def test_gram_schmidt(self):
for i in range(_sage_const_20):
dim = i
A = random_matrix(QQ, i, algorithm='unimodular')
oA1 = matrix_utils.gram_schmidt(A)
oA2, _ = A.gram_schmidt(
) # compare results with sage's built in gram_schmidt
assert oA1 == oA2
def random_even_symm_mat(n):
while True:
m = random_matrix(ZZ, n)
m = m + m.transpose()
for a in range(n):
m[(a, a)] = m[(a, a)] * ZZ(2)
if not m.is_singular():
return m
def time_search_loop(p):
y = random_vector(F, n)
g = random_matrix(F, p, n).rows()
scalars = [ [ Fstar[randint(0,q-2)] for i in range(p) ]
for s in range(100) ]
before = process_time()
for m in scalars:
e = y - sum(m[i]*g[i] for i in range(p))
return (process_time() - before)/100.
def gen_instance(n, q, h, alpha=None, m=None, seed=None, s=None):
"""
Generate FHE-style LWE instance
:param n: dimension
:param q: modulus
:param alpha: noise rate (default: 8/q)
:param h: hamming weight of the secret (default: 2/3n)
:param m: number of samples (default: n)
"""
if seed is not None:
set_random_seed(seed)
q = next_prime(ceil(q) - 1, proof=False)
if alpha is None:
stddev = 3.2
else:
stddev = alpha * q / sqrt(2 * pi)
#RR = parent(alpha*q)
#stddev = alpha*q/RR(sqrt(2*pi))
if m is None:
m = n
K = GF(q, proof=False)
while 1:
A = random_matrix(K, m, n)
if A.rank() == n:
break
if s is not None:
c = A * s
else:
if h is None:
s = random_vector(ZZ, n, x=-1, y=1)
else:
S = [-1, 1]
s = [S[randint(0, 1)] for i in range(h)]
s += [0 for _ in range(n - h)]
shuffle(s)
s = vector(ZZ, s)
c = A * s
D = DiscreteGaussian(stddev)
for i in range(m):
c[i] += D()
u = random_vector(K, m)
print '(A, c) is n-dim LWE samples (with secret s) / (A, u) is uniform samples'
return A, c, u, s
def time_search_loop(p):
y = random_vector(F, n)
g = random_matrix(F, p, n).rows()
scalars = [[Fstar[randint(0, q - 2)] for i in range(p)]
for s in range(100)]
before = time.clock()
for m in scalars:
e = y - sum(m[i] * g[i] for i in range(p))
errs = e.hamming_weight()
return (time.clock() - before) / 100.
def time_search_loop(p):
y = random_vector(F, n)
g = random_matrix(F, p, n).rows()
scalars = [ [ Fstar[randint(0,q-2)] for i in range(p) ]
for s in range(100) ]
before = time.clock()
for m in scalars:
e = y - sum(m[i]*g[i] for i in range(p))
errs = e.hamming_weight()
return (time.clock() - before)/100.
def gen_fhe_instance(n, q, alpha=None, h=None, m=None, seed=None):
"""
Generate FHE-style LWE instance
:param n: dimension
:param q: modulus
:param alpha: noise rate (default: 8/q)
:param h: hamming weight of the secret (default: 2/3n)
:param m: number of samples (default: n)
"""
if seed is not None:
set_random_seed(seed)
q = next_prime(ceil(q)-1, proof=False)
if alpha is None:
alpha = ZZ(8)/q
n, alpha, q = preprocess_params(n, alpha, q)
stddev = stddevf(alpha*q)
if m is None:
m = n
K = GF(q, proof=False)
A = random_matrix(K, m, n)
if h is None:
s = random_vector(ZZ, n, x=-1, y=1)
else:
S = [-1, 1]
s = [S[randint(0, 1)] for i in range(h)]
s += [0 for _ in range(n-h)]
shuffle(s)
s = vector(ZZ, s)
c = A*s
D = DiscreteGaussian(stddev)
for i in range(m):
c[i] += D()
return A, c
def gen_fhe_instance(n, q, alpha=None, h=None, m=None, seed=None):
"""
Generate FHE-style LWE instance
:param n: dimension
:param q: modulus
:param alpha: noise rate (default: 8/q)
:param h: hamming weight of the secret (default: 2/3n)
:param m: number of samples (default: n)
"""
if seed is not None:
set_random_seed(seed)
q = next_prime(ceil(q) - 1, proof=False)
if alpha is None:
alpha = ZZ(8) / q
n, alpha, q = preprocess_params(n, alpha, q)
stddev = stddevf(alpha * q)
if m is None:
m = n
K = GF(q, proof=False)
A = random_matrix(K, m, n)
if h is None:
s = random_vector(ZZ, n, x=-1, y=1)
else:
S = [-1, 1]
s = [S[randint(0, 1)] for i in range(h)]
s += [0 for _ in range(n - h)]
shuffle(s)
s = vector(ZZ, s)
c = A * s
D = DiscreteGaussian(stddev)
for i in range(m):
c[i] += D()
return A, c