat(A, float_type="double", flags=GSO.ROW_EXPO)
bkz = BKZReduction(M)
if seed is not None:
FPLLL.set_random_seed(seed)
if randomize:
bkz.randomize_block(0, A.nrows, density=A.ncols / 4)
LLL.reduction(A)
bkz = BKZReduction(A)
LLL.reduction(A)
bkz.lll_obj() # to initialize bkz.M etc
return A, bkz
def sample_matrix(d, lattice_type="qary", seed=None):
"""
Sample a matrix in dimension `d`.
:param d: lattice dimension
:param lattice_type: see module level documentation
:param seed: optional random seed
:returns: LLL-reduced integer matrix
.. note :: This function seeds the FPLLL RNG, i.e. it is deterministic.
"""
if seed is None:
FPLLL.set_random_seed(d)
else:
FPLLL.set_random_seed(seed)
if lattice_type == "qary":
A = IntegerMatrix.random(d, "qary", bits=30, k=d // 2, int_type="long")
elif lattice_type == "qary-lv":
A = IntegerMatrix.random(d, "qary", bits=10 * d, k=d // 2)
else:
raise ValueError("Lattice type '%s' not supported." % lattice_type)
A = LLL.reduction(A)
return A
def main_cleanbkz_mpi_master(filename, bs, cores):
try:
with open(filename, "rb") as f:
mat = pickle.load(f)
#print "len(mat)", len(mat)
#if (len(mat) > 1):
# mat = mat[0]
if isinstance(mat, IntegerMatrix):
Ainput = mat
else:
Ainput = IntegerMatrix.from_matrix(mat)
except:
Ainput = IntegerMatrix.from_file(filename)
Ainput_M = GSO.Mat(Ainput, float_type='double')
Ainput_M.update_gso()
r = [Ainput_M.get_r(i, i) for i in range(0, Ainput.nrows)]
L_Ainput_M = LLL.Reduction(Ainput_M)
L_Ainput_M()
print r
A = IntegerMatrix.from_matrix(L_Ainput_M.M.B, int_type="long")
cleanbkz_mpi = CLEANBKZ_MPI(A, cores)
#cleanbkz_mpi = BKZ2(A)
cleanbkz_mpi.lll_obj()
cleanbkz_mpi.M.update_gso()
r = [
log(cleanbkz_mpi.M.get_r(i, i)) for i in range(0, cleanbkz_mpi.A.nrows)
]
print "# starting r "
print r
params = BKZ.Param(
block_size=bs,
max_loops=5000,
min_success_probability=.01,
flags=BKZ.BOUNDED_LLL, #|BKZ.DUMP_GSO,
dump_gso_filename="gso_output.file",
strategies="default.json")
cleanbkz_mpi(params=params, min_row=0)
#print "# done. found sv", cleanbkz_mpi.M.B[0]
# done send last end signal
for i in range(1, size):
comm.send(1, i, tag=999) # *** changed to send
cleanbkz_mpi.M.update_gso()
r2 = [
log(cleanbkz_mpi.M.get_r(i, i)) for i in range(0, cleanbkz_mpi.A.nrows)
]
print cleanbkz_mpi.A[0]
print "# ending r"
print r2
return
def test_dump_r(nrows=10):
A = IntegerMatrix(nrows, nrows)
A.randomize("ntrulike", bits=10, q=1023)
M = GSO.Mat(A)
if not have_numpy:
return
M.update_gso()
r = dump_r(M, 0, nrows)
for i in range(nrows):
assert abs(M.get_r(i, i) - r[i]) < 0.001
def test_dump_r(nrows=10):
A = IntegerMatrix(nrows, nrows)
A.randomize("ntrulike", bits=10, q=1023)
M = GSO.Mat(A)
if not have_numpy:
return
M.update_gso()
r = dump_r(M, 0, nrows)
for i in range(nrows):
assert abs(M.get_r(i, i) - r[i]) < 0.001
def test_dump_mu(nrows=10):
A = IntegerMatrix(nrows, nrows)
A.randomize("ntrulike", bits=10, q=1023)
M = GSO.Mat(A)
if not have_numpy:
return
M.update_gso()
mu = dump_mu(M, 0, nrows)
for i in range(nrows):
for j in range(i):
assert abs(M.get_mu(i, j) - mu[i, j]) < 0.001
def test_dump_mu(nrows=10):
A = IntegerMatrix(nrows, nrows)
A.randomize("ntrulike", bits=10, q=1023)
M = GSO.Mat(A)
if not have_numpy:
return
M.update_gso()
mu = dump_mu(M, 0, nrows)
for i in range(nrows):
for j in range(nrows):
assert abs(M.get_mu(i, j) - mu[i, j]) < 0.001
def main_pruning(filename, bs, cores):
try:
with open(filename, "rb") as f:
mat = pickle.load(f)
#print "len(mat)", len(mat)
#if (len(mat) > 1):
# mat = mat[0]
if isinstance(mat, IntegerMatrix):
Ainput = mat
else:
Ainput = IntegerMatrix.from_matrix(mat)
except:
Ainput = IntegerMatrix.from_file(filename)
Ainput_M = GSO.Mat(Ainput, float_type='double')
Ainput_M.update_gso()
r = [Ainput_M.get_r(i, i) for i in range(0, Ainput.nrows)]
L_Ainput_M = LLL.Reduction(Ainput_M)
L_Ainput_M()
#print r
A = IntegerMatrix.from_matrix(L_Ainput_M.M.B, int_type="long")
M = GSO.Mat(A, float_type="double")
bkzobj = BKZ2(M)
bkzobj.M.update_gso()
block_size = bs
r = [M.get_r(i, i) for i in range(0, block_size)]
radius = r[0] * 0.99
preproc_cost = 5000**(rank + 1)
pr0 = Pruning.run(radius,
NPS[block_size] * preproc_cost, [r],
0.1,
metric="probability",
float_type="double",
flags=Pruning.GRADIENT | Pruning.NELDER_MEAD)
print pr0.coefficients
"""
pruning = prune(radius, NPS[block_size] * preproc_cost, [r], 0.01,
metric="probability", float_type="double",
flags=Pruning.GRADIENT|Pruning.NELDER_MEAD)
cost = sum(pruning.detailed_cost) / NPS[block_size]
print "# [rank %d] cost %.1f, precost %.1f " % (rank, cost, preproc_cost)
"""
pr0_linear = pr0.LinearPruningParams(block_size, block_size - 2)
print pr0_linear.coefficients
return
def test_dump_r(nrows=10):
A = IntegerMatrix(nrows, nrows)
A.randomize("ntrulike", bits=10, q=1023)
M = GSO.Mat(A)
if not have_numpy:
return
r = numpy.ndarray(dtype='double', shape=nrows)
M.update_gso()
dump_r(r, M, 0, nrows)
for i in range(nrows):
assert abs(M.get_r(i, i) - r[i]) < 0.001
def test_gso_init():
for m, n in dimensions:
A = make_integer_matrix(m, n)
for float_type in float_types:
M = GSO.Mat(copy(A), float_type=float_type)
del M
U = IntegerMatrix(m, m)
M = GSO.Mat(copy(A), U=U, float_type=float_type)
del M
UinvT = IntegerMatrix(m, m)
M = GSO.Mat(copy(A), U=U, UinvT=UinvT, float_type=float_type)
del M
def load_challenge_and_randomize(n):
A_pre = IntegerMatrix.from_file("svpchallenge/svpchallengedim%dseed0.txt" %
n)
LLL.reduction(A_pre)
A = IntegerMatrix.from_matrix(A_pre, int_type="long")
params = fplll_bkz.Param(block_size=n,
max_loops=1,
strategies=fplll_bkz.DEFAULT_STRATEGY,
flags=fplll_bkz.GH_BND,
min_success_probability=.8)
bkz = BKZReduction(A)
bkz.lll_obj()
bkz.randomize_block(0, n, density=n / 4)
bkz.lll_obj()
return A, bkz
def test_dump_mu(nrows=10):
A = IntegerMatrix(nrows, nrows)
A.randomize("ntrulike", bits=10, q=1023)
M = GSO.Mat(A)
if not have_numpy:
return
mu = numpy.ndarray(dtype='double', shape=(nrows, nrows))
M.update_gso()
dump_mu(mu, M, 0, nrows)
for i in range(nrows):
for j in range(nrows):
assert abs(M.get_mu(i, j) - mu[i, j]) < 0.001
def babai_nearest_plane(A, w, **kwds):
"""Return lattice vector close to `v` using Babai's nearest plane algorithm.
:param A: **reduced** basis, an instance of `list` or `IntegerMatrix`
:param w: a tuple-like object
:param int_type: (default: 'mpz') an element of `fpylll.config.int_types`
:param float_type: (default: 'mpfr') an element of `fpylll.config.float_types`
:param int_gram: See docs of `GSO.MatGSO`
:param row_expo: See docs of `GSO.MatGSO`
"""
int_type = kwds.get('int_type', 'mpz')
if isinstance(A, list):
A = IntegerMatrix.from_matrix(A, int_type=int_type)
elif not isinstance(A, IntegerMatrix):
raise TypeError("Matrix `A` type '%s' unknown." % type(A))
float_type = kwds.get('float_type', 'mpfr')
flags = GSO.DEFAULT
if kwds.get('int_gram', False):
flags |= GSO.INT_GRAM
elif kwds.get('row_expo', False):
flags |= GSO.ROW_EXPO
M = GSO.Mat(A, flags=flags, float_type=float_type, update=True)
v = M.babai(w, gso=True)
return v
def svp_time(seed, params, return_queue=None):
"""Run SVP reduction of AutoBKZ on ``A`` using ``params``.
:param A: a matrix
:param params: AutoBKZ parameters
:param queue: if not ``None``, the result is put on this queue.
"""
FPLLL.set_random_seed(seed)
A = IntegerMatrix.random(params.block_size, "qary", bits=30,
k=params.block_size//2, int_type="long")
M = GSO.Mat(A)
bkz = BKZ2(M)
tracer = BKZTreeTracer(bkz, start_clocks=True)
with tracer.context(("tour", 0)):
bkz.svp_reduction(0, params.block_size, params, tracer)
bkz.M.update_gso()
tracer.exit()
tracer.trace.data["|A_0|"] = A[0].norm()
if return_queue:
return_queue.put(tracer.trace)
else:
return tracer.trace
def svp_time(seed, params, return_queue=None):
"""Run SVP reduction of AutoBKZ on ``A`` using ``params``.
:param A: a matrix
:param params: AutoBKZ parameters
:param queue: if not ``None``, the result is put on this queue.
"""
FPLLL.set_random_seed(seed)
FPLLL.set_threads(params["threads"])
q = 33554393
k = params.block_size // 2
A = IntegerMatrix.random(params.block_size,
"qary",
q=q,
k=k,
int_type="long")
M = GSO.Mat(A)
bkz = BKZ2(M)
tracer = BKZTreeTracer(bkz, start_clocks=True)
with tracer.context(("tour", 0)):
bkz.svp_reduction(0, params.block_size, params, tracer)
bkz.M.update_gso()
tracer.exit()
log_delta = (log(A[0].norm()) - log(q) *
(k / float(params.block_size))) / float(params.block_size)
tracer.trace.data["delta"] = exp(log_delta)
if return_queue:
return_queue.put(tracer.trace)
else:
return tracer.trace
def worker_process(seed, params, queue=None):
"""
This function is called to collect statistics.
:param A: basis
:param params: BKZ parameters
:param queue: queue used for communication
"""
FPLLL.set_random_seed(seed)
A = IntegerMatrix.random(params.block_size, "qary", bits=30, k=params.block_size//2, int_type="long")
M = GSO.Mat(A)
bkz = CallbackBKZ(M) # suppresses initial LLL call
tracer = BKZTreeTracer(bkz, start_clocks=True)
with tracer.context(("tour", 0)):
bkz.svp_reduction(0, params.block_size, params, tracer)
M.update_gso()
tracer.exit()
try:
# close connection
params.strategies[params.block_size].connection.send(None)
except AttributeError:
pass
if queue:
queue.put(tracer.trace)
else:
return tracer.trace
def IntegerMatrix_to_long(A):
n = A.nrows
AA = IntegerMatrix(n, n, int_type="long")
for i in xrange(n):
for j in xrange(n):
AA[i, j] = A[i, j]
return AA
def run_LLL(A, delta=0.99, eta=0.501, **kwds):
u"""run LLL reduction for a given matrix
:param A: Integer matrix, represent in `list`
:param delta: (default: 0.99) LLL parameter `0.25 < δ ≤ 1`
:param eta: (default: 0.501) LLL parameter `0 ≤ η < √δ`
:param int_type: (default: 'mpz') an element of `fpylll.config.int_types`
:param method: one of 'wrapper', 'proved', 'heuristic', 'fast' or `None`
:param float_type: an element of `fpylll.config.float_types` or `None`
:param precision: bit precision to use if `float_type` is 'mpfr'
:param verbose: (default: `False`) print verbose outputs
:param use_siegel: (default: `False`) use Siegel's condition
instead of Lovász's condition
:param early_red: (default: `False`) perform early reduction
:returns: reduced matrix ``B``, represent in `list`
"""
kwds['delta'] = delta
kwds['eta'] = eta
int_type = kwds.pop('int_type', 'mpz')
kwds['flags'] = LLL.DEFAULT
if kwds.pop('verbose', False):
kwds['flags'] |= LLL.VERBOSE
if kwds.pop('use_siegel', False):
kwds['flags'] |= LLL.SIEGEL
if kwds.pop('early_red', False):
kwds['flags'] |= LLL.EARLY_RED
A = IntegerMatrix.from_matrix(A, int_type=int_type)
LLL.reduction(A, **kwds)
B = [[A[i, j] for j in range(A.ncols)] for i in range(A.nrows)]
return B
def svpchallenge_test ():
dim = 60
A_pre = IntegerMatrix.from_file("svpchallenge/svpchallengedim%dseed0.txt"%dim)
print "# input dim: ", dim
print "# nrows: ", A_pre.nrows
ASVP_START = time()
LLL.reduction(A_pre)
A = IntegerMatrix.from_matrix(A_pre, int_type="long")
bkz = BKZReduction(A)
bkz.lll_obj()
r = [bkz.M.get_r(i, i) for i in range(dim)]
goal = (1.05)**2 * gaussian_heuristic(r)
params = fplll_bkz.Param(block_size=20, max_loops=1,
min_success_probability=.01)
bkz(params=params)
print " done BKZ yes"
def worker_process(seed, params, queue=None):
"""
This function is called to collect statistics.
:param A: basis
:param params: BKZ parameters
:param queue: queue used for communication
"""
FPLLL.set_random_seed(seed)
A = IntegerMatrix.random(params.block_size,
"qary",
bits=30,
k=params.block_size // 2,
int_type="long")
M = GSO.Mat(A)
bkz = CallbackBKZ(M) # suppresses initial LLL call
tracer = BKZTreeTracer(bkz, start_clocks=True)
with tracer.context(("tour", 0)):
bkz.svp_reduction(0, params.block_size, params, tracer)
M.update_gso()
tracer.exit()
try:
# close connection
params.strategies[params.block_size].connection.send(None)
except AttributeError:
pass
if queue:
queue.put(tracer.trace)
else:
return tracer.trace
def run_BKZ(A, block_size=2, **kwds):
u"""run BKZ reduction for a given matrix
:param A: Integer matrix, represent in `list`
:param int_type: (default: 'mpz') an element of `fpylll.config.int_types`
:param block_size: (default: 2) an integer from 1 to ``nrows``
:param delta: (default: 0.99) LLL parameter `0.25 < δ ≤ 1`
:param verbose: (default: `False`) print verbose outputs
:param float_type: an element of `fpylll.config.float_types` or `None`
:param precision: bit precision to use if `float_type` is 'mpfr'
For more params, see docs of `fpylll.BKZ.Param`
:returns: reduced matrix ``B``, represent in `list`
"""
int_type = kwds.get('int_type', 'mpz')
float_type = kwds.get('float_type', None)
precision = kwds.get('precision', 0)
kwds['delta'] = kwds.get('delta', 0.99)
kwds["strategies"] = kwds.get('strategies', BKZ.DEFAULT_STRATEGY)
kwds['flags'] = BKZ.DEFAULT
if kwds.get('verbose', False):
kwds['flags'] |= BKZ.VERBOSE
if kwds.get("auto_abort", False):
kwds["flags"] |= BKZ.AUTO_ABORT
A = IntegerMatrix.from_matrix(A, int_type=int_type)
BKZ.reduction(A,
BKZ.Param(block_size=block_size, **kwds),
float_type=float_type,
precision=precision)
B = [[A[i, j] for j in range(A.ncols)] for i in range(A.nrows)]
return B
def build_cvp_lattice(self, signatures, dim, bounds):
b = IntegerMatrix(dim + 1, dim + 1)
for i in range(dim):
b[i, i] = (2**self.bound_func(i, dim, bounds)) * self.curve.group.n
b[dim, i] = (2**self.bound_func(i, dim, bounds)) * signatures[i][0]
b[dim, dim] = 1
return b
def load_svp_challenge(d, seed=0):
"""
Load SVP Challenge matrix in dimension `d` and ``seed``
:param d: dimension
:param seed: random seed
"""
filename = os.path.join("data", "svp-challenge", "%03d-%d.txt" % (d, seed))
if os.path.isfile(filename) is False:
import requests
logging.debug("Did not find '{filename}', downloading ...".format(
filename=filename))
r = requests.post(
"https://www.latticechallenge.org/svp-challenge/generator.php",
data={
"dimension": d,
"seed": seed,
"sent": "True"
},
)
logging.debug("%s %s" % (r.status_code, r.reason))
fn = open(filename, "w")
fn.write(r.text)
fn.close()
A = IntegerMatrix.from_file(filename)
LLL.reduction(A)
return A
def main(n=150,
block_size=60,
float_type="d",
logq=40,
verbose=False,
seed=0xdeadbeef):
print "= n: %3d, β: %2d, bits: %3d, float_type: %s, seed: 0x%08x =" % (
n, block_size, logq, float_type, seed)
print
set_random_seed(seed)
A = IntegerMatrix.random(n, "qary", k=n // 2, bits=logq)
A = LLL.reduction(A)
params = BKZ.Param(block_size=block_size,
max_loops=4,
strategies=BKZ.DEFAULT_STRATEGY,
flags=BKZ.MAX_LOOPS | BKZ.VERBOSE)
bkz = BKZReduction(GSO.Mat(copy.copy(A), float_type=float_type))
bkz(params)
print bkz.trace
bkz2 = BKZ2(GSO.Mat(copy.copy(A), float_type=float_type))
bkz2(params)
print bkz2.trace
if verbose:
print
print bkz.trace.report()
def test5():
from fpylll import CVP, GSO, IntegerMatrix
# todo: tests with builtin CVP
global DEBUG
DEBUG = True
n = 15
q = 4201
# n = 31
d = 10
np.random.seed(1337)
V1 = [[np.random.randint(q) for _ in range(n)] for _ in range(n - 1)]
V2 = [[np.random.randint(q) for _ in range(n)] for _ in range(1000)]
v1, v2 = closest_pairs(V1, V2, n, d)
print(v1)
print('closest to v1:', v2)
B = IntegerMatrix.from_matrix(V1)
# M = GSO.Mat(B)
# M.update_gso()
# res = M.babai(V2[0])
res = CVP.closest_vector(B, v2.tolist())
print('asd')
print(res)
def test_callback_enum(d=40):
FPLLL.set_random_seed(0x1337)
A = LLL.reduction(IntegerMatrix.random(100, "qary", k=50, q=7681))
M = GSO.Mat(A)
M.update_gso()
# we are not imposing a constraint
enum_obj = Enumeration(M)
solutions = enum_obj.enumerate(0, d, 0.99*M.get_r(0, 0), 0)
max_dist, sol = solutions[0]
assert(A.multiply_left(sol)[0] != 2)
# now we do
def callback(new_sol_coord):
if A.multiply_left(new_sol_coord)[0] == 2:
return True
else:
return False
enum_obj = Enumeration(M, callbackf=callback)
solutions = enum_obj.enumerate(0, d, 0.99*M.get_r(0, 0), 0)
max_dist, sol = solutions[0]
assert(A.multiply_left(sol)[0] == 2)
def solve_hnp(samples):
d = len(samples)
q = order
B = IntegerMatrix(d + 2, d + 2)
for i in range(d):
t, u, v = samples[i]
scale = q / v
B[i, i] = q * scale
B[d, i] = t * scale
B[d + 1, i] = u * scale
B[d, d] = 1
B[d + 1, d + 1] = q
M = GSO.Mat(B)
L_red = LLL.Reduction(M)
bkzparam = BKZ.Param(block_size=20)
B_red = BKZ.Reduction(M, L_red, bkzparam)
B_red()
if B[1, d + 1] > 0:
x = -1 * B[1, d]
else:
x = B[1, d]
if x < 0:
x += q
private_value = 834818473318008049647448379209460658614088501345180055220225408308906924726
print x == private_value
priv = ec.derive_private_key(x, pub.curve, OSSL)
original = ec.derive_private_key(private_value, pub.curve, OSSL)
return priv, original
def test_ntru_gsa(n):
# read from file
filename = 'lwe_n'+str(n)+'.txt'
data = open(filename, 'r').readlines()
q = int(data[0])
B = eval(",".join([s_.replace('\n','').replace(" ", ", ") for s_ in data[1:n+1]]))
B = IntegerMatrix.from_matrix(B)
c = eval(data[n+1].replace(" ", ','))
beta, nsamples, prep_rt, GSA = find_beta(n, q, n)
print('beta, nsamples:', beta, nsamples)
print('GSA predicted:')
print(GSA)
print('beta, nsamples: ', beta, nsamples)
Basis = primal_lattice_basis(B, c, q, nsamples)
g6k = Siever(Basis)
d = g6k.full_n
g6k.lll(0, g6k.full_n)
print(g6k.MatGSO)
slope = basis_quality(g6k.M)["/"]
print("Intial Slope = %.5f\n" % slope)
print('GSA input:')
print([g6k.M.get_r(i, i) for i in range(d)])
print('d:', d)
target_norm = ceil( (2./3)*d + 1) + 1
print("target_norm:", target_norm)
#
# Preprocessing
#
if beta < 50:
print("Starting a fpylll BKZ-%d tour. " % (beta))
sys.stdout.flush()
bkz = BKZReduction(g6k.M)
par = fplll_bkz.Param(beta,
strategies=fplll_bkz.DEFAULT_STRATEGY,
max_loops=1)
bkz(par)
else:
print("Starting a pnjBKZ-%d tour. " % (beta))
pump_n_jump_bkz_tour(g6k, tracer, beta, jump=jump,
verbose=verbose,
extra_dim4free=extra_dim4free,
dim4free_fun=dim4free_fun,
goal_r0=target_norm,
pump_params=pump_params)
#T_BKZ = time.time() - T0_BKZ
print('GSA output:')
print([g6k.M.get_r(i, i) for i in range(d)])
return 1
def run_DBKZ(A, block_size=2, verbose=False):
"""
"""
A = IntegerMatrix.from_matrix(A)
_ = DBKZ(A)(block_size=block_size) # minimal implementation
B = [[A[i, j] for j in range(A.ncols)] for i in range(A.nrows)]
return B
def copy_to_IntegerMatrix_long(self, A):
n = A.nrows
l = A.ncols
AA = IntegerMatrix(n, l, int_type="long")
for i in xrange(n):
for j in xrange(l):
AA[i, j] = A[i, j]
return AA
def svpchallenge_par3(bs_diff=10, cores=2, start_dim=80, end_dim=80+2, BS_RANDOM_RANGE = 10):
for dim in range(start_dim, start_dim+2, 2):
A_pre = IntegerMatrix.from_file("svpchallenge/svpchallengedim%dseed0.txt"%dim)
print "# input dim: ", dim
print "# nrows: ", A_pre.nrows
ASVP_START = time()
LLL.reduction(A_pre)
A = IntegerMatrix.from_matrix(A_pre, int_type="long")
bkz = BKZReduction(A)
bkz.lll_obj()
r = [bkz.M.get_r(i, i) for i in range(dim)]
goal = (1.05)**2 * gaussian_heuristic(r)
bs_ulim = dim - bs_diff
interacting_parrallel_asvp(A, bs_ulim, goal, cores, BS_RANDOM_RANGE)
ASVP_TIME = time() - ASVP_START
print ("\nSUMMARY", {"input dim": dim, "bs_range": (bs_ulim - BS_RANDOM_RANGE, bs_ulim), "time": ASVP_TIME})
def test_multisol():
A = make_integer_matrix()
m = GSO.Mat(A)
lll_obj = LLL.Reduction(m)
lll_obj()
solutions = []
solutions = Enumeration(m, nr_solutions=200).enumerate(0, 27, 48.5, 0)
assert len(solutions)== 126 / 2
for sol, _ in solutions:
sol = IntegerMatrix.from_iterable(1, A.nrows, map(lambda x: int(round(x)), sol))
sol = tuple((sol*A)[0])
dist = sum([x**2 for x in sol])
assert dist==48
solutions = []
solutions = Enumeration(m, nr_solutions=126 / 2).enumerate(0, 27, 100., 0)
assert len(solutions)== 126 / 2
for sol, _ in solutions:
sol = IntegerMatrix.from_iterable(1, A.nrows, map(lambda x: int(round(x)), sol))
sol = tuple((sol*A)[0])
dist = sum([x**2 for x in sol])
assert dist==48
def test_cvp():
for m, n in dimensions:
A = make_integer_matrix(m, n)
A = LLL.reduction(A)
M = GSO.Mat(A)
M.update_gso()
t = list(make_integer_matrix(n, n)[0])
v0 = CVP.closest_vector(A, t)
E = Enumeration(M)
v1, _ = E.enumerate(0, A.nrows, 2, 40, M.from_canonical(t))
v1 = IntegerMatrix.from_iterable(1, A.nrows, map(lambda x: int(round(x)), v1))
v1 = tuple((v1*A)[0])
assert v0 == v1
def test_gso_io():
for m, n in dimensions:
if m <= 2 or n <= 2:
continue
A = make_integer_matrix(m, n)
v = list(A[0])
LLL.reduction(A)
for float_type in float_types:
M = GSO.Mat(copy(A), float_type=float_type)
M.update_gso()
w = M.babai(v)
v_ = IntegerMatrix.from_iterable(1, m, w) * A
v_ = list(v_[0])
assert v == v_
def prepare(n, m):
A = [IntegerMatrix.random(n, "qary", bits=n, k=n) for _ in range(m)]
M = [GSO.Mat(a) for a in A]
L = [LLL.Reduction(m) for m in M]
[l() for l in L]
return M
def prepare(n):
A = IntegerMatrix.random(n, "qary", bits=n/2, k=n/2)
M = GSO.Mat(A)
L = LLL.Reduction(M)
L()
return M
def make_integer_matrix(n):
A = IntegerMatrix.random(n, "uniform", bits=30)
return A
def make_integer_matrix(m, n):
A = IntegerMatrix(m, n)
A.randomize("uniform", bits=m+n)
return A
def make_integer_matrix(m, n):
A = IntegerMatrix(m, n)
A.randomize(algorithm="ntrulike", bits=30, q=2147483647)
return A
def silke(A, c, beta, h, m=None, scale=1, float_type="double"):
"""
:param A: LWE matrix
:param c: LWE vector
:param beta: BKW block size
:param m: number of samples to consider
:param scale: scale rhs of lattice by this factor
"""
from fpylll import BKZ, IntegerMatrix, LLL, GSO
from fpylll.algorithms.bkz2 import BKZReduction as BKZ2
if m is None:
m = A.nrows()
L = dual_instance1(A, scale=scale)
L = IntegerMatrix.from_matrix(L)
L = LLL.reduction(L, flags=LLL.VERBOSE)
M = GSO.Mat(L, float_type=float_type)
bkz = BKZ2(M)
t = 0.0
param = BKZ.Param(block_size=beta,
strategies=BKZ.DEFAULT_STRATEGY,
auto_abort=True,
max_loops=16,
flags=BKZ.VERBOSE|BKZ.AUTO_ABORT|BKZ.MAX_LOOPS)
bkz(param)
t += bkz.stats.total_time
H = copy(L)
import pickle
pickle.dump(L, open("L-%d-%d.sobj"%(L.nrows, beta), "wb"))
E = []
Y = set()
V = set()
y_i = vector(ZZ, tuple(L[0]))
Y.add(tuple(y_i))
E.append(apply_short1(y_i, A, c, scale=scale)[1])
v = L[0].norm()
v_ = v/sqrt(L.ncols)
v_r = 3.2*sqrt(L.ncols - A.ncols())*v_/scale
v_l = sqrt(h)*v_
fmt = u"{\"t\": %5.1fs, \"log(sigma)\": %5.1f, \"log(|y|)\": %5.1f, \"log(E[sigma]):\" %5.1f}"
print
print fmt%(t,
log(abs(E[-1]), 2),
log(L[0].norm(), 2),
log(sqrt(v_r**2 + v_l**2), 2))
print
for i in range(m):
t = cputime()
M = GSO.Mat(L, float_type=float_type)
bkz = BKZ2(M)
t = cputime()
bkz.randomize_block(0, L.nrows, stats=None, density=3)
LLL.reduction(L)
y_i = vector(ZZ, tuple(L[0]))
l_n = L[0].norm()
if L[0].norm() > H[0].norm():
L = copy(H)
t = cputime(t)
Y.add(tuple(y_i))
V.add(y_i.norm())
E.append(apply_short1(y_i, A, c, scale=scale)[1])
if len(V) >= 2:
fmt = u"{\"i\": %4d, \"t\": %5.1fs, \"log(|e_i|)\": %5.1f, \"log(|y_i|)\": %5.1f,"
fmt += u"\"log(sigma)\": (%5.1f,%5.1f), \"log(|y|)\": (%5.1f,%5.1f), |Y|: %5d}"
print fmt%(i+2, t, log(abs(E[-1]), 2), log(l_n, 2), log_mean(E), log_var(E), log_mean(V), log_var(V), len(Y))
return E
def make_integer_matrix(n):
A = IntegerMatrix.random(n, "ntrulike", bits=30)
return A
def shortest_vector(self, update_reduced_basis=True, algorithm="fplll", *args, **kwds):
r"""
Return a shortest vector.
INPUT:
- ``update_reduced_basis`` -- (default: ``True``) set this flag if
the found vector should be used to improve the basis
- ``algorithm`` -- (default: ``"fplll"``) either ``"fplll"`` or
``"pari"``
- ``*args`` -- passed through to underlying implementation
- ``**kwds`` -- passed through to underlying implementation
OUTPUT:
A shortest non-zero vector for this lattice.
EXAMPLES::
sage: from sage.modules.free_module_integer import IntegerLattice
sage: A = sage.crypto.gen_lattice(type='random', n=1, m=30, q=2^40, seed=42)
sage: L = IntegerLattice(A, lll_reduce=False)
sage: min(v.norm().n() for v in L.reduced_basis)
6.03890756700000e10
sage: L.shortest_vector().norm().n()
3.74165738677394
sage: L = IntegerLattice(A, lll_reduce=False)
sage: min(v.norm().n() for v in L.reduced_basis)
6.03890756700000e10
sage: L.shortest_vector(algorithm="pari").norm().n()
3.74165738677394
sage: L = IntegerLattice(A, lll_reduce=True)
sage: L.shortest_vector(algorithm="pari").norm().n()
3.74165738677394
"""
if algorithm == "pari":
if self._basis_is_LLL_reduced:
B = self.basis_matrix().change_ring(ZZ)
qf = self.gram_matrix()
else:
B = self.reduced_basis.LLL()
qf = B*B.transpose()
count, length, vectors = qf._pari_().qfminim()
v = vectors.python().columns()[0]
w = v*B
elif algorithm == "fplll":
from fpylll import IntegerMatrix, SVP
L = IntegerMatrix.from_matrix(self.reduced_basis)
w = vector(ZZ, SVP.shortest_vector(L, *args, **kwds))
else:
raise ValueError("algorithm '{}' unknown".format(algorithm))
if update_reduced_basis:
self.update_reduced_basis(w)
return w
