def test_state():
poly = galois.Poly.Degrees([7,1,0])
lfsr = galois.LFSR(poly, state=1, config="galois")
assert np.array_equal(lfsr.state, [0, 0, 0, 0, 0, 0, 1])
lfsr = galois.LFSR(poly, state=4, config="galois")
assert np.array_equal(lfsr.state, [0, 0, 0, 0, 1, 0, 0])
def test_exceptions():
poly = galois.Poly.Degrees([7,1,0])
with pytest.raises(TypeError):
galois.LFSR(poly.coeffs)
with pytest.raises(TypeError):
galois.LFSR(poly, state=float(poly.integer))
with pytest.raises(TypeError):
galois.LFSR(poly.coeffs, config=1)
with pytest.raises(ValueError):
galois.LFSR(poly, config="invalid-argument")
def test_output_is_reversed_state():
poly = galois.Poly.Degrees([7, 1, 0])
state = galois.GF2.Zeros(7)
state[-1] = 1
lfsr = galois.LFSR(poly, state=state)
y = lfsr.step(7)
assert np.array_equal(y, state[::-1])
def test_gf3_output():
"""
Sage:
F = GF(3)
key = [F(2),F(0),F(0),F(2)]
fill = [F(1),F(0),F(0),F(0)]
n = 200
s = lfsr_sequence(key,fill,n); np.array(s)
"""
GF = galois.GF(3)
poly = galois.Poly([2, 0, 0, 2, 1],
field=GF) # galois.conway_poly(3, 4) / GF(2)
state = GF([0, 0, 0, 1])
y_truth = GF([
1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2,
0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0,
2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2,
1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2,
1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0,
0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1,
0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0,
0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 2,
2, 0, 0, 1, 0, 0, 0, 2
])
lfsr = galois.LFSR(poly, state=state)
y = lfsr.step(y_truth.size)
assert np.array_equal(y, y_truth)
def test_step_exceptions():
poly = galois.Poly.Degrees([7,1,0])
lfsr = galois.LFSR(poly, config="galois")
with pytest.raises(TypeError):
lfsr.step(10.0)
with pytest.raises(ValueError):
lfsr.step(0)
with pytest.raises(ValueError):
lfsr.step(-1)
def test_gf2_output_2():
"""
The states of the Galois LFSR generate the binary extension field with the connection polynomial as its
irreducible polynomial.
"""
GF = galois.GF2
poly = galois.conway_poly(2, 8)
state = GF([0,0,0,0,0,0,0,1])
lfsr = galois.LFSR(poly, state=state, config="galois")
GFE = galois.GF(2**8, irreducible_poly=poly)
alpha = GFE.primitive_element
for i in range(GFE.order - 1):
np.array_equal(lfsr.state, (alpha**i).vector())
lfsr.step()
def test_gf2_output_2():
"""
Sage:
F = GF(2)
o = F(0); l = F(1)
key = [l,l,o,l]
fill = [l,l,o,l]
n = 20
s = lfsr_sequence(key,fill,n); s
"""
GF = galois.GF2
poly = galois.Poly([1, 1, 0, 1, 1], field=GF)
state = GF([1, 0, 1, 1])
y_truth = GF([1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1])
lfsr = galois.LFSR(poly, state=state)
y = lfsr.step(y_truth.size)
assert np.array_equal(y, y_truth)
def test_gfp_large_output():
"""
Sage:
F = GF(36893488147419103183)
key = [F(3),F(0),F(3),F(1)]
fill = [F(1),F(0),F(0),F(0)]
n = 20
s = lfsr_sequence(key,fill,n); np.array(s)
"""
GF = galois.GF(36893488147419103183)
poly = galois.Poly([3, 0, 3, 1, 1],
field=GF) # Not a primitive polynomial...
state = GF([0, 0, 0, 1])
y_truth = GF([
1, 0, 0, 0, 3, 3, 12, 21, 66, 138, 372, 849, 2163, 5124, 12729, 30648,
75324, 182640, 446799, 1086663, 2653032, 6460941, 15760434, 38403246,
93643644, 228236205, 556448439, 1356366792, 3306643041, 8060452032,
19649726472, 47900182944, 116769291483, 284651196411, 693908250276,
1691562388341, 4123595013618, 10052235767874, 24504745559556,
59736140028201
])
lfsr = galois.LFSR(poly, state=state)
y = lfsr.step(y_truth.size)
assert np.array_equal(y, y_truth)
def test_repr():
poly = galois.Poly.Degrees([7,1,0])
lfsr = galois.LFSR(poly, config="galois")
assert repr(lfsr) == "<Galois LFSR: poly=Poly(x^7 + x + 1, GF(2))>"
def test_repr():
poly = galois.Poly.Degrees([7, 1, 0])
lfsr = galois.LFSR(poly)
assert repr(lfsr) == "<Fibonacci LFSR: poly=Poly(x^7 + x + 1, GF(2))>"
