def test_field_caching(self):
f2_cached = pfield.GF(2)
self.assertEqual(self.f2(1), f2_cached(1))
self.assertEqual(self.f2(1) * f2_cached(1), 1)
f19_cached = pfield.GF(19)
self.assertEqual(self.f19(3), f19_cached(3))
self.assertEqual(self.f19(3) * f19_cached(3), 9)
f101_cached = pfield.GF(101)
self.assertEqual(self.f101(3), f101_cached(3))
self.assertEqual(self.f101(3) * f101_cached(23), 69)
def SecFld(p=None, l=None):
"""Secure prime field of l-bit order p."""
if p is None:
if l is None:
l = 1
p = pfield.find_prime_root(l, blum=False)[0]
else:
l = p.bit_length()
assert p > len(Share.runtime.parties
), 'Prime field order must exceed number of parties.'
# p >= number of parties for MDS
field = pfield.GF(p)
field.is_signed = False
if (l, p) not in _sectypes:
class SecureFld(Share):
__slots__ = ()
def __init__(self, value=None):
super().__init__(field, value)
SecureFld.field = field
SecureFld.bit_length = l
name = 'SecFld' + str(SecureFld.bit_length) + '(' + str(
SecureFld.field.modulus) + ')'
_sectypes[(l, p)] = type(name, (SecureFld, ), {'__slots__': ()})
return _sectypes[(l, p)]
def _pfield(l, f, p, n):
k = runtime.options.sec_param
if p is None:
p = pfield.find_prime_root(l + max(f, k + 1) + 1, n=n)
else:
assert p.bit_length() > l + max(f, k + 1), f'Prime {p} too small.'
return pfield.GF(p, f)
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 _SecNum(l, f, n=2):
k = Share.runtime.options.security_parameter
field = pfield.GF(pfield.find_prime_root(l + max(f, k + 1) + 1, n=n), f)
class SecureNum(Share):
__slots__ = ()
def __init__(self, value=None):
super().__init__(field, value)
SecureNum.field = field
SecureNum.bit_length = l
return SecureNum
def _SecNum(l, f, p, n):
k = runtime.options.security_parameter
if p is None:
p = pfield.find_prime_root(l + max(f, k + 1) + 1, n=n)
else:
assert p.bit_length() > l + max(f, k + 1), f'Prime {p} too small.'
field = pfield.GF(p, f)
class SecureNum(Share):
__slots__ = ()
def __init__(self, value=None):
super().__init__(field, value)
SecureNum.field = field
SecureNum.bit_length = l
return SecureNum
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 = pfield.GF(2)
self.f19 = pfield.GF(19) # 19 % 4 = 3
self.f101 = pfield.GF(101) # 101 % 4 = 1
self.f19.is_signed = False
self.f101.is_signed = False
def setUp(self):
self.f2 = pfield.GF(2)
self.f19 = pfield.GF(19) # 19 % 4 = 3
self.f101 = pfield.GF(101) # 101 % 4 = 1