def test_field_caching(self):
f2_cached = bfield.GF(2)
self.assertEqual(self.f2(1), f2_cached(1))
self.assertEqual(self.f2(1) * f2_cached(1), self.f2(1))
f256_cached = bfield.GF(283)
self.assertEqual(self.f256(3), f256_cached(3))
self.assertEqual(self.f256(3) * f256_cached(3), self.f256(5))
self.assertEqual(self.f256(48) * f256_cached(16), self.f256(45))
def SecFld(order=None, modulus=None, char2=None, l=None):
"""Secure prime or binary field of (l+1)-bit order.
Field is prime by default, and if order (or modulus) is prime.
Field is binary if order is a power of 2, if modulus is a
polynomial, or if char2 is True.
"""
if isinstance(modulus, str):
modulus = gf2x.Polynomial(modulus)
if isinstance(modulus, gf2x.Polynomial):
char2 = char2 or (char2 is None)
assert char2 # binary field
modulus = int(modulus)
if order is not None:
if order == 2:
assert modulus is None or modulus == 2 or modulus == 3
if modulus is None or modulus == 2:
# default: prime field
char2 = char2 or False
else:
char2 = char2 or (char2 is None)
assert char2 # binary field
elif gmpy.is_prime(order):
modulus = modulus or order
assert modulus == order
char2 = char2 or False
assert not char2 # prime field
elif order % 2 == 0:
assert modulus is None or modulus.bit_length() == order.bit_length(
)
char2 = char2 or (char2 is None)
assert char2 # binary field
else:
raise ValueError('only prime fields and binary fields supported')
l = l or order.bit_length() - 1
assert l == order.bit_length() - 1
if modulus is None:
l = l or 1
if char2:
modulus = int(bfield.find_irreducible(l))
else:
modulus = pfield.find_prime_root(l + 1, blum=False)[0]
l = modulus.bit_length() - 1
if char2:
field = bfield.GF(modulus)
else:
field = pfield.GF(modulus)
assert runtime.threshold == 0 or field.order > len(runtime.parties), \
'Field order must exceed number of parties, unless threshold is 0.'
# field.order >= number of parties for MDS
field.is_signed = False
return _SecFld(l, field)
def test_f256(self):
f256 = self.f256
self.assertFalse(f256(0))
self.assertTrue(f256(1))
self.assertEqual(f256(1) + 0, f256(0) + f256(1))
self.assertEqual(f256(1) + 1, f256(0))
self.assertEqual(f256(3) * 0, f256(0))
self.assertEqual(f256(3) * 1, f256(3))
self.assertEqual(f256(16) * f256(16), f256(27))
self.assertEqual(f256(32) * f256(16), f256(54))
self.assertEqual(f256(57) * f256(67), f256(137))
self.assertEqual(f256(67) * f256(57), f256(137))
self.assertEqual(f256(137) / f256(57), f256(67))
self.assertEqual(f256(137) / f256(67), f256(57))
a = f256(0)
b = f256(1)
a += b
self.assertEqual(a, f256(1))
a += 1
self.assertEqual(a, f256(0))
a -= b
self.assertEqual(a, f256(1))
a *= b
self.assertEqual(a, f256(1))
a *= 1
self.assertEqual(a, f256(1))
a /= 1
self.assertEqual(a, f256(1))
a <<= 0
a >>= 0
self.assertEqual(a, f256(1))
a <<= 2
self.assertEqual(a, f256(4))
a >>= 2
self.assertEqual(a, f256(1))
a = f256(3) # generator x + 1
s = [int((a**i).value) for i in range(255)]
self.assertListEqual(sorted(s), list(range(1, 256)))
s = [int((a**i).value) for i in range(-255, 0)]
self.assertListEqual(sorted(s), list(range(1, 256)))
f256 = bfield.GF(391) # primitive polynomial x^8 + x^7 + x^2 + x + 1
a = f256(2) # generator x
s = [int((a**i).value) for i in range(255)]
self.assertListEqual(sorted(s), list(range(1, 256)))
def SecFld(order=None, modulus=None, char2=None, l=None):
"""Secure prime or binary field of (l+1)-bit order.
Field is prime by default, and if order (or modulus) is prime.
Field is binary if order is a power of 2, if modulus is a
polynomial, or if char2 is True.
"""
if isinstance(modulus, str):
modulus = gf2x.Polynomial(modulus)
if isinstance(modulus, gf2x.Polynomial):
char2 = char2 or (char2 is None)
assert char2 # binary field
modulus = int(modulus)
if order is not None:
if order == 2:
assert modulus is None or modulus == 2 or modulus == 3
if modulus is None or modulus == 2:
# default: prime field
char2 = char2 or False
else:
char2 = char2 or (char2 is None)
assert char2 # binary field
elif gmpy.is_prime(order):
modulus = modulus or order
assert modulus == order
char2 = char2 or False
assert not char2 # prime field
elif order % 2 == 0:
assert modulus is None or modulus.bit_length() == order.bit_length(
)
char2 = char2 or (char2 is None)
assert char2 # binary field
else:
raise ValueError('only prime fields and binary fields supported')
l = l or order.bit_length() - 1
assert l == order.bit_length() - 1
if modulus is None:
l = l or 1
if char2:
modulus = int(bfield.find_irreducible(l))
else:
modulus = pfield.find_prime_root(l + 1, blum=False)[0]
l = modulus.bit_length() - 1
if char2:
field = bfield.GF(modulus)
else:
field = pfield.GF(modulus)
assert runtime.threshold == 0 or field.order > len(runtime.parties), \
'Field order must exceed number of parties, unless threshold is 0.'
# field.order >= number of parties for MDS
field.is_signed = False
if (modulus, char2) not in _sectypes:
class SecureFld(Share):
__slots__ = ()
def __init__(self, value=None):
super().__init__(field, value)
SecureFld.field = field
SecureFld.bit_length = l
name = f'SecFld{SecureFld.bit_length}({SecureFld.field.modulus})'
_sectypes[(modulus, char2)] = type(name, (SecureFld, ),
{'__slots__': ()})
return _sectypes[(modulus, char2)]
def setUp(self):
self.f2 = pfield.GF(2)
self.f19 = pfield.GF(19)
self.f256 = bfield.GF(283)
def setUp(self):
self.f2 = bfield.GF(2)
self.f256 = bfield.GF(283) # AES polynomial (283)_2 = x^8 + x^4 + x^3 + x + 1