Generate key stream from the binary string M.
INPUT:
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
Create a linear feedback shift register (LFSR) cipher.
INPUT:
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
The connection polynomial defining the LFSR of the cipher.
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: e.connection_polynomial()
x^2 + x + 1
The initial state of the LFSR cipher.
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: e.initial_state()
[0, 1]
INPUT:
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'
Create a shrinking generator cipher.
INPUT:
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
((x^7 + x + 1, [0, 1, 0, 1, 0, 0, 0]), (x^9 + x^3 + 1, [0, 0, 1, 0, 0, 0, 1, 0, 1]))
The LFSR cipher generating the decimating key stream.
EXAMPLE:
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.decimating_cipher()
(x^9 + x^3 + 1, [0, 0, 1, 0, 0, 0, 1, 0, 1])
The LFSR cipher generating the output key stream.
EXAMPLE:
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.keystream_cipher()
(x^7 + x + 1, [0, 1, 0, 1, 0, 0, 0])