def __init__(self, A, ncores=2):
"""Create new BKZ object.
:param A: an integer matrix, a GSO object or an LLL object
:param ncores: number of cores to use
"""
self.ncores = ncores
BKZ2.__init__(self, A)
def load_matrix_file(filepath,
randomize=False,
seed=None,
float_type="double"):
"""
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=float_type)
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)
M = GSO.Mat(A, float_type=float_type)
bkz = BKZReduction(M)
bkz.lll_obj() # to initialize bkz.M etc
return A, bkz
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 recycled_svp_preprocessing(self, kappa, block_size, param, stats,
preproc_block_size):
prepar = param.__class__(block_size=preproc_block_size,
strategies=param.strategies,
flags=BKZ.GH_BND)
clean = BKZ2.tour(self, prepar, kappa, kappa + block_size)
return clean
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 load_prebkz(n, s=0, blocksize=40):
"""
"""
filename = "qarychallenge/prebkz-%02d-dim-%03d-seed-%02d.txt" % (blocksize,
n, s)
if not os.path.isdir("qarychallenge"):
os.mkdir("qarychallenge")
if os.path.isfile(filename) is False:
set_random_seed(s)
A = IntegerMatrix.random(n, "qary", q=2**30, k=n // 2)
print "Did not find '{filename}'. Creating and reducing".format(
filename=filename)
print "created, ",
sys.stdout.flush()
A = LLL.reduction(A)
print "LLLed, ",
sys.stdout.flush()
if A.nrows >= 160:
float_type = "long double"
elif A.nrows >= 200:
float_type = "dd"
else:
float_type = "double"
M = GSO.Mat(A, float_type=float_type, flags=GSO.ROW_EXPO)
bkz = BKZReduction(M)
for b in range(10, blocksize + 1):
print "\r created, LLLed, BKZed %d" % b,
sys.stdout.flush()
par = fplll_bkz.Param(b,
strategies=fplll_bkz.DEFAULT_STRATEGY,
max_loops=1,
flags=fplll_bkz.MAX_LOOPS)
bkz(par)
print
fn = open(filename, "w")
fn.write(str(A))
fn.close()
return load_matrix_file(filename, randomize=False)
def svp_preprocessing(self, kappa, block_size, param, tracer=dummy_tracer):
"""
Run sequential BKZ 2.0 preprocessing.
:param kappa: current index
:param block_size: block size
:param params: BKZ parameters
:param tracer: object for maintaining statistics
"""
clean = True
clean &= BKZ1.svp_preprocessing(self, kappa, block_size, param, tracer)
for preproc in param.strategies[block_size].preprocessing_block_sizes:
prepar = param.__class__(block_size=preproc, strategies=param.strategies, flags=BKZ.GH_BND)
clean &= BKZ2.tour(self, prepar, kappa, kappa + block_size)
return clean
def svp_preprocessing(self, kappa, block_size, param, tracer=dummy_tracer):
"""
Run sequential BKZ 2.0 preprocessing.
:param kappa: current index
:param block_size: block size
:param params: BKZ parameters
:param tracer: object for maintaining statistics
"""
clean = True
clean &= BKZ1.svp_preprocessing(self, kappa, block_size, param, tracer)
for preproc in param.strategies[block_size].preprocessing_block_sizes:
prepar = param.__class__(block_size=preproc,
strategies=param.strategies,
flags=BKZ.GH_BND)
clean &= BKZ2.tour(self, prepar, kappa, kappa + block_size)
return clean
def get_pruning(self, kappa, block_size, param, stats):
"""
Ask for pruning parameters from coordinating process.
:param kappa: index
:param block_size: block size
:param param: access to strategy objects
:param stats: passed on
"""
strategy = param.strategies[block_size]
radius = self.M.get_r(kappa, kappa) * self.lll_obj.delta
r = [self.M.get_r(i, i) for i in range(kappa, kappa+block_size)]
gh_radius = gaussian_heuristic(r)
if (param.flags & BKZ.GH_BND and block_size > 30):
radius = min(radius, gh_radius * param.gh_factor)
try:
ret = radius, 0, strategy.get_pruning(tuple(r), radius, stats, param.min_success_probability)
except TypeError:
ret = BKZ2.get_pruning(self, kappa, block_size, param, stats)
return ret
def get_pruning(self, kappa, block_size, param, stats):
"""
Ask for pruning parameters from coordinating process.
:param kappa: index
:param block_size: block size
:param param: access to strategy objects
:param stats: passed on
"""
strategy = param.strategies[block_size]
radius = self.M.get_r(kappa, kappa) * self.lll_obj.delta
r = [self.M.get_r(i, i) for i in range(kappa, kappa+block_size)]
gh_radius = gaussian_heuristic(r)
if (param.flags & BKZ.GH_BND and block_size > 30):
radius = min(radius, gh_radius * param.gh_factor)
try:
ret = radius, strategy.get_pruning(tuple(r), radius, stats, param.min_success_probability)
except TypeError:
ret = BKZ2.get_pruning(self, kappa, block_size, param, stats)
return ret
r0 = bkz.M.get_r(0, 0)
print "OPPORT_ENUM", {
"n": n,
"Time": round(ENUM_TIME, 2),
"ghf": round(r0 / gh, 4)
}
AV_ENUM += ENUM_TIME / sample_rep
########### Timing SubSieve
A, bkz = load_challenge_and_randomize(n)
SUBSIEVE_START = time()
d = iterated_sub_sieve(A, goal=goal)
SUBSIEVE_TIME = time() - SUBSIEVE_START
bkz = BKZReduction(A)
bkz.lll_obj()
r0 = bkz.M.get_r(0, 0)
print "SUB_SIEVE ", {
"n": n,
"Time": round(SUBSIEVE_TIME, 2),
"ghf": round(r0 / gh, 4)
}, {
"d": d
}
AV_SIEVE += SUBSIEVE_TIME / sample_rep
print
print "OPPORT_ENUM average :", AV_ENUM
print "SUB_SIEVE average :", AV_SIEVE
def lwe_kernel(arg0, params=None, seed=None):
"""
Run the primal attack against Darmstadt LWE instance (n, alpha).
:param n: the dimension of the LWE-challenge secret
:param params: parameters for LWE:
- lwe/alpha: the noise rate of the LWE-challenge
- lwe/m: the number of samples to use for the primal attack
- lwe/goal_margin: accept anything that is
goal_margin * estimate(length of embedded vector)
as an lwe solution
- lwe/svp_bkz_time_factor: if > 0, run a larger pump when
svp_bkz_time_factor * time(BKZ tours so far) is expected
to be enough time to find a solution
- bkz/blocksizes: given as low:high:inc perform BKZ reduction
with blocksizes in range(low, high, inc) (after some light)
prereduction
- bkz/tours: the number of tours to do for each blocksize
- bkz/jump: the number of blocks to jump in a BKZ tour after
each pump
- bkz/extra_dim4free: lift to indices extra_dim4free earlier in
the lattice than the currently sieved block
- bkz/fpylll_crossover: use enumeration based BKZ from fpylll
below this blocksize
- bkz/dim4free_fun: in blocksize x, try f(x) dimensions for free,
give as 'lambda x: f(x)', e.g. 'lambda x: 11.5 + 0.075*x'
- pump/down_sieve: sieve after each insert in the pump-down
phase of the pump
- dummy_tracer: use a dummy tracer which captures less information
- verbose: print information throughout the lwe challenge attempt
"""
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
# params for underlying BKZ
extra_dim4free = params.pop("bkz/extra_dim4free")
jump = params.pop("bkz/jump")
dim4free_fun = params.pop("bkz/dim4free_fun")
pump_params = pop_prefixed_params("pump", params)
fpylll_crossover = params.pop("bkz/fpylll_crossover")
blocksizes = params.pop("bkz/blocksizes")
tours = params.pop("bkz/tours")
# flow of the lwe solver
svp_bkz_time_factor = params.pop("lwe/svp_bkz_time_factor")
goal_margin = params.pop("lwe/goal_margin")
# generation of lwe instance and Kannan's embedding
alpha = params.pop("lwe/alpha")
m = params.pop("lwe/m")
decouple = svp_bkz_time_factor > 0
# misc
dont_trace = params.pop("dummy_tracer")
verbose = params.pop("verbose")
A, c, q = load_lwe_challenge(n=n, alpha=alpha)
print "-------------------------"
print "Primal attack, LWE challenge n=%d, alpha=%.4f" % (n, alpha)
if m is None:
try:
min_cost_param = gsa_params(n=A.ncols, alpha=alpha, q=q,
samples=A.nrows, decouple=decouple)
(b, s, m) = min_cost_param
except TypeError:
raise TypeError("No winning parameters.")
else:
try:
min_cost_param = gsa_params(n=A.ncols, alpha=alpha, q=q, samples=m,
decouple=decouple)
(b, s, _) = min_cost_param
except TypeError:
raise TypeError("No winning parameters.")
print "Chose %d samples. Predict solution at bkz-%d + svp-%d" % (m, b, s)
print
target_norm = goal_margin * (alpha*q)**2 * m + 1
if blocksizes is not None:
blocksizes = range(10, 40) + eval("range(%s)" % re.sub(":", ",", blocksizes)) # noqa
else:
blocksizes = range(10, 50) + [b-20, b-17] + range(b - 14, b + 25, 2)
B = primal_lattice_basis(A, c, q, m=m)
g6k = Siever(B, params)
print "GSO precision: ", g6k.M.float_type
if dont_trace:
tracer = dummy_tracer
else:
tracer = SieveTreeTracer(g6k, root_label=("lwe"), start_clocks=True)
d = g6k.full_n
g6k.lll(0, g6k.full_n)
slope = basis_quality(g6k.M)["/"]
print "Intial Slope = %.5f\n" % slope
T0 = time.time()
T0_BKZ = time.time()
for blocksize in blocksizes:
for tt in range(tours):
# BKZ tours
if blocksize < fpylll_crossover:
if verbose:
print "Starting a fpylll BKZ-%d tour. " % (blocksize),
sys.stdout.flush()
bkz = BKZReduction(g6k.M)
par = fplll_bkz.Param(blocksize,
strategies=fplll_bkz.DEFAULT_STRATEGY,
max_loops=1)
bkz(par)
else:
if verbose:
print "Starting a pnjBKZ-%d tour. " % (blocksize)
pump_n_jump_bkz_tour(g6k, tracer, blocksize, 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
if verbose:
slope = basis_quality(g6k.M)["/"]
fmt = "slope: %.5f, walltime: %.3f sec"
print fmt % (slope, time.time() - T0)
g6k.lll(0, g6k.full_n)
if g6k.M.get_r(0, 0) <= target_norm:
break
# overdoing n_max would allocate too much memory, so we are careful
svp_Tmax = svp_bkz_time_factor * T_BKZ
n_max = int(58 + 2.85 * log(svp_Tmax * params.threads)/log(2.))
rr = [g6k.M.get_r(i, i) for i in range(d)]
for n_expected in range(2, d-2):
x = (target_norm/goal_margin) * n_expected/(1.*d)
if 4./3 * gaussian_heuristic(rr[d-n_expected:]) > x:
break
print "Without otf, would expect solution at pump-%d. n_max=%d in the given time." % (n_expected, n_max) # noqa
if n_expected >= n_max - 1:
continue
n_max += 1
# Larger SVP
llb = d - blocksize
while gaussian_heuristic([g6k.M.get_r(i, i) for i in range(llb, d)]) < target_norm * (d - llb)/(1.*d): # noqa
llb -= 1
f = d-llb-n_max
if verbose:
print "Starting svp pump_{%d, %d, %d}, n_max = %d, Tmax= %.2f sec" % (llb, d-llb, f, n_max, svp_Tmax) # noqa
pump(g6k, tracer, llb, d-llb, f, verbose=verbose,
goal_r0=target_norm * (d - llb)/(1.*d))
if verbose:
slope = basis_quality(g6k.M)["/"]
fmt = "\n slope: %.5f, walltime: %.3f sec"
print fmt % (slope, time.time() - T0)
print
g6k.lll(0, g6k.full_n)
T0_BKZ = time.time()
if g6k.M.get_r(0, 0) <= target_norm:
break
if g6k.M.get_r(0, 0) <= target_norm:
print "Finished! TT=%.2f sec" % (time.time() - T0)
print g6k.M.B[0]
alpha_ = int(alpha*1000)
filename = 'lwechallenge/%03d-%03d-solution.txt' % (n, alpha_)
fn = open(filename, "w")
fn.write(str(g6k.M.B[0]))
fn.close()
return
raise ValueError("No solution found.")
# -*- coding: utf-8 -*-
from fpylll import IntegerMatrix, LLL, GSO
from fpylll import BKZ as fplll_bkz
from fpylll.algorithms.bkz2 import BKZReduction
from fpylll.tools.bkz_stats import dummy_tracer
from time import time
from fpylll import Enumeration, EnumerationError
import sys
from fpylll.util import gaussian_heuristic
from middleware import SubSieveLib
for n in range(40, 90, 2):
A_pre = IntegerMatrix.from_file("svpchallenge/svpchallengedim%dseed0.txt" %
n)
LLL.reduction(A_pre)
A = IntegerMatrix.from_matrix(A_pre, int_type="long")
bkz = BKZReduction(A)
bkz.lll_obj()
bkz.randomize_block(0, n, density=n / 4)
bkz.lll_obj()
START = time()
siever = SubSieveLib(n, 0, bkz.lll_obj.M)
siever.sieve()
TIME = time() - START
print(n, TIME)
del siever
def ntru_kernel(arg0, params=None, seed=None):
"""
Run the primal attack against Darmstadt LWE instance (n, alpha).
:param n: the dimension of the LWE-challenge secret
:param params: parameters for LWE:
- lwe/alpha: the noise rate of the LWE-challenge
- lwe/m: the number of samples to use for the primal attack
- lwe/goal_margin: accept anything that is
goal_margin * estimate(length of embedded vector)
as an lwe solution
- lwe/svp_bkz_time_factor: if > 0, run a larger pump when
svp_bkz_time_factor * time(BKZ tours so far) is expected
to be enough time to find a solution
- bkz/blocksizes: given as low:high:inc perform BKZ reduction
with blocksizes in range(low, high, inc) (after some light)
prereduction
- bkz/tours: the number of tours to do for each blocksize
- bkz/jump: the number of blocks to jump in a BKZ tour after
each pump
- bkz/extra_dim4free: lift to indices extra_dim4free earlier in
the lattice than the currently sieved block
- bkz/fpylll_crossover: use enumeration based BKZ from fpylll
below this blocksize
- bkz/dim4free_fun: in blocksize x, try f(x) dimensions for free,
give as 'lambda x: f(x)', e.g. 'lambda x: 11.5 + 0.075*x'
- pump/down_sieve: sieve after each insert in the pump-down
phase of the pump
- dummy_tracer: use a dummy tracer which captures less information
- verbose: print information throughout the lwe challenge attempt
"""
# Pool.map only supports a single parameter
if params is None and seed is None:
n, params, seed = arg0
else:
n = arg0
params = copy.copy(params)
# params for underlying BKZ
extra_dim4free = params.pop("bkz/extra_dim4free")
jump = params.pop("bkz/jump")
dim4free_fun = params.pop("bkz/dim4free_fun")
pump_params = pop_prefixed_params("pump", params)
fpylll_crossover = params.pop("bkz/fpylll_crossover")
blocksizes = params.pop("bkz/blocksizes")
tours = params.pop("bkz/tours")
# flow of the lwe solver
svp_bkz_time_factor = params.pop("lwe/svp_bkz_time_factor")
goal_margin = params.pop("lwe/goal_margin")
# generation of lwe instance and Kannan's embedding
alpha = params.pop("lwe/alpha")
m = params.pop("lwe/m")
decouple = svp_bkz_time_factor > 0
# misc
dont_trace = params.pop("dummy_tracer")
verbose = params.pop("verbose")
filename = 'ntru_n_'+str(n)+'.txt'
H, q = read_ntru_from_file(filename)
print("-------------------------")
print("Hybrid attack on NTRU n=%d" %n)
# compute the attack parameters
paramset_NTRU1 = {'n': n, 'q': q, 'w': 2*(n/3)}
print(paramset_NTRU1)
beta, g, rt = plain_hybrid_compleixty(paramset_NTRU1, verbose = True)
B = ntru_plain_hybrid_basis(A, g, q, m=m)
g6k = Siever(B, params)
print("GSO precision: ", g6k.M.float_type)
if dont_trace:
tracer = dummy_tracer
else:
tracer = SieveTreeTracer(g6k, root_label=("ntru"), start_clocks=True)
d = g6k.full_n
g6k.lll(0, g6k.full_n)
slope = basis_quality(g6k.M)["/"]
print("Intial Slope = %.5f\n" % slope)
T0 = time.time()
T0_BKZ = time.time()
for blocksize in blocksizes:
for tt in range(tours):
# BKZ tours
if blocksize < fpylll_crossover:
if verbose:
print("Starting a fpylll BKZ-%d tour. " % (blocksize), end=' ')
sys.stdout.flush()
bkz = BKZReduction(g6k.M)
par = fplll_bkz.Param(blocksize,
strategies=fplll_bkz.DEFAULT_STRATEGY,
max_loops=1)
bkz(par)
else:
if verbose:
print("Starting a pnjBKZ-%d tour. " % (blocksize))
pump_n_jump_bkz_tour(g6k, tracer, blocksize, 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
if verbose:
slope = basis_quality(g6k.M)["/"]
fmt = "slope: %.5f, walltime: %.3f sec"
print(fmt % (slope, time.time() - T0))
g6k.lll(0, g6k.full_n)
if g6k.M.get_r(0, 0) <= target_norm:
break
# overdoing n_max would allocate too much memory, so we are careful
svp_Tmax = svp_bkz_time_factor * T_BKZ
n_max = int(58 + 2.85 * log(svp_Tmax * params.threads)/log(2.))
rr = [g6k.M.get_r(i, i) for i in range(d)]
for n_expected in range(2, d-2):
x = (target_norm/goal_margin) * n_expected/(1.*d)
if 4./3 * gaussian_heuristic(rr[d-n_expected:]) > x:
break
print("Without otf, would expect solution at pump-%d. n_max=%d in the given time." % (n_expected, n_max)) # noqa
if n_expected >= n_max - 1:
continue
n_max += 1
# Larger SVP
llb = d - blocksize
while gaussian_heuristic([g6k.M.get_r(i, i) for i in range(llb, d)]) < target_norm * (d - llb)/(1.*d): # noqa
llb -= 1
f = d-llb-n_max
if verbose:
print("Starting svp pump_{%d, %d, %d}, n_max = %d, Tmax= %.2f sec" % (llb, d-llb, f, n_max, svp_Tmax)) # noqa
pump(g6k, tracer, llb, d-llb, f, verbose=verbose,
goal_r0=target_norm * (d - llb)/(1.*d))
if verbose:
slope = basis_quality(g6k.M)["/"]
fmt = "\n slope: %.5f, walltime: %.3f sec"
print(fmt % (slope, time.time() - T0))
print()
g6k.lll(0, g6k.full_n)
T0_BKZ = time.time()
if g6k.M.get_r(0, 0) <= target_norm:
break
if g6k.M.get_r(0, 0) <= target_norm:
print("Finished! TT=%.2f sec" % (time.time() - T0))
print(g6k.M.B[0])
alpha_ = int(alpha*1000)
filename = 'lwechallenge/%03d-%03d-solution.txt' % (n, alpha_)
fn = open(filename, "w")
fn.write(str(g6k.M.B[0]))
fn.close()
return
"""
raise ValueError("No solution found.")
def ntru():
"""
Attempt to solve an ntru instance.
"""
description = ntru.__doc__
args, all_params = parse_args(description,
ntru__m=None,
lwe__goal_margin=1.5,
lwe__svp_bkz_time_factor=1,
bkz__blocksizes=None,
bkz__tours=1,
bkz__jump=1,
bkz__extra_dim4free=12,
bkz__fpylll_crossover=51,
bkz__dim4free_fun="default_dim4free_fun",
pump__down_sieve=True,
dummy_tracer=True, # set to control memory
verbose=True
)
stats = run_all(ntru_kernel, list(all_params.values()), # noqa
lower_bound=args.lower_bound,
upper_bound=args.upper_bound,
step_size=args.step_size,
trials=args.trials,
workers=args.workers,
seed=args.seed)
def __init__(self, A, recycling_pool_max_size=1):
"""Create new BKZ object.
:param A: an integer matrix, a GSO object or an LLL object
"""
BKZ2.__init__(self, A)
self.recycling_pool_max_size = recycling_pool_max_size
