def _factor_minpoly_modp(minpoly_coeff, p):
"""
Factor theminpoly modulo p, and return two values in a tuple.
We call gcd(square factors mod p, difference of minpoly and its modp) Z.
1) degree of Z
2) (minpoly mod p) / Z
"""
Fp = finitefield.FinitePrimeField.getInstance(p)
theminpoly_p = uniutil.polynomial([(d, Fp.createElement(c)) for (d, c) in enumerate(minpoly_coeff)], Fp)
modpfactors = theminpoly_p.factor()
mini_p = arith1.product([t for (t, e) in modpfactors])
quot_p = theminpoly_p.exact_division(mini_p)
mini = _min_abs_poly(mini_p)
quot = _min_abs_poly(quot_p)
minpoly = uniutil.polynomial(enumerate(minpoly_coeff), Z)
f_p = _mod_p((mini * quot - minpoly).scalar_exact_division(p), p)
gcd = f_p.getRing().gcd
common_p = gcd(gcd(mini_p, quot_p), f_p) # called Z
uniq_p = theminpoly_p // common_p
uniq = _min_abs_poly(uniq_p)
return common_p.degree(), uniq
def _factor_minpoly_modp(minpoly_coeff, p):
"""
Factor theminpoly modulo p, and return two values in a tuple.
We call gcd(square factors mod p, difference of minpoly and its modp) Z.
1) degree of Z
2) (minpoly mod p) / Z
"""
Fp = finitefield.FinitePrimeField.getInstance(p)
theminpoly_p = uniutil.polynomial([(d, Fp.createElement(c)) for (d, c) in enumerate(minpoly_coeff)], Fp)
modpfactors = theminpoly_p.factor()
mini_p = arith1.product([t for (t, e) in modpfactors])
quot_p = theminpoly_p.exact_division(mini_p)
mini = _min_abs_poly(mini_p)
quot = _min_abs_poly(quot_p)
minpoly = uniutil.polynomial(enumerate(minpoly_coeff), Z)
f_p = _mod_p((mini * quot - minpoly).scalar_exact_division(p), p)
gcd = f_p.getRing().gcd
common_p = gcd(gcd(mini_p, quot_p), f_p) # called Z
uniq_p = theminpoly_p // common_p
uniq = _min_abs_poly(uniq_p)
return common_p.degree(), uniq
def isIdeal(self):
"""
Check whether given lattice is a ideal lattice.
"""
n = self.basis.column
Compo = []
for i in range(n):
for j in range(n):
if i == j + 1:
Compo.append(1)
else:
Compo.append(0)
M = Matrix(n, n, Compo)
d = self.basis.determinant()
B = self.basis.hermiteNormalForm()
z = B.compo[n-1][n-1]
A = B.adjugateMatrix()
z = B.compo[n-1][n-1]
P = A*M*B
for i in range(n):
for j in range(n):
P.compo[i][j] = P.compo[i][j]%d
sum = 0
for i in range(n):
for j in range(n-1):
sum = sum + P.compo[i][j]
if sum == 0:
c_compo = []
for i in range(n):
c_compo.append(P.compo[i][n-1])
else:
return False
c_sum = 0
for i in range(n):
c_sum = c_sum + c_compo[i]
if c_sum == 0:
c_compo = []
for i in range(n):
c_compo.append(d)
c = Vector(c_compo)
if z == 1:
qstar = c
poly = B*qstar
elif gcd(z, d//z) != 1:
qstar = c
poly = B*qstar
else:
sum0 = 0
for i in range(n):
sum0 = sum0 + c.compo[i]%z
if sum0 == 0:
qstar_compo = []
for j in range(n):
qstar_compo.append(CRT([(c.compo[j]//z, d//z), (0, z)]))
qstar = Vector(qstar_compo)
poly = B*qstar
else:
return False
sum1 = 0
for i in range(n):
sum1 = sum1 + poly.compo[i]%(d//z)
if sum1 == 0:
q_compo = []
for j in range(n):
q_compo.append(poly.compo[j]//d)
q = Vector(q_compo)
return True, q
else:
return False
def isIdeal(self):
"""
Check whether given lattice is a ideal lattice.
"""
n = self.basis.column
Compo = []
for i in range(n):
for j in range(n):
if i == j + 1:
Compo.append(1)
else:
Compo.append(0)
M = Matrix(n, n, Compo)
d = self.basis.determinant()
B = self.basis.hermiteNormalForm()
z = B.compo[n - 1][n - 1]
A = B.adjugateMatrix()
z = B.compo[n - 1][n - 1]
P = A * M * B
for i in range(n):
for j in range(n):
P.compo[i][j] = P.compo[i][j] % d
sum = 0
for i in range(n):
for j in range(n - 1):
sum = sum + P.compo[i][j]
if sum == 0:
c_compo = []
for i in range(n):
c_compo.append(P.compo[i][n - 1])
else:
return False
c_sum = 0
for i in range(n):
c_sum = c_sum + c_compo[i]
if c_sum == 0:
c_compo = []
for i in range(n):
c_compo.append(d)
c = Vector(c_compo)
if z == 1:
qstar = c
poly = B * qstar
elif gcd(z, d // z) != 1:
qstar = c
poly = B * qstar
else:
sum0 = 0
for i in range(n):
sum0 = sum0 + c.compo[i] % z
if sum0 == 0:
qstar_compo = []
for j in range(n):
qstar_compo.append(CRT([(c.compo[j] // z, d // z),
(0, z)]))
qstar = Vector(qstar_compo)
poly = B * qstar
else:
return False
sum1 = 0
for i in range(n):
sum1 = sum1 + poly.compo[i] % (d // z)
if sum1 == 0:
q_compo = []
for j in range(n):
q_compo.append(poly.compo[j] // d)
q = Vector(q_compo)
return True, q
else:
return False
