def _SecFld(field):
l = (field.order - 1).bit_length()
name = f'SecFld{l}({field.__name__})'
secfld = type(name, (SecureFiniteField, ), {'__slots__': ()})
secfld.__doc__ = 'Class of secret-shared finite field elements.'
t = runtime.threshold
m = len(runtime.parties)
q = field.order
if t == 0 or m < q: # TODO: cover case m=q using MDS codes
secfld.subfield = None
secfld.field = field
else:
secfld.subfield = field
assert field.ext_deg == 1 # TODO: cover case ext_deg > 1
e = math.ceil(math.log(m + 1, q)) # ensure q**e > m with e>=2
modulus = finfields.find_irreducible(field.characteristic, e)
secfld.field = finfields.GF(modulus)
@classmethod
def out_conv(cls, a): # field -> subfield
assert a.value.degree() <= 0
return cls.subfield(int(a))
secfld._output_conversion = out_conv
secfld.bit_length = l
globals(
)[name] = secfld # TODO: check name dynamic SecureFiniteField type sufficiently unique
return secfld
def SecFld(order=None,
modulus=None,
char=None,
ext_deg=None,
min_order=None,
signed=False):
"""Secure finite field of order q = p**d.
Order q >= min_order.
Field is prime (d = 1) by default and if modulus is prime.
Extension degree d > 1 if order is a prime power p**d with d > 1,
if modulus is a polynomial or a string or an integer > char,
or if ext_deg is an integer > 1, or if min_order > char.
"""
# TODO: raise errors instead of assert statements
if order is not None:
p, d = gmpy2.factor_prime_power(order)
char = char or p
assert char == p
ext_deg = ext_deg or d
assert ext_deg == d
# order now represented by (char, ext_deg)
if isinstance(modulus, str):
char = char or 2
modulus = gfpx.GFpX(char)(modulus)
if isinstance(modulus, int):
if char and modulus > char:
modulus = gfpx.GFpX(char)(modulus)
if isinstance(modulus, gfpx.Polynomial):
char = char or modulus.p
assert char == modulus.p
ext_deg = ext_deg or modulus.degree()
elif isinstance(modulus, int):
char = char or modulus
assert char == modulus
ext_deg = ext_deg or 1
assert ext_deg == 1
else:
assert modulus is None
if min_order is None:
char = char or 2
ext_deg = ext_deg or 1
min_order = char**ext_deg
else:
if char is None:
ext_deg = ext_deg or 1
root, exact = gmpy2.iroot(min_order, ext_deg)
min_char = root + (not exact
) # ceiling of min_order^(1/ext_deg)
char = int(gmpy2.next_prime(min_char - 1))
else:
if ext_deg is None:
ext_deg = math.ceil(math.log(min_order, char))
if ext_deg == 1:
modulus = char
else:
modulus = finfields.find_irreducible(char, ext_deg)
order = order or char**ext_deg
min_order = min_order or order
assert min_order <= order
field = finfields.GF(modulus)
assert runtime.threshold == 0 or field.order > len(runtime.parties), \
'Field order must exceed number of parties, unless threshold is 0.'
# TODO: field.order >= number of parties for MDS
field.is_signed = signed
return _SecFld(field)