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LeakLWE2
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Merge branch 'master' of https://git.aprilas.fr/tfeneuil/LeakLWE2

master
Thibauld Feneuil 4 年之前
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共有 15 個檔案被更改，包括 9 行新增 和 8508 行删除
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**/.ipynb_checkpoints/**
**/__pycache__/**
*.pyc

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@@ -1,161 +0,0 @@
from multiprocessing import Pool
from map_drop import map_drop
from numpy.random import seed as np_seed
import time
load("../framework/instance_gen.sage")

Derr = build_centered_binomial_law(6)
modulus = 11

try:
N_tests = int(sys.argv[1])
threads = int(sys.argv[2])
except:
N_tests = 5
threads = 1


def v(i):
return canonical_vec(d, i)


qvec_donttouch = 35


def randv():
vv = v(randint(qvec_donttouch, d - 1))
vv -= v(randint(qvec_donttouch, d - 1))
vv += v(randint(qvec_donttouch, d - 1))
vv -= v(randint(qvec_donttouch, d - 1))
vv += v(randint(qvec_donttouch, d - 1))
return vv


def one_experiment(id, aargs):
(N_hints, T_hints) = aargs
mu, variance = average_variance(Derr)
set_random_seed(id)
np_seed(seed=id)
A, b, dbdd1 = initialize_from_LWE_instance(DBDD, n, q,
m, D_e, D_s,
verbosity=0)
A, b, dbdd2 = initialize_from_LWE_instance(DBDD,
n, q, m, D_e,
D_s,
verbosity=0)

dbdd1._keep_basis = False
dbdd2._keep_basis = True
dbdd1_time = 0.
dbdd2_time = 0.
for j in range(N_hints):
vv = randv()
##print(vv)
if T_hints == "Perfect":
start_time = time.time()
dbdd1.integrate_perfect_hint(vv, dbdd1.leak(vv), estimate=False)
middle_time = time.time()
dbdd2.integrate_perfect_hint(vv, dbdd2.leak(vv), estimate=False)
end_time = time.time()
if T_hints == "Approx":
start_time = time.time()
dbdd1.integrate_approx_hint(vv, dbdd1.leak(vv) +
draw_from_distribution(Derr),
variance, estimate=False)
middle_time = time.time()
dbdd2.integrate_approx_hint(vv, dbdd2.leak(vv) +
draw_from_distribution(Derr),
variance, estimate=False)
end_time = time.time()
if T_hints == "Modular":
start_time = time.time()
dbdd1.integrate_modular_hint(vv, dbdd1.leak(vv) % modulus,
modulus, smooth=True, estimate=False)
middle_time = time.time()
dbdd2.integrate_modular_hint(vv, dbdd2.leak(vv) % modulus,
modulus, smooth=True, estimate=False)
end_time = time.time()
dbdd1_time += middle_time - start_time
dbdd2_time += end_time - middle_time

print('q-vectors')
start_time = time.time()
dbdd1.integrate_q_vectors(q, indices=range(35))
beta_pred_1, _ = dbdd1.estimate_attack(probabilistic=True)
beta1, _ = dbdd1.attack()
middle_time = time.time()
dbdd2.integrate_q_vectors(q, indices=range(35))
beta_pred_2, _ = dbdd2.estimate_attack(probabilistic=True)
beta2, _ = dbdd2.attack()
end_time = time.time()
dbdd1_time += middle_time - start_time
dbdd2_time += end_time - middle_time

return (beta, beta1, beta2, dbdd1_time, dbdd2_time)


dic = {" ": None}


def validation_prediction(N_tests, N_hints, T_hints):
# Estimation
import datetime
ttt = datetime.datetime.now()
res = map_drop(N_tests, threads, one_experiment, (N_hints, T_hints))
beta_real = RR(sum([r[0] for r in res])) / N_tests
beta_pred_full = RR(sum([r[1] for r in res])) / N_tests
beta_pred_light = RR(sum([r[2] for r in res])) / N_tests
dbdd1_time = RR(sum([r[3] for r in res])) / N_tests
dbdd2_time = RR(sum([r[4] for r in res])) / N_tests

print("%d,\t %.3f,\t %.3f,\t %.3f,\t %.3f,\t %.3f \t\t" %
(N_hints, beta_real, beta_pred_full, beta_pred_light, dbdd1_time, dbdd2_time), end=" \t")
print("Time:", datetime.datetime.now() - ttt)
return beta_pred_full


logging("Number of threads : %d" % threads, style="DATA")
logging("Number of Samples : %d" % N_tests, style="DATA")
logging(" Validation tests ", style="HEADER")

n = 70
m = n
q = 3301
D_s = build_centered_binomial_law(40)
D_e = build_centered_binomial_law(40)
d = m + n

#print("\n \n None")

#print("hints,\t real,\t pred_full, \t pred_light,")

#beta_pred = validation_prediction(N_tests, 0, "None")

print("\n \n Perfect")

print("hints,\t real,\t pred_full, \t pred_light,")
for h in range(2, 100):
beta_pred = validation_prediction(N_tests, h, "Perfect") # Line 0
if beta_pred < 3:
break

print("\n \n Modular")

print("hints,\t real,\t pred_full, \t pred_light,")
for h in range(2, 200, 2):
beta_pred = validation_prediction(N_tests, h, "Modular") # Line 0
if beta_pred < 3:
break

print("\n \n Approx")

print("hints,\t real,\t pred_full, \t pred_light,")
for h in range(4, 200, 4):
beta_pred = validation_prediction(N_tests, h, "Approx") # Line 0
if beta_pred < 3:
break

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@@ -1,6 +0,0 @@
{
"cells": [],
"metadata": {},
"nbformat": 4,
"nbformat_minor": 2
}

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@@ -1,560 +0,0 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"load(\"../framework/instance_gen.sage\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[4;37m Build DBDD from LWE \u001b[0m\n",
"\u001b[1;33m n= 70 \t m= 70 \t q=3301 \u001b[0m\n",
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[1;33m dim=141 \t δ=1.012362 \t β=45.40 \u001b[0m\n",
"\u001b[0m \u001b[0m\n"
]
}
],
"source": [
"n = 70\n",
"m = n\n",
"q = 3301\n",
"D_s = build_centered_binomial_law(40)\n",
"D_e = D_s\n",
"A, b, dbdd = initialize_from_LWE_instance(DBDD, n, q, m, D_e, D_s)\n",
"# In such parameter range, no need to integrate q-vectors\n",
"beta, delta = dbdd.estimate_attack()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[4;37m Running the Attack \u001b[0m\n",
"1\n"
]
},
{
"ename": "ValueError",
"evalue": "Float type 'ld' not understood.",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-14-b4e7e86f62fe>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0msecret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mattack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m<string>\u001b[0m in \u001b[0;36mattack\u001b[0;34m(self, beta_max, beta_pre, randomize, tours)\u001b[0m\n",
"\u001b[0;32msrc/fpylll/fplll/gso.pyx\u001b[0m in \u001b[0;36mfpylll.fplll.gso.MatGSO.__init__\u001b[0;34m()\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: Float type 'ld' not understood."
]
}
],
"source": [
"secret = dbdd.attack()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(17, -12, 9, -15)"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Simulating perfect hints\n",
"v0 = vec([randint(0, 1) for i in range(m + n)])\n",
"v1 = vec([randint(0, 1) for i in range(m + n)])\n",
"v2 = vec([randint(0, 1) for i in range(m + n)])\n",
"v3 = vec([randint(0, 1) for i in range(m + n)]) \n",
"# Computing l = <vi, s>\n",
"dbdd.leak(v0), dbdd.leak(v1), dbdd.leak(v2), dbdd.leak(v3)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=140, δ=1.01252495, β=41.94 \u001b[0m\n",
"\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=139, δ=1.01275154, β=38.44 \u001b[0m\n",
"\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=138, δ=1.01293762, β=34.79 \u001b[0m\n",
"\u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01314871, β=30.92 \u001b[0m\n"
]
}
],
"source": [
"_ = dbdd.integrate_perfect_hint(v0, 25) \n",
"_ = dbdd.integrate_perfect_hint(v1, 12) \n",
"_ = dbdd.integrate_perfect_hint(v2, -14) \n",
"_ = dbdd.integrate_perfect_hint(v3, -3)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1, 1, 0, 3)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Simulating modular hints\n",
"v0 = vec([randint(0, 1) for i in range(m + n)])\n",
"v1 = vec([randint(0, 1) for i in range(m + n)])\n",
"v2 = vec([randint(0, 1) for i in range(m + n)])\n",
"v3 = vec([randint(0, 1) for i in range(m + n)]) \n",
"# Computing l = <vi, s> mod k\n",
"dbdd.leak(v0)%2, dbdd.leak(v1)%3, dbdd.leak(v2)%4, dbdd.leak(v3)%5"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[1;37m integrate modular hint \u001b[0m \u001b[0m (smooth) \u001b[0m "
]
},
{
"ename": "NotImplementedError",
"evalue": "",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mNotImplementedError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-6-0bba940b5cde>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;31m# Integrate modular hints\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mintegrate_modular_hint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mInteger\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
"\u001b[0;32m<string>\u001b[0m in \u001b[0;36mdecorated\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n",
"\u001b[0;32m<string>\u001b[0m in \u001b[0;36mdecorated\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n",
"\u001b[0;32m<string>\u001b[0m in \u001b[0;36mintegrate_modular_hint\u001b[0;34m(self, v, l, k, smooth)\u001b[0m\n",
"\u001b[0;31mNotImplementedError\u001b[0m: "
]
}
],
"source": [
"# Integrate modular hints\n",
"_ = dbdd.integrate_modular_hint(v0, 1, 2, False) \n",
"_ = dbdd.integrate_modular_hint(v1, 1, 3, True)\n",
"_ = dbdd.integrate_modular_hint(v2, 0, 4, True) \n",
"_ = dbdd.integrate_modular_hint(v3, 3, 5, True)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-5, 24, 9, 54)"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Simulating approximate hints\n",
"v0 = vec([randint(0, 1) for i in range(m + n)])\n",
"v1 = vec([randint(0, 1) for i in range(m + n)])\n",
"v2 = vec([randint(0, 1) for i in range(m + n)])\n",
"v3 = vec([randint(0, 1) for i in range(m + n)]) \n",
"# Computing l = <vi, s> + noise\n",
"dbdd.leak(v0) + 2, dbdd.leak(v1) + 1, dbdd.leak(v2) - 1, dbdd.leak(v3)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01334785, β=26.99 \u001b[0m\n",
"\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01342129, β=25.49 \u001b[0m\n",
"\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01350341, β=24.44 \u001b[0m\n",
"\u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (conditionning) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=137, δ=1.01362755, β=23.65 \u001b[0m\n"
]
}
],
"source": [
"# Integrate approximate hints\n",
"var = 10\n",
"_ = dbdd.integrate_approx_hint(v0, -5, var, aposteriori=False) \n",
"_ = dbdd.integrate_approx_hint(v1, 24, var, aposteriori=False) \n",
"_ = dbdd.integrate_approx_hint(v2, 9, var, aposteriori=False) \n",
"_ = dbdd.integrate_approx_hint(v3, 54, var, aposteriori=False)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[1;33m dim=137 \t δ=1.013628 \t β=23.65 \u001b[0m\n",
"\u001b[0m \u001b[0m\n",
"\u001b[4;37m Running the Attack \u001b[0m\n",
"1\n"
]
},
{
"ename": "ValueError",
"evalue": "Float type 'ld' not understood.",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-21-7c2ddea6b769>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0mbeta\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdelta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mestimate_attack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0msecret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdbdd\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mattack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;32m<string>\u001b[0m in \u001b[0;36mattack\u001b[0;34m(self, beta_max, beta_pre, randomize, tours)\u001b[0m\n",
"\u001b[0;32msrc/fpylll/fplll/gso.pyx\u001b[0m in \u001b[0;36mfpylll.fplll.gso.MatGSO.__init__\u001b[0;34m()\u001b[0m\n",
"\u001b[0;31mValueError\u001b[0m: Float type 'ld' not understood."
]
}
],
"source": [
"beta, delta = dbdd.estimate_attack()\n",
"secret = dbdd.attack()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[0m --- Demonstration mode (no averaging) --- \u001b[0m\n",
"\u001b[0m Set of parameters: CCS1 \u001b[0m\n",
"\u001b[4;37m Attack without hints: 268.83 bikz \u001b[0m\n",
"\u001b[4;37m Build DBDD from LWE \u001b[0m\n",
"\u001b[1;33m n=352 \t m=352 \t q=2048 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = -1.047495308214138 + χ(σ²=0.074) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00520912, β=268.64 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00533686, β=258.80 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = -1.047495308214138 + χ(σ²=0.074) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00547581, β=248.73 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00560729, β=239.71 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 0.00843621399176955 + χ(σ²=0.016) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00573966, β=231.20 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00587017, β=223.15 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = 0.00843621399176955 + χ(σ²=0.016) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00600691, β=214.98 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = 0.00843621399176955 + χ(σ²=0.016) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00613813, β=207.71 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u351 = 1.211598111935266 + χ(σ²=0.177) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=705, δ=1.00614016, β=207.61 \u001b[0m\n",
"\u001b[4;37m Integrating q-vectors \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 2048*c703 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=704, δ=1.00614274, β=207.50 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 2048*c653 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=654, δ=1.00623802, β=202.43 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 2048*c603 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=604, δ=1.00629226, β=199.59 \u001b[0m\n",
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[3;34m ln(dvol)=2229.2964391 \t ln(Bvol)=1761.2869858 \t ln(Svol)=-936.0189067 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",
"\u001b[1;33m dim=584 \t δ=1.006299 \t β=199.30 \u001b[0m\n",
"\u001b[0m \u001b[0m\n",
"\u001b[4;37m Hybrid attack estimation \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=517 \t delta=1.007041 \t beta=165.65 \t guesses= 50 \u001b[0m \u001b[1;33m Proba success = 0.784776775862473 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=449 \t delta=1.008001 \t beta=132.43 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.615874587933098 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=374 \t delta=1.009401 \t beta=96.94 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.227714429544019 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=295 \t delta=1.011563 \t beta=58.46 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.0417737457149379 \u001b[0m\n",
"\u001b[0m Set of parameters: CCS2 \u001b[0m\n",
"\u001b[4;37m Attack without hints: 447.85 bikz \u001b[0m\n",
"\u001b[4;37m Build DBDD from LWE \u001b[0m\n",
"\u001b[1;33m n=592 \t m=592 \t q=4096 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00368084, β=447.74 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.146460874616214 + χ(σ²=0.127) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00376168, β=434.18 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00383428, β=422.44 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00391176, β=410.48 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00398557, β=399.57 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00406105, β=388.84 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00412447, β=380.28 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00419601, β=370.82 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00426402, β=362.29 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00433281, β=353.83 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u500 = 1.146460874616214 + χ(σ²=0.127) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00440385, β=345.52 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = -1.00569376313933 + χ(σ²=0.011) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00447868, β=337.11 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u591 = 0.000494369678659709 + χ(σ²=0.001) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1185, δ=1.00453370, β=331.08 \u001b[0m\n",
"\u001b[4;37m Integrating q-vectors \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1183 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1184, δ=1.00453416, β=330.92 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1133 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1134, δ=1.00460786, β=323.20 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1083 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1084, δ=1.00467681, β=316.15 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c1033 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1034, δ=1.00473859, β=309.91 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c983 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=984, δ=1.00479311, β=304.69 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c933 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=934, δ=1.00483487, β=300.74 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 4096*c883 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=884, δ=1.00485996, β=298.46 \u001b[0m\n",
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[3;34m ln(dvol)=3529.6911796 \t ln(Bvol)=2195.8902680 \t ln(Svol)=-2667.6018232 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",
"\u001b[1;33m dim=857 \t δ=1.004864 \t β=298.11 \u001b[0m\n",
"\u001b[0m \u001b[0m\n",
"\u001b[4;37m Hybrid attack estimation \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=804 \t delta=1.005161 \t beta=272.46 \t guesses= 50 \u001b[0m \u001b[1;33m Proba success = 0.986359509012097 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=750 \t delta=1.005502 \t beta=247.03 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.972905081018585 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=696 \t delta=1.005890 \t beta=221.82 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.959634178028866 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=642 \t delta=1.006345 \t beta=196.85 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.946544296671780 \u001b[0m\n",
"\u001b[0m Set of parameters: CCS3 \u001b[0m\n",
"\u001b[4;37m Attack without hints: 491.98 bikz \u001b[0m\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[4;37m Build DBDD from LWE \u001b[0m\n",
"\u001b[1;33m n=752 \t m=752 \t q=32768 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = -2.187046263345110 + χ(σ²=0.163) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1505, δ=1.00344395, β=491.89 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1505, δ=1.00349544, β=481.73 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00354986, β=471.38 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00359717, β=462.61 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00363783, β=455.33 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00369078, β=445.99 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = 1.604094165813716 + χ(σ²=0.242) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00373686, β=438.27 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00378107, β=430.89 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00382418, β=424.06 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00386791, β=417.19 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u500 = 1.201824086229531 + χ(σ²=0.162) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00392265, β=408.79 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00396794, β=402.16 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u600 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00401167, β=395.78 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u650 = 2.998692810457516 + χ(σ²=0.003) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1504, δ=1.00406457, β=388.40 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u700 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00411096, β=382.00 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u750 = 0.0001125935934245342 + χ(σ²=0.000) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00416366, β=374.99 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u751 = -1.01352265043897 + χ(σ²=0.030) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00416457, β=374.89 \u001b[0m\n",
"\u001b[4;37m Integrating q-vectors \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1503 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1502, δ=1.00416557, β=374.77 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1453 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1452, δ=1.00420958, β=369.15 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1403 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1402, δ=1.00424963, β=364.09 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1353 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1352, δ=1.00428447, β=359.71 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1303 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1302, δ=1.00431461, β=356.11 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1253 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1252, δ=1.00433620, β=353.47 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1203 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1202, δ=1.00434902, β=352.01 \u001b[0m\n",
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[3;34m ln(dvol)=5873.7705379 \t ln(Bvol)=4429.2104838 \t ln(Svol)=-2889.1201083 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",
"\u001b[1;33m dim=1177 \t δ=1.004350 \t β=351.81 \u001b[0m\n",
"\u001b[0m \u001b[0m\n",
"\u001b[4;37m Hybrid attack estimation \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1122 \t delta=1.004547 \t beta=329.58 \t guesses= 50 \u001b[0m \u001b[1;33m Proba success = 0.997189039098024 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1068 \t delta=1.004764 \t beta=307.51 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.994385979697240 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1013 \t delta=1.005004 \t beta=285.60 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.991590799586837 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=959 \t delta=1.005270 \t beta=263.86 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.988803476618439 \u001b[0m\n",
"\u001b[0m Set of parameters: CCS4 \u001b[0m\n",
"\u001b[4;37m Attack without hints: 584.09 bikz \u001b[0m\n",
"\u001b[4;37m Build DBDD from LWE \u001b[0m\n",
"\u001b[1;33m n=864 \t m=864 \t q=32768 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u0 = 3.00000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1728, δ=1.00304787, β=583.29 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u50 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1712, δ=1.00311466, β=566.08 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = 4.03571428571429 + χ(σ²=0.066) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1698, δ=1.00317667, β=550.73 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u150 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1686, δ=1.00323493, β=536.95 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u200 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1671, δ=1.00330361, β=521.49 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 1.635097971811619 + χ(σ²=0.234) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1649, δ=1.00339599, β=501.70 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1632, δ=1.00347647, β=485.47 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1613, δ=1.00356554, β=468.44 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1602, δ=1.00362960, β=456.74 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1585, δ=1.00371670, β=441.61 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u500 = 3.00000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1567, δ=1.00381197, β=425.91 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1554, δ=1.00389208, β=413.45 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u600 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1535, δ=1.00399725, β=397.84 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u650 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1518, δ=1.00409770, β=383.81 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u700 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1503, δ=1.00419478, β=371.06 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u750 = 1.190473351615596 + χ(σ²=0.156) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1490, δ=1.00428223, β=359.95 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u800 = -1.009176115880109 + χ(σ²=0.026) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1475, δ=1.00438267, β=347.93 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u850 = 1.635097971811619 + χ(σ²=0.234) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1459, δ=1.00449591, β=335.17 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u863 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1455, δ=1.00452419, β=332.09 \u001b[0m\n",
"\u001b[4;37m Integrating q-vectors \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1727 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1454, δ=1.00452460, β=331.95 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1677 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1404, δ=1.00458760, β=325.29 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1627 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1354, δ=1.00464808, β=319.05 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1577 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1304, δ=1.00470490, β=313.30 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1527 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1254, δ=1.00475783, β=308.13 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1477 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1204, δ=1.00480390, β=303.65 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1427 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1154, δ=1.00484348, β=300.02 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1377 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1104, δ=1.00487098, β=297.43 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1327 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1054, δ=1.00488544, β=296.15 \u001b[0m\n",
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[3;34m ln(dvol)=5223.8138965 \t ln(Bvol)=4657.9490534 \t ln(Svol)=-1131.7296863 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",
"\u001b[1;33m dim=1039 \t δ=1.004886 \t β=296.07 \u001b[0m\n",
"\u001b[0m \u001b[0m\n",
"\u001b[4;37m Hybrid attack estimation \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=963 \t delta=1.005249 \t beta=265.50 \t guesses= 50 \u001b[0m \u001b[1;33m Proba success = 0.818477853233848 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=886 \t delta=1.005675 \t beta=235.28 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.669905996234288 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=808 \t delta=1.006181 \t beta=205.45 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.548303221666322 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=729 \t delta=1.006800 \t beta=175.62 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.256443378603881 \u001b[0m\n",
"\u001b[0m Set of parameters: NIST1 \u001b[0m\n",
"\u001b[4;37m Attack without hints: 487.00 bikz \u001b[0m\n",
"\u001b[4;37m Build DBDD from LWE \u001b[0m\n",
"\u001b[1;33m n=640 \t m=640 \t q=32768 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = 3.069447793585725 + χ(σ²=0.444) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1281, δ=1.00346927, β=486.85 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 1.321045392022008 + χ(σ²=0.399) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1271, δ=1.00354851, β=471.62 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = 1.755049101352603 + χ(σ²=0.765) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1266, δ=1.00360481, β=461.28 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = -4.57717926440819 + χ(σ²=1.097) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1262, δ=1.00365626, β=451.99 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 4.090359168241965 + χ(σ²=0.159) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1253, δ=1.00373273, β=438.88 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = -2.41906805640610 + χ(σ²=0.436) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1243, δ=1.00381626, β=425.31 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = -2.661084529507207 + χ(σ²=0.837) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1235, δ=1.00389158, β=413.53 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u350 = -2.41906805640610 + χ(σ²=0.436) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1230, δ=1.00395482, β=404.11 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u400 = 1.321045392022008 + χ(σ²=0.399) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1223, δ=1.00403038, β=393.22 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = -2.661084529507207 + χ(σ²=0.837) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1216, δ=1.00410464, β=382.87 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u500 = 1.321045392022008 + χ(σ²=0.399) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1211, δ=1.00417085, β=374.17 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = 4.090359168241965 + χ(σ²=0.159) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1206, δ=1.00423643, β=365.69 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u600 = 1.755049101352603 + χ(σ²=0.765) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1194, δ=1.00434773, β=352.15 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u639 = -1.515323025952966 + χ(σ²=1.992) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1189, δ=1.00441030, β=344.75 \u001b[0m\n",
"\u001b[4;37m Integrating q-vectors \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1279 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1188, δ=1.00441100, β=344.68 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1229 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1138, δ=1.00443703, β=341.70 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 32768*c1179 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1088, δ=1.00445220, β=340.08 \u001b[0m\n",
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[3;34m ln(dvol)=4931.2206559 \t ln(Bvol)=5364.9591775 \t ln(Svol)=867.4770433 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",
"\u001b[1;33m dim=1065 \t δ=1.004453 \t β=339.89 \u001b[0m\n",
"\u001b[0m \u001b[0m\n",
"\u001b[4;37m Hybrid attack estimation \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=978 \t delta=1.004823 \t beta=301.82 \t guesses= 50 \u001b[0m \u001b[1;33m Proba success = 0.333906700218510 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=884 \t delta=1.005297 \t beta=261.80 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.00102495772223270 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=787 \t delta=1.005904 \t beta=221.11 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 1.17943929438748e-6 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=691 \t delta=1.006660 \t beta=181.81 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 7.67683727015403e-12 \u001b[0m\n",
"\u001b[0m Set of parameters: NIST2 \u001b[0m\n",
"\u001b[4;37m Attack without hints: 708.06 bikz \u001b[0m\n",
"\u001b[4;37m Build DBDD from LWE \u001b[0m\n",
"\u001b[1;33m n=976 \t m=976 \t q=65536 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u0 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1953, δ=1.00264550, β=707.92 \u001b[0m\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u50 = 3.025380710659899 + χ(σ²=0.169) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1950, δ=1.00267055, β=699.04 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u100 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1942, δ=1.00270492, β=686.89 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u150 = 5.235337243401759 + χ(σ²=0.243) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1932, δ=1.00274506, β=673.32 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u200 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1923, δ=1.00278259, β=660.89 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u250 = 4.01405228758170 + χ(σ²=0.028) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1917, δ=1.00281478, β=650.62 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u300 = 3.025380710659899 + χ(σ²=0.169) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1907, δ=1.00285614, β=637.75 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u350 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1895, δ=1.00290400, β=623.42 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u400 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1884, δ=1.00295046, β=610.02 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u450 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1875, δ=1.00299260, β=598.21 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u500 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1862, δ=1.00304489, β=583.99 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u550 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1851, δ=1.00309357, β=571.39 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u600 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1845, δ=1.00312943, β=562.34 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u650 = 3.025380710659899 + χ(σ²=0.169) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1840, δ=1.00316311, β=553.98 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u700 = 4.01405228758170 + χ(σ²=0.028) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1832, δ=1.00320516, β=543.91 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u750 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1824, δ=1.00324807, β=533.92 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate perfect hint \u001b[0m \u001b[3;34m u800 = 0.000000000000000 \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1814, δ=1.00329760, β=522.78 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u850 = -1.089403973506705 + χ(σ²=0.393) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1808, δ=1.00333637, β=514.35 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u900 = -2.447576689126436 + χ(σ²=0.398) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1801, δ=1.00337834, β=505.41 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u950 = 4.01405228758170 + χ(σ²=0.028) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1792, δ=1.00342669, β=495.42 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate approx hint \u001b[0m \u001b[0m (aposteriori) \u001b[0m \u001b[3;34m u975 = 1.292442281128725 + χ(σ²=0.218) \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1789, δ=1.00344645, β=491.43 \u001b[0m\n",
"\u001b[4;37m Integrating q-vectors \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1951 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1788, δ=1.00344701, β=491.33 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1901 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1738, δ=1.00347079, β=486.57 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1851 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1688, δ=1.00349212, β=482.41 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1801 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1638, δ=1.00350973, β=478.94 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1751 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1588, δ=1.00352409, β=476.27 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1701 ∈ Λ \u001b[0m \u001b[3;32m \t Worthy hint ! \u001b[0m \u001b[1;33m dim=1538, δ=1.00353300, β=474.54 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;37m integrate short vector hint \u001b[0m \u001b[3;34m 65536*c1651 ∈ Λ \u001b[0m \u001b[3;31m \t Unworthy hint, Rejected. \u001b[0m\n",
"\u001b[4;37m Attack Estimation \u001b[0m\n",
"\u001b[3;34m ln(dvol)=7436.1356246 \t ln(Bvol)=7497.0799049 \t ln(Svol)=121.8885608 \tδ(β)=100000000000000000000.000000 \u001b[0m\n",
"\u001b[1;33m dim=1489 \t δ=1.003536 \t β=473.94 \u001b[0m\n",
"\u001b[0m \u001b[0m\n",
"\u001b[4;37m Hybrid attack estimation \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1405 \t delta=1.003735 \t beta=438.59 \t guesses= 50 \u001b[0m \u001b[1;33m Proba success = 0.802156595500351 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1324 \t delta=1.003948 \t beta=405.08 \t guesses= 100 \u001b[0m \u001b[1;33m Proba success = 0.603232864940319 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1240 \t delta=1.004199 \t beta=370.52 \t guesses= 150 \u001b[0m \u001b[1;33m Proba success = 0.265895477646676 \u001b[0m\n",
"\u001b[0m [...50] \u001b[0m \u001b[1;33m dim=1152 \t delta=1.004501 \t beta=334.55 \t guesses= 200 \u001b[0m \u001b[1;33m Proba success = 0.0905624388817529 \u001b[0m\n"
]
}
],
"source": [
"load('exploiting_SCA_from_Bos_et_al.sage')"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"ename": "TypeError",
"evalue": "version() takes 0 positional arguments but 1 was given",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-25-576b6e31d0fc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mfpylll\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mversion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfpylll\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mTypeError\u001b[0m: version() takes 0 positional arguments but 1 was given"
]
}
],
"source": [
"import fpylll\n",
"version(fpylll)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "SageMath 9.0",
"language": "sage",
"name": "sagemath"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

+ 1
- 1
framework/DBDD.sage 查看文件

@@ -30,7 +30,7 @@ class DBDD(DBDD_generic):
self.D = kwargs.get('D', None) # The dual Basis (only B or D is active)
assert self.D.T * self.B == identity_matrix(B.nrows())
self._dim = B.nrows()
self._maintains_basis = True
self._maintains_basis = False
self.S = S
self.PP = 0 * S # Span of the projections so far (orthonormal)
self.mu = mu

二進制
framework/__pycache__/__init__.cpython-37.pyc 查看文件


二進制
framework/__pycache__/instance_gen.cpython-37.pyc 查看文件


二進制
framework/__pycache__/test.cpython-37.pyc 查看文件


二進制
framework/__pycache__/test2.cpython-37.pyc 查看文件


+ 5
- 0
framework/geometry.sage 查看文件

@@ -96,9 +96,14 @@ def remove_linear_dependencies(B, dim=None):
r = K.dimensions()[0]
else:
r = nrows-dim
<<<<<<< HEAD

if r == 1 and False:
print("Use Better Algo")
=======
if r == 1 and False:
>>>>>>> 81324f49c90b518d464e18b0204408a3aa6b5eff
# Find a linear dependency
if K is None:
K = B.left_kernel().basis_matrix()

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