def __init__(self, parent, key):
"""
Create a substitution cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = SubstitutionCryptosystem(S)
sage: E
Substitution cryptosystem on Free alphabetic string monoid on A-Z
sage: K = S([ 25-i for i in range(26) ])
sage: K
ZYXWVUTSRQPONMLKJIHGFEDCBA
sage: e = E(K)
sage: m = S("THECATINTHEHAT")
sage: e(m)
GSVXZGRMGSVSZG
TESTS::
sage: S = AlphabeticStrings()
sage: E = SubstitutionCryptosystem(S)
sage: E == loads(dumps(E))
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, e1, e2):
"""
Create a shrinking generator cipher.
INPUT:
- ``parent`` - parent
- ``poly`` - connection polynomial
- ``IS`` - initial state
EXAMPLES::
sage: FF = FiniteField(2)
sage: P.<x> = PolynomialRing(FF)
sage: LFSR = LFSRCryptosystem(FF)
sage: IS_1 = [ FF(a) for a in [0,1,0,1,0,0,0] ]
sage: e1 = LFSR((x^7 + x + 1,IS_1))
sage: IS_2 = [ FF(a) for a in [0,0,1,0,0,0,1,0,1] ]
sage: e2 = LFSR((x^9 + x^3 + 1,IS_2))
sage: E = ShrinkingGeneratorCryptosystem()
sage: e = E((e1,e2))
sage: e
Shrinking generator cipher on Free binary string monoid
"""
if not isinstance(e1, LFSRCipher):
raise TypeError("Argument e1 (= %s) must be a LFSR cipher." % e1)
if not isinstance(e2, LFSRCipher):
raise TypeError("Argument e2 (= %s) must be a LFSR cipher." % e2)
SymmetricKeyCipher.__init__(self, parent, key = (e1, e2))
def __init__(self, parent, key):
r"""
Create a shift cipher.
INPUT:
- ``parent`` -- a ``ShiftCryptosystem`` object.
- ``key`` -- a secret key.
EXAMPLES::
sage: S = ShiftCryptosystem(AlphabeticStrings()); S
Shift cryptosystem on Free alphabetic string monoid on A-Z
sage: P = S.encoding("The shift cryptosystem generalizes the Caesar cipher.")
sage: P
THESHIFTCRYPTOSYSTEMGENERALIZESTHECAESARCIPHER
sage: K = 7
sage: C = S.enciphering(K, P); C
AOLZOPMAJYFWAVZFZALTNLULYHSPGLZAOLJHLZHYJPWOLY
sage: S.deciphering(K, C)
THESHIFTCRYPTOSYSTEMGENERALIZESTHECAESARCIPHER
sage: S.deciphering(K, C) == P
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
"""
Create a substitution cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = SubstitutionCryptosystem(S)
sage: E
Substitution cryptosystem on Free alphabetic string monoid on A-Z
sage: K = S([ 25-i for i in range(26) ])
sage: K
ZYXWVUTSRQPONMLKJIHGFEDCBA
sage: e = E(K)
sage: m = S("THECATINTHEHAT")
sage: e(m)
GSVXZGRMGSVSZG
TESTS::
sage: S = AlphabeticStrings()
sage: E = SubstitutionCryptosystem(S)
sage: E == loads(dumps(E))
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
"""
Create a Hill cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = HillCryptosystem(S,3)
sage: E
Hill cryptosystem on Free alphabetic string monoid on A-Z of block length 3
sage: M = E.key_space()
sage: A = M([[1,0,1],[0,1,1],[2,2,3]])
sage: A
[1 0 1]
[0 1 1]
[2 2 3]
sage: e = E(A); e
Hill cipher on Free alphabetic string monoid on A-Z of block length 3
sage: e(S("LAMAISONBLANCHE"))
JYVKSKQPELAYKPV
TESTS::
sage: S = AlphabeticStrings()
sage: E = HillCryptosystem(S,3)
sage: E == loads(dumps(E))
True
"""
# TODO: some type checking that the key is an invertible matrix?
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
r"""
Create a shift cipher.
INPUT:
- ``parent`` -- a ``ShiftCryptosystem`` object.
- ``key`` -- a secret key.
EXAMPLES::
sage: S = ShiftCryptosystem(AlphabeticStrings()); S
Shift cryptosystem on Free alphabetic string monoid on A-Z
sage: P = S.encoding("The shift cryptosystem generalizes the Caesar cipher.")
sage: P
THESHIFTCRYPTOSYSTEMGENERALIZESTHECAESARCIPHER
sage: K = 7
sage: C = S.enciphering(K, P); C
AOLZOPMAJYFWAVZFZALTNLULYHSPGLZAOLJHLZHYJPWOLY
sage: S.deciphering(K, C)
THESHIFTCRYPTOSYSTEMGENERALIZESTHECAESARCIPHER
sage: S.deciphering(K, C) == P
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
"""
Create a Hill cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = HillCryptosystem(S,3)
sage: E
Hill cryptosystem on Free alphabetic string monoid on A-Z of block length 3
sage: M = E.key_space()
sage: A = M([[1,0,1],[0,1,1],[2,2,3]])
sage: A
[1 0 1]
[0 1 1]
[2 2 3]
sage: e = E(A); e
Hill cipher on Free alphabetic string monoid on A-Z of block length 3
sage: e(S("LAMAISONBLANCHE"))
JYVKSKQPELAYKPV
TESTS::
sage: S = AlphabeticStrings()
sage: E = HillCryptosystem(S,3)
sage: E == loads(dumps(E))
True
"""
# TODO: some type checking that the key is an invertible matrix?
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, poly, IS):
"""
Create a linear feedback shift register (LFSR) cipher.
INPUT:
- ``parent`` - parent
- ``poly`` - connection polynomial
- ``IS`` - initial state
EXAMPLES::
sage: FF = FiniteField(2)
sage: P.<x> = PolynomialRing(FF)
sage: E = LFSRCryptosystem(FF)
sage: E
LFSR cryptosystem over Finite Field of size 2
sage: IS = [ FF(a) for a in [0,1,1,1,0,1,1] ]
sage: g = x^7 + x + 1
sage: e = E((g,IS))
sage: B = BinaryStrings()
sage: m = B.encoding("THECATINTHEHAT")
sage: e(m)
0010001101111010111010101010001100000000110100010101011100001011110010010000011111100100100011001101101000001111
sage: FF = FiniteField(2)
sage: P.<x> = PolynomialRing(FF)
sage: LFSR = LFSRCryptosystem(FF)
sage: e = LFSR((x^2+x+1,[FF(0),FF(1)]))
sage: B = e.domain()
sage: m = B.encoding("The cat in the hat.")
sage: e(m)
00111001110111101011111001001101110101011011101000011001100101101011001000000011100101101010111100000101110100111111101100000101110101111010111101000011
sage: m == e(e(m))
True
TESTS::
sage: FF = FiniteField(2)
sage: P.<x> = PolynomialRing(FF)
sage: E = LFSRCryptosystem(FF)
sage: E == loads(dumps(E))
True
"""
SymmetricKeyCipher.__init__(self, parent, key = (poly, IS))
def __init__(self, parent, key):
"""
Create a transposition cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = TranspositionCryptosystem(S,14)
sage: E
Transposition cryptosystem on Free alphabetic string monoid on A-Z of block length 14
sage: K = [ 14-i for i in range(14) ]
sage: K
[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
sage: e = E(K)
sage: m = S("THECATINTHEHAT")
sage: e(m)
TAHEHTNITACEHT
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = TranspositionCryptosystem(S,15);
sage: m = S("THECATANDTHEHAT")
sage: G = E.key_space()
sage: G
Symmetric group of order 15! as a permutation group
sage: g = G([ 3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13 ])
sage: e = E(g)
sage: e(m)
EHTTACDNAEHTTAH
TESTS::
sage: S = AlphabeticStrings()
sage: E = TranspositionCryptosystem(S,14)
sage: E == loads(dumps(E))
True
"""
n = parent.block_length()
if isinstance(key, list) and not len(key) == n:
raise ValueError, "key (= %s) must have block length %s" % (key, n)
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
"""
Create a transposition cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = TranspositionCryptosystem(S,14)
sage: E
Transposition cryptosystem on Free alphabetic string monoid on A-Z of block length 14
sage: K = [ 14-i for i in range(14) ]
sage: K
[14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
sage: e = E(K)
sage: m = S("THECATINTHEHAT")
sage: e(m)
TAHEHTNITACEHT
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = TranspositionCryptosystem(S,15);
sage: m = S("THECATANDTHEHAT")
sage: G = E.key_space()
sage: G
Symmetric group of order 15! as a permutation group
sage: g = G([ 3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13 ])
sage: e = E(g)
sage: e(m)
EHTTACDNAEHTTAH
TESTS::
sage: S = AlphabeticStrings()
sage: E = TranspositionCryptosystem(S,14)
sage: E == loads(dumps(E))
True
"""
n = parent.block_length()
if isinstance(key, list) and not len(key) == n:
raise ValueError, "key (= %s) must have block length %s" % (key, n)
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
r"""
Create an affine cipher.
INPUT:
- ``parent`` -- an ``AffineCryptosystem`` object.
- ``key`` -- a secret key. Let `N` be the size of the cipher domain.
A key of this affine cipher is an ordered pair
`(a, b) \in \ZZ_N \times \ZZ_N` such that `\gcd(a, N) = 1`.
EXAMPLES:
Testing of dumping and loading object::
sage: A = AffineCryptosystem(AlphabeticStrings())
sage: AC = A(3, 5)
sage: AC == loads(dumps(AC))
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
r"""
Create an affine cipher.
INPUT:
- ``parent`` -- an ``AffineCryptosystem`` object.
- ``key`` -- a secret key. Let `N` be the size of the cipher domain.
A key of this affine cipher is an ordered pair
`(a, b) \in \ZZ_N \times \ZZ_N` such that `\gcd(a, N) = 1`.
EXAMPLES:
Testing of dumping and loading object::
sage: A = AffineCryptosystem(AlphabeticStrings())
sage: AC = A(3, 5)
sage: AC == loads(dumps(AC))
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
"""
Create a Vigenere cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = VigenereCryptosystem(S,11)
sage: K = S("SHAKESPEARE")
sage: e = E(K)
sage: m = S("THECATINTHEHAT")
sage: e(m)
LOEMELXRTYIZHT
TESTS::
sage: S = AlphabeticStrings()
sage: E = VigenereCryptosystem(S,11)
sage: E == loads(dumps(E))
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
def __init__(self, parent, key):
"""
Create a Vigenere cipher.
INPUT: Parent and key
EXAMPLES::
sage: S = AlphabeticStrings()
sage: E = VigenereCryptosystem(S,11)
sage: K = S("SHAKESPEARE")
sage: e = E(K)
sage: m = S("THECATINTHEHAT")
sage: e(m)
LOEMELXRTYIZHT
TESTS::
sage: S = AlphabeticStrings()
sage: E = VigenereCryptosystem(S,11)
sage: E == loads(dumps(E))
True
"""
SymmetricKeyCipher.__init__(self, parent, key)
