def __call__(self, M, mode = "ECB"):
r"""
INPUT:
- ``M`` - a StringMonoidElement
- ``mode`` - ignored (default: 'ECB')
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: B = BinaryStrings()
sage: m = B.encoding("THECATINTHEHAT")
sage: c = e(m)
sage: c.decoding()
"t\xb6\xc1'\x83\x17\xae\xc9ZO\x84V\x7fX"
sage: e(e(m)) == m
True
sage: m.decoding()
'THECATINTHEHAT'
"""
B = self.domain() # = plaintext_space = ciphertext_space
if not isinstance(M, StringMonoidElement) and M.parent() == B:
raise TypeError("Argument M (= %s) must be a string in the plaintext space." % M)
(e1, e2) = self.key()
MStream = M._element_list
g1 = e1.connection_polynomial()
n1 = g1.degree()
IS_1 = e1.initial_state()
g2 = e2.connection_polynomial()
n2 = g2.degree()
IS_2 = e2.initial_state()
k = 0
N = len(M)
n = max(n1,n2)
CStream = []
while k < N:
r = max(N-k,2*n)
KStream = lfsr_sequence(g1.list(), IS_1, r)
DStream = lfsr_sequence(g2.list(), IS_2, r)
for i in range(r-n):
if DStream[i] != 0:
CStream.append(int(MStream[k]+KStream[i]))
k += 1
if k == N:
break
IS_1 = KStream[r-n-1:r-n+n1]
IS_2 = DStream[r-n-1:r-n+n2]
return B(CStream)
def __call__(self, M, mode = "ECB"):
r"""
Generate key stream from the binary string ``M``.
INPUT:
- ``M`` - a StringMonoidElement
- ``mode`` - ignored (default: 'ECB')
EXAMPLE::
sage: k = GF(2)
sage: P.<x> = PolynomialRing( k )
sage: LFSR = LFSRCryptosystem( k )
sage: e = LFSR((x^2+x+1,[k(0), k(1)]))
sage: B = e.domain()
sage: m = B.encoding('The cat in the hat.')
sage: e(m)
00111001110111101011111001001101110101011011101000011001100101101011001000000011100101101010111100000101110100111111101100000101110101111010111101000011
"""
B = self.domain() # = plaintext_space = ciphertext_space
if not isinstance(M, StringMonoidElement) and M.parent() == B:
raise TypeError("Argument M (= %s) must be a string in the plaintext space." % M)
(poly, IS) = self.key()
n = B.ngens() # two for binary strings
N = len(M)
Melt = M._element_list
Kelt = lfsr_sequence(poly.list(), IS, N)
return B([ (Melt[i]+int(Kelt[i]))%n for i in range(N) ])