def test_square(self):
f1 = self.e.field
f2 = GF2QuotientRing(0x211)
for f in [f1,f2]:
for k in xrange(3,250,7):
assert f.mulraw(k,k) == f.squareraw(k)
e = f.wrap(k)
assert e*e == f.square(e)
def test2(self):
for p, initstate in [(615, 0x92), (456, 0x37), (59857573, 0x123),
(0x10000000000b7, 23)]:
field = GF2QuotientRing(p)
e = field.wrap(initstate)
bits = [(e << k).coeffs >> (field.degree - 1)
for k in xrange(2 * field.degree)]
p, n = berlekamp_massey(bits)
assert p == field.coeffs
def decimate(field,j):
e = field.wrap(1)
u = e
n = field.degree
m = e << j
bits = []
for k in range(2*n):
bits.append(u.coeffs >> (n-1))
u *= m
return GF2QuotientRing(berlekamp_massey(bits)[0])
def test_inv(self):
e = self.e
e23 = GF2Element(23, self.FIELD)
e23inv = e23.inv
assert e23inv.coeffs == 0xa5
assert e23inv*e23 == e
with pytest.raises(ValueError):
GF2Element(0, self.FIELD).inv
for k in xrange(1,1<<self.FIELD.degree):
ek = GF2Element(k, self.FIELD)
assert (ek.inv)*ek == e
F8b = GF2QuotientRing(0x180)
with pytest.raises(ValueError):
GF2Element(2, F8b).inv
class Test_TracePattern(object):
FIELD = GF2QuotientRing(0x187)
def setup(self):
self.e = GF2Element(1, self.FIELD)
def test_0(self):
for w in xrange(1,60):
tr1 = GF2TracePattern.from_pattern(self.FIELD, w)
tr2 = GF2TracePattern.from_mask(self.FIELD, tr1.mask)
assert tr1.pattern == w
assert tr2 == tr1
def test_1(self):
w,winv,tr0 = self.FIELD.trace_constants
tr1 = GF2TracePattern.from_mask(self.FIELD, 1 << (self.FIELD.degree - 1))
assert tr1.pattern == w
u = 1
# now make that tr1 acts like an LFSR output
for k in xrange(100):
u = self.FIELD.lshiftraw1(u)
assert tr1(u) == (u >> (self.FIELD.degree - 1))
def test_2(self):
tr2 = GF2TracePattern.from_pattern(self.FIELD, 1)
assert tr2 == self.FIELD.trace
def test_3(self):
for w in [1,2,3,4,7,81,self.FIELD.coeffs >> 1]:
tr = GF2TracePattern.from_pattern(self.FIELD, w)
for u in xrange(100):
assert tr(u) == self.FIELD.mul(w,u).trace
def test_delay(self):
tr0 = GF2TracePattern.from_mask(self.FIELD, 0x80)
bits0 = []
tr1 = tr0.delay(4)
bits1 = []
tr2 = tr0.delay(9)
bits2 = []
u = 1
for k in xrange(100):
bits0.append(tr0(u))
bits1.append(tr1(u))
bits2.append(tr2(u))
u = self.FIELD.lshiftraw1(u)
assert bits0[:-4] == bits1[4:]
assert bits0[:-9] == bits2[9:]
def test_mul(self):
tr0 = GF2TracePattern.from_mask(self.FIELD, 0x80)
assert (tr0 * 32) == tr0.delay(-5)
def test_polyval2(self):
def plain_polyval(u,g,qr):
y = 0
uk = 1
while g > 0:
if g & 1:
y ^= uk
g >>= 1
uk = qr.mulraw(uk,u)
return y
r = random.Random()
r.seed(123)
qr = GF2QuotientRing((1<<48) + 0xb7)
p = (1<<48)-1
assert checkPeriod(qr,p)==p
for i in xrange(100):
u = r.getrandbits(48)
g = r.getrandbits(48)
assert qr.polyvalraw(u,g) == plain_polyval(u,g,qr)
e123 = qr.wrap(123)
assert e123.polyval(0b100101) == e123**5 + e123**2 + 1
def prof(request):
return PolyRingOverField(GF2QuotientRing(0x211))
def __init__(self, field):
self.field = GF2QuotientRing.cast(field);
class Test_Element(object):
FIELD = GF2QuotientRing(0x187)
def setup(self):
self.e = GF2Element(1, self.FIELD)
def test_toolarge(self):
with pytest.raises(ValueError):
GF2Element(0x100, self.FIELD)
with pytest.raises(ValueError):
e1 = GF2Element(0x1, self.FIELD)
e1 * 0x100
with pytest.raises(ValueError):
e1 = GF2Element(0x1, self.FIELD)
e1 + 0x1111
def test_lshift(self):
e = self.e
assert e.coeffs == 1
assert e.field == self.FIELD
assert (e << 1).coeffs == 2
assert (e << 2).coeffs == 4
assert (e << 40).coeffs == 0x62
assert (e << 255).coeffs == 1
assert (e << 254).coeffs == 0xc3
assert (e << 253).coeffs == 0xa2
assert (e << -1).coeffs == 0xc3
assert (e << -2).coeffs == 0xa2
assert (e << -215).coeffs == 0x62
def test_rshift(self):
e = self.e
assert (e >> 1).coeffs == 0xc3
assert (e >> 2).coeffs == 0xa2
assert (e >> 215).coeffs == 0x62
assert (e >> 253).coeffs == 4
assert (e >> 254).coeffs == 2
assert (e >> 255).coeffs == 1
assert (e >> -1).coeffs == 2
assert (e >> -2).coeffs == 4
assert (e >> -40).coeffs == 0x62
def test_mul(self):
e = self.e
e2 = GF2Element(2, self.FIELD)
e3 = GF2Element(3, self.FIELD)
assert (e2*e3).coeffs == 6
assert (e2*3).coeffs == 6
assert (2*e3).coeffs == 6
def test_add(self):
e = self.e
e2 = GF2Element(2, self.FIELD)
e3 = GF2Element(3, self.FIELD)
assert (e2+e3).coeffs == 1
assert (e2+3).coeffs == 1
assert (2+e3).coeffs == 1
def test_pow(self):
e3 = GF2Element(3, self.FIELD)
assert (e3 ** 2).coeffs == 0x5
assert (e3 ** 4).coeffs == 0x11
assert (e3 ** 5).coeffs == 0x33
assert (e3 ** 100).coeffs == 0xa7
def test_pow2(self):
f2 = GF2QuotientRing(0x211)
e = f2.wrap(73)
ey = e
for k in xrange(1,200):
assert (e ** k) == ey
ey *= e
def test_powvect(self):
e = self.e
assert self.FIELD.powvect(e,[2,4,5,100]) == [e**2, e**4, e**5, e**100]
def test_square(self):
f1 = self.e.field
f2 = GF2QuotientRing(0x211)
for f in [f1,f2]:
for k in xrange(3,250,7):
assert f.mulraw(k,k) == f.squareraw(k)
e = f.wrap(k)
assert e*e == f.square(e)
def test_inv(self):
e = self.e
e23 = GF2Element(23, self.FIELD)
e23inv = e23.inv
assert e23inv.coeffs == 0xa5
assert e23inv*e23 == e
with pytest.raises(ValueError):
GF2Element(0, self.FIELD).inv
for k in xrange(1,1<<self.FIELD.degree):
ek = GF2Element(k, self.FIELD)
assert (ek.inv)*ek == e
F8b = GF2QuotientRing(0x180)
with pytest.raises(ValueError):
GF2Element(2, F8b).inv
def test_div(self):
e2 = GF2Element(2, self.FIELD)
e3 = GF2Element(3, self.FIELD)
eq = e2/e3
assert (eq).coeffs == 0x83
assert e2 == e3*eq
assert e2/3 == eq
assert 2/e3 == eq
def test_log(self):
e=self.e
for k in xrange(1,100):
u = e << k
assert u.log == k
with pytest.raises(ValueError):
self.FIELD.wrap(0).log
def test_mulx(self):
x = 2
y = 1
for k in xrange(1,100):
y2 = _gf2mulxmod(y,self.FIELD.coeffs)
y = self.FIELD.mulraw(x,y)
assert y == y2
def test_mulxinv(self):
x = 2
xinv = self.FIELD.invraw(x)
y = 1
for k in xrange(1,100):
y2 = _gf2mulxinvmod(y,self.FIELD.coeffs)
y = self.FIELD.mulraw(xinv,y)
assert y == y2
def test_trace(self):
w, winv, trace = self.FIELD.trace_constants
assert w == 0x6
assert winv == 0x41
u = self.FIELD.wrap(1)
u2 = u
assert u.trace == self.FIELD.degree & 1
for k in xrange(100):
u <<= 1
u2 <<= 2
assert u.trace == (winv*u).coeffs >> (self.FIELD.degree - 1)
assert u.trace == u2.trace
def test_polyval(self):
e23 = GF2Element(23, self.FIELD)
assert (e23**3 + e23**2 + 1) == self.FIELD.polyval(e23, 0b1101)
assert (e23**9 + e23**4 + e23**3) == self.FIELD.polyval(e23, 0b1000011000)
assert e23.polyval(0b11101) == e23**4 + e23**3 + e23**2 + 1
def test_polyval2(self):
def plain_polyval(u,g,qr):
y = 0
uk = 1
while g > 0:
if g & 1:
y ^= uk
g >>= 1
uk = qr.mulraw(uk,u)
return y
r = random.Random()
r.seed(123)
qr = GF2QuotientRing((1<<48) + 0xb7)
p = (1<<48)-1
assert checkPeriod(qr,p)==p
for i in xrange(100):
u = r.getrandbits(48)
g = r.getrandbits(48)
assert qr.polyvalraw(u,g) == plain_polyval(u,g,qr)
e123 = qr.wrap(123)
assert e123.polyval(0b100101) == e123**5 + e123**2 + 1
def setup(self):
self.field = GF2QuotientRing(0x187)