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"""Common features for bignum in test generation framework."""
# Copyright The Mbed TLS Contributors
# SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later
#
from abc import abstractmethod
import enum
from typing import Iterator, List, Tuple, TypeVar, Any
from copy import deepcopy
from itertools import chain
from math import ceil
from . import test_case
from . import test_data_generation
from .bignum_data import INPUTS_DEFAULT, MODULI_DEFAULT
T = TypeVar('T') #pylint: disable=invalid-name
def invmod(a: int, n: int) -> int:
"""Return inverse of a to modulo n.
Equivalent to pow(a, -1, n) in Python 3.8+. Implementation is equivalent
to long_invmod() in CPython.
"""
b, c = 1, 0
while n:
q, r = divmod(a, n)
a, b, c, n = n, c, b - q*c, r
# at this point a is the gcd of the original inputs
if a == 1:
return b
raise ValueError("Not invertible")
def invmod_positive(a: int, n: int) -> int:
"""Return a non-negative inverse of a to modulo n."""
inv = invmod(a, n)
return inv if inv >= 0 else inv + n
def hex_to_int(val: str) -> int:
"""Implement the syntax accepted by mbedtls_test_read_mpi().
This is a superset of what is accepted by mbedtls_test_read_mpi_core().
"""
if val in ['', '-']:
return 0
return int(val, 16)
def quote_str(val: str) -> str:
return "\"{}\"".format(val)
def bound_mpi(val: int, bits_in_limb: int) -> int:
"""First number exceeding number of limbs needed for given input value."""
return bound_mpi_limbs(limbs_mpi(val, bits_in_limb), bits_in_limb)
def bound_mpi_limbs(limbs: int, bits_in_limb: int) -> int:
"""First number exceeding maximum of given number of limbs."""
bits = bits_in_limb * limbs
return 1 << bits
def limbs_mpi(val: int, bits_in_limb: int) -> int:
"""Return the number of limbs required to store value."""
bit_length = max(val.bit_length(), 1)
return (bit_length + bits_in_limb - 1) // bits_in_limb
def combination_pairs(values: List[T]) -> List[Tuple[T, T]]:
"""Return all pair combinations from input values."""
return [(x, y) for x in values for y in values]
def bits_to_limbs(bits: int, bits_in_limb: int) -> int:
""" Return the appropriate ammount of limbs needed to store
a number contained in input bits"""
return ceil(bits / bits_in_limb)
def hex_digits_for_limb(limbs: int, bits_in_limb: int) -> int:
""" Return the hex digits need for a number of limbs. """
return 2 * ((limbs * bits_in_limb) // 8)
def hex_digits_max_int(val: str, bits_in_limb: int) -> int:
""" Return the first number exceeding maximum the limb space
required to store the input hex-string value. This method
weights on the input str_len rather than numerical value
and works with zero-padded inputs"""
n = ((1 << (len(val) * 4)) - 1)
l = limbs_mpi(n, bits_in_limb)
return bound_mpi_limbs(l, bits_in_limb)
def zfill_match(reference: str, target: str) -> str:
""" Zero pad target hex-string to match the limb size of
the reference input """
lt = len(target)
lr = len(reference)
target_len = lr if lt < lr else lt
return "{:x}".format(int(target, 16)).zfill(target_len)
class OperationCommon(test_data_generation.BaseTest):
"""Common features for bignum binary operations.
This adds functionality common in binary operation tests.
Attributes:
symbol: Symbol to use for the operation in case description.
input_values: List of values to use as test case inputs. These are
combined to produce pairs of values.
input_cases: List of tuples containing pairs of test case inputs. This
can be used to implement specific pairs of inputs.
unique_combinations_only: Boolean to select if test case combinations
must be unique. If True, only A,B or B,A would be included as a test
case. If False, both A,B and B,A would be included.
input_style: Controls the way how test data is passed to the functions
in the generated test cases. "variable" passes them as they are
defined in the python source. "arch_split" pads the values with
zeroes depending on the architecture/limb size. If this is set,
test cases are generated for all architectures.
arity: the number of operands for the operation. Currently supported
values are 1 and 2.
"""
symbol = ""
input_values = INPUTS_DEFAULT # type: List[str]
input_cases = [] # type: List[Any]
dependencies = [] # type: List[Any]
unique_combinations_only = False
input_styles = ["variable", "fixed", "arch_split"] # type: List[str]
input_style = "variable" # type: str
limb_sizes = [32, 64] # type: List[int]
arities = [1, 2]
arity = 2
suffix = False # for arity = 1, symbol can be prefix (default) or suffix
def __init__(self, val_a: str, val_b: str = "0", bits_in_limb: int = 32) -> None:
self.val_a = val_a
self.val_b = val_b
# Setting the int versions here as opposed to making them @properties
# provides earlier/more robust input validation.
self.int_a = hex_to_int(val_a)
self.int_b = hex_to_int(val_b)
self.dependencies = deepcopy(self.dependencies)
if bits_in_limb not in self.limb_sizes:
raise ValueError("Invalid number of bits in limb!")
if self.input_style == "arch_split":
self.dependencies.append("MBEDTLS_HAVE_INT{:d}".format(bits_in_limb))
self.bits_in_limb = bits_in_limb
@property
def boundary(self) -> int:
if self.arity == 1:
return self.int_a
elif self.arity == 2:
return max(self.int_a, self.int_b)
raise ValueError("Unsupported number of operands!")
@property
def limb_boundary(self) -> int:
return bound_mpi(self.boundary, self.bits_in_limb)
@property
def limbs(self) -> int:
return limbs_mpi(self.boundary, self.bits_in_limb)
@property
def hex_digits(self) -> int:
return hex_digits_for_limb(self.limbs, self.bits_in_limb)
def format_arg(self, val: str) -> str:
if self.input_style not in self.input_styles:
raise ValueError("Unknown input style!")
if self.input_style == "variable":
return val
else:
return val.zfill(self.hex_digits)
def format_result(self, res: int) -> str:
res_str = '{:x}'.format(res)
return quote_str(self.format_arg(res_str))
@property
def arg_a(self) -> str:
return self.format_arg(self.val_a)
@property
def arg_b(self) -> str:
if self.arity == 1:
raise AttributeError("Operation is unary and doesn't have arg_b!")
return self.format_arg(self.val_b)
def arguments(self) -> List[str]:
args = [quote_str(self.arg_a)]
if self.arity == 2:
args.append(quote_str(self.arg_b))
return args + self.result()
def description(self) -> str:
"""Generate a description for the test case.
If not set, case_description uses the form A `symbol` B, where symbol
is used to represent the operation. Descriptions of each value are
generated to provide some context to the test case.
"""
if not self.case_description:
if self.arity == 1:
format_string = "{1:x} {0}" if self.suffix else "{0} {1:x}"
self.case_description = format_string.format(
self.symbol, self.int_a
)
elif self.arity == 2:
self.case_description = "{:x} {} {:x}".format(
self.int_a, self.symbol, self.int_b
)
return super().description()
@property
def is_valid(self) -> bool:
return True
@abstractmethod
def result(self) -> List[str]:
"""Get the result of the operation.
This could be calculated during initialization and stored as `_result`
and then returned, or calculated when the method is called.
"""
raise NotImplementedError
@classmethod
def get_value_pairs(cls) -> Iterator[Tuple[str, str]]:
"""Generator to yield pairs of inputs.
Combinations are first generated from all input values, and then
specific cases provided.
"""
if cls.arity == 1:
yield from ((a, "0") for a in cls.input_values)
elif cls.arity == 2:
if cls.unique_combinations_only:
yield from combination_pairs(cls.input_values)
else:
yield from (
(a, b)
for a in cls.input_values
for b in cls.input_values
)
else:
raise ValueError("Unsupported number of operands!")
@classmethod
def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
if cls.input_style not in cls.input_styles:
raise ValueError("Unknown input style!")
if cls.arity not in cls.arities:
raise ValueError("Unsupported number of operands!")
if cls.input_style == "arch_split":
test_objects = (cls(a, b, bits_in_limb=bil)
for a, b in cls.get_value_pairs()
for bil in cls.limb_sizes)
special_cases = (cls(*args, bits_in_limb=bil) # type: ignore
for args in cls.input_cases
for bil in cls.limb_sizes)
else:
test_objects = (cls(a, b)
for a, b in cls.get_value_pairs())
special_cases = (cls(*args) for args in cls.input_cases)
yield from (valid_test_object.create_test_case()
for valid_test_object in filter(
lambda test_object: test_object.is_valid,
chain(test_objects, special_cases)
)
)
class ModulusRepresentation(enum.Enum):
"""Representation selector of a modulus."""
# Numerical values aligned with the type mbedtls_mpi_mod_rep_selector
INVALID = 0
MONTGOMERY = 2
OPT_RED = 3
def symbol(self) -> str:
"""The C symbol for this representation selector."""
return 'MBEDTLS_MPI_MOD_REP_' + self.name
@classmethod
def supported_representations(cls) -> List['ModulusRepresentation']:
"""Return all representations that are supported in positive test cases."""
return [cls.MONTGOMERY, cls.OPT_RED]
class ModOperationCommon(OperationCommon):
#pylint: disable=abstract-method
"""Target for bignum mod_raw test case generation."""
moduli = MODULI_DEFAULT # type: List[str]
montgomery_form_a = False
disallow_zero_a = False
def __init__(self, val_n: str, val_a: str, val_b: str = "0",
bits_in_limb: int = 64) -> None:
super().__init__(val_a=val_a, val_b=val_b, bits_in_limb=bits_in_limb)
self.val_n = val_n
# Setting the int versions here as opposed to making them @properties
# provides earlier/more robust input validation.
self.int_n = hex_to_int(val_n)
def to_montgomery(self, val: int) -> int:
return (val * self.r) % self.int_n
def from_montgomery(self, val: int) -> int:
return (val * self.r_inv) % self.int_n
def convert_from_canonical(self, canonical: int,
rep: ModulusRepresentation) -> int:
"""Convert values from canonical representation to the given representation."""
if rep is ModulusRepresentation.MONTGOMERY:
return self.to_montgomery(canonical)
elif rep is ModulusRepresentation.OPT_RED:
return canonical
else:
raise ValueError('Modulus representation not supported: {}'
.format(rep.name))
@property
def boundary(self) -> int:
return self.int_n
@property
def arg_a(self) -> str:
if self.montgomery_form_a:
value_a = self.to_montgomery(self.int_a)
else:
value_a = self.int_a
return self.format_arg('{:x}'.format(value_a))
@property
def arg_n(self) -> str:
return self.format_arg(self.val_n)
def format_arg(self, val: str) -> str:
return super().format_arg(val).zfill(self.hex_digits)
def arguments(self) -> List[str]:
return [quote_str(self.arg_n)] + super().arguments()
@property
def r(self) -> int: # pylint: disable=invalid-name
l = limbs_mpi(self.int_n, self.bits_in_limb)
return bound_mpi_limbs(l, self.bits_in_limb)
@property
def r_inv(self) -> int:
return invmod(self.r, self.int_n)
@property
def r2(self) -> int: # pylint: disable=invalid-name
return pow(self.r, 2)
@property
def is_valid(self) -> bool:
if self.int_a >= self.int_n:
return False
if self.disallow_zero_a and self.int_a == 0:
return False
if self.arity == 2 and self.int_b >= self.int_n:
return False
return True
def description(self) -> str:
"""Generate a description for the test case.
It uses the form A `symbol` B mod N, where symbol is used to represent
the operation.
"""
if not self.case_description:
return super().description() + " mod {:x}".format(self.int_n)
return super().description()
@classmethod
def input_cases_args(cls) -> Iterator[Tuple[Any, Any, Any]]:
if cls.arity == 1:
yield from ((n, a, "0") for a, n in cls.input_cases)
elif cls.arity == 2:
yield from ((n, a, b) for a, b, n in cls.input_cases)
else:
raise ValueError("Unsupported number of operands!")
@classmethod
def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
if cls.input_style not in cls.input_styles:
raise ValueError("Unknown input style!")
if cls.arity not in cls.arities:
raise ValueError("Unsupported number of operands!")
if cls.input_style == "arch_split":
test_objects = (cls(n, a, b, bits_in_limb=bil)
for n in cls.moduli
for a, b in cls.get_value_pairs()
for bil in cls.limb_sizes)
special_cases = (cls(*args, bits_in_limb=bil)
for args in cls.input_cases_args()
for bil in cls.limb_sizes)
else:
test_objects = (cls(n, a, b)
for n in cls.moduli
for a, b in cls.get_value_pairs())
special_cases = (cls(*args) for args in cls.input_cases_args())
yield from (valid_test_object.create_test_case()
for valid_test_object in filter(
lambda test_object: test_object.is_valid,
chain(test_objects, special_cases)
))
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