def __init__(self, parent, value):
"""
TESTS::
sage: F = GF(3).algebraic_closure()
sage: TestSuite(F.gen(2)).run(skip=['_test_pickling'])
.. NOTE::
The ``_test_pickling`` test has to be skipped because
there is no coercion map between the parents of ``x``
and ``loads(dumps(x))``.
"""
if is_FiniteFieldElement(value):
n = value.parent().degree()
else:
from sage.rings.integer import Integer
n = Integer(1)
self._value = parent._subfield(n).coerce(value)
self._level = n
FieldElement.__init__(self, parent)
def __init__(self, parent, value):
"""
TEST::
sage: F = GF(3).algebraic_closure()
sage: TestSuite(F.gen(2)).run(skip=['_test_pickling'])
.. NOTE::
The ``_test_pickling`` test has to be skipped because
there is no coercion map between the parents of ``x``
and ``loads(dumps(x))``.
"""
if is_FiniteFieldElement(value):
n = value.parent().degree()
else:
from sage.rings.integer import Integer
n = Integer(1)
self._value = parent._subfield(n).coerce(value)
self._level = n
FieldElement.__init__(self, parent)
def __init__(self, *args, **kwargs):
"""
Construct a substitution box (S-box) for a given lookup table
`S`.
INPUT:
- ``S`` - a finite iterable defining the S-box with integer or
finite field elements
- ``big_endian`` - controls whether bits shall be ordered in
big endian order (default: ``True``)
EXAMPLES:
We construct a 3-bit S-box where e.g. the bits (0,0,1) are
mapped to (1,1,1).::
sage: from sage.crypto.sbox import SBox
sage: S = SBox(7,6,0,4,2,5,1,3); S
(7, 6, 0, 4, 2, 5, 1, 3)
sage: S(0)
7
TESTS::
sage: from sage.crypto.sbox import SBox
sage: S = SBox()
Traceback (most recent call last):
...
TypeError: No lookup table provided.
sage: S = SBox(1, 2, 3)
Traceback (most recent call last):
...
TypeError: Lookup table length is not a power of 2.
sage: S = SBox(5, 6, 0, 3, 4, 2, 1, 2)
sage: S.n
3
"""
if "S" in kwargs:
S = kwargs["S"]
elif len(args) == 1:
S = args[0]
elif len(args) > 1:
S = args
else:
raise TypeError("No lookup table provided.")
_S = []
for e in S:
if is_FiniteFieldElement(e):
e = e.polynomial().change_ring(ZZ).subs( e.parent().characteristic() )
_S.append(e)
S = _S
if not ZZ(len(S)).is_power_of(2):
raise TypeError("Lookup table length is not a power of 2.")
self._S = S
self.m = ZZ(len(S)).exact_log(2)
self.n = ZZ(max(S)).nbits()
self._F = GF(2)
self._big_endian = kwargs.get("big_endian",True)
self.differential_uniformity = self.maximal_difference_probability_absolute
def __init__(self, *args, **kwargs):
"""
Construct a substitution box (S-box) for a given lookup table
`S`.
INPUT:
- ``S`` - a finite iterable defining the S-box with integer or
finite field elements
- ``big_endian`` - controls whether bits shall be ordered in
big endian order (default: ``True``)
EXAMPLE:
We construct a 3-bit S-box where e.g. the bits (0,0,1) are
mapped to (1,1,1).::
sage: S = mq.SBox(7,6,0,4,2,5,1,3); S
(7, 6, 0, 4, 2, 5, 1, 3)
sage: S(0)
7
TESTS::
sage: S = mq.SBox()
Traceback (most recent call last):
...
TypeError: No lookup table provided.
sage: S = mq.SBox(1, 2, 3)
Traceback (most recent call last):
...
TypeError: Lookup table length is not a power of 2.
sage: S = mq.SBox(5, 6, 0, 3, 4, 2, 1, 2)
sage: S.n
3
"""
if "S" in kwargs:
S = kwargs["S"]
elif len(args) == 1:
S = args[0]
elif len(args) > 1:
S = args
else:
raise TypeError("No lookup table provided.")
_S = []
for e in S:
if is_FiniteFieldElement(e):
e = e.polynomial().change_ring(ZZ).subs( e.parent().characteristic() )
_S.append(e)
S = _S
if not ZZ(len(S)).is_power_of(2):
raise TypeError("Lookup table length is not a power of 2.")
self._S = S
self.m = ZZ(len(S)).exact_log(2)
self.n = ZZ(max(S)).nbits()
self._F = GF(2)
self._big_endian = kwargs.get("big_endian",True)
self.differential_uniformity = self.maximal_difference_probability_absolute