mbedtls/scripts/mbedtls_dev/bignum_core.py

"""Framework classes for generation of bignum core test cases."""
# Copyright The Mbed TLS Contributors
# SPDX-License-Identifier: Apache-2.0
#
# Licensed under the Apache License, Version 2.0 (the "License"); you may
# not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import random

from abc import ABCMeta
from typing import Dict, Iterator, List, Tuple

from . import test_case
from . import test_data_generation
from . import bignum_common

class BignumCoreTarget(test_data_generation.BaseTarget, metaclass=ABCMeta):
    #pylint: disable=abstract-method
    """Target for bignum core test case generation."""
    target_basename = 'test_suite_bignum_core.generated'


class BignumCoreShiftR(BignumCoreTarget, metaclass=ABCMeta):
    """Test cases for mbedtls_bignum_core_shift_r()."""
    count = 0
    test_function = "mpi_core_shift_r"
    test_name = "Core shift right"

    DATA = [
        ('00', '0', [0, 1, 8]),
        ('01', '1', [0, 1, 2, 8, 64]),
        ('dee5ca1a7ef10a75', '64-bit',
         list(range(11)) + [31, 32, 33, 63, 64, 65, 71, 72]),
        ('002e7ab0070ad57001', '[leading 0 limb]',
         [0, 1, 8, 63, 64]),
        ('a1055eb0bb1efa1150ff', '80-bit',
         [0, 1, 8, 63, 64, 65, 72, 79, 80, 81, 88, 128, 129, 136]),
        ('020100000000000000001011121314151617', '138-bit',
         [0, 1, 8, 9, 16, 72, 73, 136, 137, 138, 144]),
    ]

    def __init__(self, input_hex: str, descr: str, count: int) -> None:
        self.input_hex = input_hex
        self.number_description = descr
        self.shift_count = count
        self.result = bignum_common.hex_to_int(input_hex) >> count

    def arguments(self) -> List[str]:
        return ['"{}"'.format(self.input_hex),
                str(self.shift_count),
                '"{:0{}x}"'.format(self.result, len(self.input_hex))]

    def description(self) -> str:
        return 'Core shift {} >> {}'.format(self.number_description,
                                            self.shift_count)

    @classmethod
    def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
        for input_hex, descr, counts in cls.DATA:
            for count in counts:
                yield cls(input_hex, descr, count).create_test_case()

class BignumCoreCTLookup(BignumCoreTarget, metaclass=ABCMeta):
    """Test cases for mbedtls_mpi_core_ct_uint_table_lookup()."""
    test_function = "mpi_core_ct_uint_table_lookup"
    test_name = "Constant time MPI table lookup"

    bitsizes = [
        (32, "One limb"),
        (192, "Smallest curve sized"),
        (512, "Largest curve sized"),
        (2048, "Small FF/RSA sized"),
        (4096, "Large FF/RSA sized"),
        ]

    window_sizes = [0, 1, 2, 3, 4, 5, 6]

    def __init__(self,
                 bitsize: int, descr: str, window_size: int) -> None:
        self.bitsize = bitsize
        self.bitsize_description = descr
        self.window_size = window_size

    def arguments(self) -> List[str]:
        return [str(self.bitsize), str(self.window_size)]

    def description(self) -> str:
        return '{} - {} MPI with {} bit window'.format(
            BignumCoreCTLookup.test_name,
            self.bitsize_description,
            self.window_size
            )

    @classmethod
    def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
        for bitsize, bitsize_description in cls.bitsizes:
            for window_size in cls.window_sizes:
                yield (cls(bitsize, bitsize_description, window_size)
                       .create_test_case())

class BignumCoreOperation(bignum_common.OperationCommon, BignumCoreTarget, metaclass=ABCMeta):
    #pylint: disable=abstract-method
    """Common features for bignum core operations."""
    input_values = [
        "0", "1", "3", "f", "fe", "ff", "100", "ff00", "fffe", "ffff", "10000",
        "fffffffe", "ffffffff", "100000000", "1f7f7f7f7f7f7f",
        "8000000000000000", "fefefefefefefefe", "fffffffffffffffe",
        "ffffffffffffffff", "10000000000000000", "1234567890abcdef0",
        "fffffffffffffffffefefefefefefefe", "fffffffffffffffffffffffffffffffe",
        "ffffffffffffffffffffffffffffffff", "100000000000000000000000000000000",
        "1234567890abcdef01234567890abcdef0",
        "fffffffffffffffffffffffffffffffffffffffffffffffffefefefefefefefe",
        "fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe",
        "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
        "10000000000000000000000000000000000000000000000000000000000000000",
        "1234567890abcdef01234567890abcdef01234567890abcdef01234567890abcdef0",
        (
            "4df72d07b4b71c8dacb6cffa954f8d88254b6277099308baf003fab73227f34029"
            "643b5a263f66e0d3c3fa297ef71755efd53b8fb6cb812c6bbf7bcf179298bd9947"
            "c4c8b14324140a2c0f5fad7958a69050a987a6096e9f055fb38edf0c5889eca4a0"
            "cfa99b45fbdeee4c696b328ddceae4723945901ec025076b12b"
        )
    ]

    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:
            self.case_description = "{:x} {} {:x}".format(
                self.int_a, self.symbol, self.int_b
            )
        return super().description()

    @classmethod
    def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
        for a_value, b_value in cls.get_value_pairs():
            yield cls(a_value, b_value).create_test_case()


class BignumCoreOperationArchSplit(BignumCoreOperation):
    #pylint: disable=abstract-method
    """Common features for bignum core operations where the result depends on
    the limb size."""

    def __init__(self, val_a: str, val_b: str, bits_in_limb: int) -> None:
        super().__init__(val_a, val_b)
        bound_val = max(self.int_a, self.int_b)
        self.bits_in_limb = bits_in_limb
        self.bound = bignum_common.bound_mpi(bound_val, self.bits_in_limb)
        limbs = bignum_common.limbs_mpi(bound_val, self.bits_in_limb)
        byte_len = limbs * self.bits_in_limb // 8
        self.hex_digits = 2 * byte_len
        if self.bits_in_limb == 32:
            self.dependencies = ["MBEDTLS_HAVE_INT32"]
        elif self.bits_in_limb == 64:
            self.dependencies = ["MBEDTLS_HAVE_INT64"]
        else:
            raise ValueError("Invalid number of bits in limb!")
        self.arg_a = self.arg_a.zfill(self.hex_digits)
        self.arg_b = self.arg_b.zfill(self.hex_digits)

    def pad_to_limbs(self, val) -> str:
        return "{:x}".format(val).zfill(self.hex_digits)

    @classmethod
    def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
        for a_value, b_value in cls.get_value_pairs():
            yield cls(a_value, b_value, 32).create_test_case()
            yield cls(a_value, b_value, 64).create_test_case()

class BignumCoreAddAndAddIf(BignumCoreOperationArchSplit):
    """Test cases for bignum core add and add-if."""
    count = 0
    symbol = "+"
    test_function = "mpi_core_add_and_add_if"
    test_name = "mpi_core_add_and_add_if"

    def result(self) -> List[str]:
        result = self.int_a + self.int_b

        carry, result = divmod(result, self.bound)

        return [
            bignum_common.quote_str(self.pad_to_limbs(result)),
            str(carry)
        ]

class BignumCoreSub(BignumCoreOperation):
    """Test cases for bignum core sub."""
    count = 0
    symbol = "-"
    test_function = "mpi_core_sub"
    test_name = "mbedtls_mpi_core_sub"
    unique_combinations_only = False

    def result(self) -> List[str]:
        if self.int_a >= self.int_b:
            result_4 = result_8 = self.int_a - self.int_b
            carry = 0
        else:
            bound_val = max(self.int_a, self.int_b)
            bound_4 = bignum_common.bound_mpi(bound_val, 32)
            result_4 = bound_4 + self.int_a - self.int_b
            bound_8 = bignum_common.bound_mpi(bound_val, 64)
            result_8 = bound_8 + self.int_a - self.int_b
            carry = 1
        return [
            "\"{:x}\"".format(result_4),
            "\"{:x}\"".format(result_8),
            str(carry)
        ]


class BignumCoreMLA(BignumCoreOperation):
    """Test cases for fixed-size multiply accumulate."""
    count = 0
    test_function = "mpi_core_mla"
    test_name = "mbedtls_mpi_core_mla"
    unique_combinations_only = False

    input_values = [
        "0", "1", "fffe", "ffffffff", "100000000", "20000000000000",
        "ffffffffffffffff", "10000000000000000", "1234567890abcdef0",
        "fffffffffffffffffefefefefefefefe",
        "100000000000000000000000000000000",
        "1234567890abcdef01234567890abcdef0",
        "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff",
        "1234567890abcdef01234567890abcdef01234567890abcdef01234567890abcdef0",
        (
            "4df72d07b4b71c8dacb6cffa954f8d88254b6277099308baf003fab73227f"
            "34029643b5a263f66e0d3c3fa297ef71755efd53b8fb6cb812c6bbf7bcf17"
            "9298bd9947c4c8b14324140a2c0f5fad7958a69050a987a6096e9f055fb38"
            "edf0c5889eca4a0cfa99b45fbdeee4c696b328ddceae4723945901ec02507"
            "6b12b"
        )
    ] # type: List[str]
    input_scalars = [
        "0", "3", "fe", "ff", "ffff", "10000", "ffffffff", "100000000",
        "7f7f7f7f7f7f7f7f", "8000000000000000", "fffffffffffffffe"
    ] # type: List[str]

    def __init__(self, val_a: str, val_b: str, val_s: str) -> None:
        super().__init__(val_a, val_b)
        self.arg_scalar = val_s
        self.int_scalar = bignum_common.hex_to_int(val_s)
        if bignum_common.limbs_mpi(self.int_scalar, 32) > 1:
            self.dependencies = ["MBEDTLS_HAVE_INT64"]

    def arguments(self) -> List[str]:
        return [
            bignum_common.quote_str(self.arg_a),
            bignum_common.quote_str(self.arg_b),
            bignum_common.quote_str(self.arg_scalar)
        ] + self.result()

    def description(self) -> str:
        """Override and add the additional scalar."""
        if not self.case_description:
            self.case_description = "0x{} + 0x{} * 0x{}".format(
                self.arg_a, self.arg_b, self.arg_scalar
            )
        return super().description()

    def result(self) -> List[str]:
        result = self.int_a + (self.int_b * self.int_scalar)
        bound_val = max(self.int_a, self.int_b)
        bound_4 = bignum_common.bound_mpi(bound_val, 32)
        bound_8 = bignum_common.bound_mpi(bound_val, 64)
        carry_4, remainder_4 = divmod(result, bound_4)
        carry_8, remainder_8 = divmod(result, bound_8)
        return [
            "\"{:x}\"".format(remainder_4),
            "\"{:x}\"".format(carry_4),
            "\"{:x}\"".format(remainder_8),
            "\"{:x}\"".format(carry_8)
        ]

    @classmethod
    def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
        """Override for additional scalar input."""
        for a_value, b_value in cls.get_value_pairs():
            for s_value in cls.input_scalars:
                cur_op = cls(a_value, b_value, s_value)
                yield cur_op.create_test_case()


class BignumCoreMontmul(BignumCoreTarget):
    """Test cases for Montgomery multiplication."""
    count = 0
    test_function = "mpi_core_montmul"
    test_name = "mbedtls_mpi_core_montmul"

    start_2_mpi4 = False
    start_2_mpi8 = False

    replay_test_cases = [
        (2, 1, 1, 1, "19", "1", "1D"), (2, 1, 1, 1, "7", "1", "9"),
        (2, 1, 1, 1, "4", "1", "9"),
        (
            12, 1, 6, 1, (
                "3C246D0E059A93A266288A7718419EC741661B474C58C032C5EDAF92709402"
                "B07CC8C7CE0B781C641A1EA8DB2F4343"
            ), "1", (
                "66A198186C18C10B2F5ED9B522752A9830B69916E535C8F047518A889A43A5"
                "94B6BED27A168D31D4A52F88925AA8F5"
            )
        ), (
            8, 1, 4, 1,
            "1E442976B0E63D64FCCE74B999E470CA9888165CB75BFA1F340E918CE03C6211",
            "1", "B3A119602EE213CDE28581ECD892E0F592A338655DCE4CA88054B3D124D0E561"
        ), (
            22, 1, 11, 1, (
                "7CF5AC97304E0B63C65413F57249F59994B0FED1D2A8D3D83ED5FA38560FFB"
                "82392870D6D08F87D711917FD7537E13B7E125BE407E74157776839B0AC9DB"
                "23CBDFC696104353E4D2780B2B4968F8D8542306BCA7A2366E"
            ), "1", (
                "284139EA19C139EBE09A8111926AAA39A2C2BE12ED487A809D3CB5BC558547"
                "25B4CDCB5734C58F90B2F60D99CC1950CDBC8D651793E93C9C6F0EAD752500"
                "A32C56C62082912B66132B2A6AA42ADA923E1AD22CEB7BA0123"
            )
        )
    ] # type: List[Tuple[int, int, int, int, str, str, str]]

    random_test_cases = [
        ("2", "2", "3", ""), ("1", "2", "3", ""), ("2", "1", "3", ""),
        ("6", "5", "7", ""), ("3", "4", "7", ""), ("1", "6", "7", ""), ("5", "6", "7", ""),
        ("3", "4", "B", ""), ("7", "4", "B", ""), ("9", "7", "B", ""), ("2", "a", "B", ""),
        ("25", "16", "29", "(0x29 is prime)"), ("8", "28", "29", ""),
        ("18", "21", "29", ""), ("15", "f", "29", ""),
        ("e2", "ea", "FF", ""), ("43", "72", "FF", ""),
        ("d8", "70", "FF", ""), ("3c", "7c", "FF", ""),
        ("99", "b9", "101", "(0x101 is prime)"), ("65", "b2", "101", ""),
        ("81", "32", "101", ""), ("51", "dd", "101", ""),
        ("d5", "143", "38B", "(0x38B is prime)"), ("3d", "387", "38B", ""),
        ("160", "2e5", "38B", ""), ("10f", "137", "38B", ""),
        ("7dac", "25a", "8003", "(0x8003 is prime)"), ("6f1c", "3286", "8003", ""),
        ("59ed", "2f3f", "8003", ""), ("6893", "736d", "8003", ""),
        ("d199", "2832", "10001", "(0x10001 is prime)"), ("c3b2", "3e5b", "10001", ""),
        ("abe4", "214e", "10001", ""), ("4360", "a05d", "10001", ""),
        ("3f5a1", "165b2", "7F7F7", ""), ("3bd29", "37863", "7F7F7", ""),
        ("60c47", "64819", "7F7F7", ""), ("16584", "12c49", "7F7F7", ""),
        ("1ff03f", "610347", "800009", "(0x800009 is prime)"), ("340fd5", "19812e", "800009", ""),
        ("3fe2e8", "4d0dc7", "800009", ""), ("40356", "e6392", "800009", ""),
        ("dd8a1d", "266c0e", "100002B", "(0x100002B is prime)"),
        ("3fa1cb", "847fd6", "100002B", ""), ("5f439d", "5c3196", "100002B", ""),
        ("18d645", "f72dc6", "100002B", ""),
        ("20051ad", "37def6e", "37EEE9D", "(0x37EEE9D is prime)"),
        ("2ec140b", "3580dbf", "37EEE9D", ""), ("1d91b46", "190d4fc", "37EEE9D", ""),
        ("34e488d", "1224d24", "37EEE9D", ""),
        ("2a4fe2cb", "263466a9", "8000000B", "(0x8000000B is prime)"),
        ("5643fe94", "29a1aefa", "8000000B", ""), ("29633513", "7b007ac4", "8000000B", ""),
        ("2439cef5", "5c9d5a47", "8000000B", ""),
        ("4de3cfaa", "50dea178", "8CD626B9", "(0x8CD626B9 is prime)"),
        ("b8b8563", "10dbbbac", "8CD626B9", ""), ("4e8a6151", "5574ec19", "8CD626B9", ""),
        ("69224878", "309cfc23", "8CD626B9", ""),
        ("fb6f7fb6", "afb05423", "10000000F", "(0x10000000F is prime)"),
        ("8391a243", "26034dcd", "10000000F", ""), ("d26b98c", "14b2d6aa", "10000000F", ""),
        ("6b9f1371", "a21daf1d", "10000000F", ""),
        (
            "9f49435ad", "c8264ade8", "174876E7E9",
            "0x174876E7E9 is prime (dec) 99999999977"
        ),
        ("c402da434", "1fb427acf", "174876E7E9", ""),
        ("f6ebc2bb1", "1096d39f2a", "174876E7E9", ""),
        ("153b7f7b6b", "878fda8ff", "174876E7E9", ""),
        ("2c1adbb8d6", "4384d2d3c6", "8000000017", "(0x8000000017 is prime)"),
        ("2e4f9cf5fb", "794f3443d9", "8000000017", ""),
        ("149e495582", "3802b8f7b7", "8000000017", ""),
        ("7b9d49df82", "69c68a442a", "8000000017", ""),
        ("683a134600", "6dd80ea9f6", "864CB9076D", "(0x864CB9076D is prime)"),
        ("13a870ff0d", "59b099694a", "864CB9076D", ""),
        ("37d06b0e63", "4d2147e46f", "864CB9076D", ""),
        ("661714f8f4", "22e55df507", "864CB9076D", ""),
        ("2f0a96363", "52693307b4", "F7F7F7F7F7", ""),
        ("3c85078e64", "f2275ecb6d", "F7F7F7F7F7", ""),
        ("352dae68d1", "707775b4c6", "F7F7F7F7F7", ""),
        ("37ae0f3e0b", "912113040f", "F7F7F7F7F7", ""),
        ("6dada15e31", "f58ed9eff7", "1000000000F", "(0x1000000000F is prime)"),
        ("69627a7c89", "cfb5ebd13d", "1000000000F", ""),
        ("a5e1ad239b", "afc030c731", "1000000000F", ""),
        ("f1cc45f4c5", "c64ad607c8", "1000000000F", ""),
        ("2ebad87d2e31", "4c72d90bca78", "800000000005", "(0x800000000005 is prime)"),
        ("a30b3cc50d", "29ac4fe59490", "800000000005", ""),
        ("33674e9647b4", "5ec7ee7e72d3", "800000000005", ""),
        ("3d956f474f61", "74070040257d", "800000000005", ""),
        ("48348e3717d6", "43fcb4399571", "800795D9BA47", "(0x800795D9BA47 is prime)"),
        ("5234c03cc99b", "2f3cccb87803", "800795D9BA47", ""),
        ("3ed13db194ab", "44b8f4ba7030", "800795D9BA47", ""),
        ("1c11e843bfdb", "95bd1b47b08", "800795D9BA47", ""),
        ("a81d11cb81fd", "1e5753a3f33d", "1000000000015", "(0x1000000000015 is prime)"),
        ("688c4db99232", "36fc0cf7ed", "1000000000015", ""),
        ("f0720cc07e07", "fc76140ed903", "1000000000015", ""),
        ("2ec61f8d17d1", "d270c85e36d2", "1000000000015", ""),
        (
            "6a24cd3ab63820", "ed4aad55e5e348", "100000000000051",
            "(0x100000000000051 is prime)"
        ),
        ("e680c160d3b248", "31e0d8840ed510", "100000000000051", ""),
        ("a80637e9aebc38", "bb81decc4e1738", "100000000000051", ""),
        ("9afa5a59e9d630", "be9e65a6d42938", "100000000000051", ""),
        ("ab5e104eeb71c000", "2cffbd639e9fea00", "ABCDEF0123456789", ""),
        ("197b867547f68a00", "44b796cf94654800", "ABCDEF0123456789", ""),
        ("329f9483a04f2c00", "9892f76961d0f000", "ABCDEF0123456789", ""),
        ("4a2e12dfb4545000", "1aa3e89a69794500", "ABCDEF0123456789", ""),
        (
            "8b9acdf013d140f000", "12e4ceaefabdf2b2f00", "25A55A46E5DA99C71C7",
            "0x25A55A46E5DA99C71C7 is the 3rd repunit prime(dec) 11111111111111111111111"
        ),
        ("1b8d960ea277e3f5500", "14418aa980e37dd000", "25A55A46E5DA99C71C7", ""),
        ("7314524977e8075980", "8172fa45618ccd0d80", "25A55A46E5DA99C71C7", ""),
        ("ca14f031769be63580", "147a2f3cf2964ca9400", "25A55A46E5DA99C71C7", ""),
        (
            "18532ba119d5cd0cf39735c0000", "25f9838e31634844924733000000",
            "314DC643FB763F2B8C0E2DE00879",
            "0x314DC643FB763F2B8C0E2DE00879 is (dec)99999999977^3"
        ),
        (
            "a56e2d2517519e3970e70c40000", "ec27428d4bb380458588fa80000",
            "314DC643FB763F2B8C0E2DE00879", ""
        ),
        (
            "1cb5e8257710e8653fff33a00000", "15fdd42fe440fd3a1d121380000",
            "314DC643FB763F2B8C0E2DE00879", ""
        ),
        (
            "e50d07a65fc6f93e538ce040000", "1f4b059ca609f3ce597f61240000",
            "314DC643FB763F2B8C0E2DE00879", ""
        ),
        (
            "1ea3ade786a095d978d387f30df9f20000000",
            "127c448575f04af5a367a7be06c7da0000000",
            "47BF19662275FA2F6845C74942ED1D852E521",
            "0x47BF19662275FA2F6845C74942ED1D852E521 is (dec) 99999999977^4"
        ),
        (
            "16e15b0ca82764e72e38357b1f10a20000000",
            "43e2355d8514bbe22b0838fdc3983a0000000",
            "47BF19662275FA2F6845C74942ED1D852E521", ""
        ),
        (
            "be39332529d93f25c3d116c004c620000000",
            "5cccec42370a0a2c89c6772da801a0000000",
            "47BF19662275FA2F6845C74942ED1D852E521", ""
        ),
        (
            "ecaa468d90de0eeda474d39b3e1fc0000000",
            "1e714554018de6dc0fe576bfd3b5660000000",
            "47BF19662275FA2F6845C74942ED1D852E521", ""
        ),
        (
            "32298816711c5dce46f9ba06e775c4bedfc770e6700000000000000",
            "8ee751fd5fb24f0b4a653cb3a0c8b7d9e724574d168000000000000",
            "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931",
            (
                "0x97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931"
                " is (dec) 99999999977^6"
            )
        ),
        (
            "29213b9df3cfd15f4b428645b67b677c29d1378d810000000000000",
            "6cbb732c65e10a28872394dfdd1936d5171c3c3aac0000000000000",
            "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", ""
        ),
        (
            "6f18db06ad4abc52c0c50643dd13098abccd4a232f0000000000000",
            "7e6bf41f2a86098ad51f98dfc10490ba3e8081bc830000000000000",
            "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", ""
        ),
        (
            "62d3286cd706ad9d73caff63f1722775d7e8c731208000000000000",
            "530f7ba02ae2b04c2fe3e3d27ec095925631a6c2528000000000000",
            "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931", ""
        ),
        (
            "a6c6503e3c031fdbf6009a89ed60582b7233c5a85de28b16000000000000000",
            "75c8ed18270b583f16d442a467d32bf95c5e491e9b8523798000000000000000",
            "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499",
            (
                "0xDD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499"
                " is (dec) 99999999977^7"
            )
        ),
        (
            "bf84d1f85cf6b51e04d2c8f4ffd03532d852053cf99b387d4000000000000000",
            "397ba5a743c349f4f28bc583ecd5f06e0a25f9c6d98f09134000000000000000",
            "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", ""
        ),
        (
            "6db11c3a4152ed1a2aa6fa34b0903ec82ea1b88908dcb482000000000000000",
            "ac8ac576a74ad6ca48f201bf89f77350ce86e821358d85920000000000000000",
            "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", ""
        ),
        (
            "3001d96d7fe8b733f33687646fc3017e3ac417eb32e0ec708000000000000000",
            "925ddbdac4174e8321a48a32f79640e8cf7ec6f46ea235a80000000000000000",
            "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499", ""
        ),
        (
            "1029048755f2e60dd98c8de6d9989226b6bb4f0db8e46bd1939de560000000000000000000",
            "51bb7270b2e25cec0301a03e8275213bb6c2f6e6ec93d4d46d36ca0000000000000000000",
            "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41",
            (
                "0x141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146"
                "380E41 is 99999999977^8"
            )
        ),
        (
            "1c5337ff982b3ad6611257dbff5bbd7a9920ba2d4f5838a0cc681ce000000000000000000",
            "520c5d049ca4702031ba728591b665c4d4ccd3b2b86864d4c160fd2000000000000000000",
            "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41",
            ""
        ),
        (
            "57074dfa00e42f6555bae624b7f0209f218adf57f73ed34ab0ff90c000000000000000000",
            "41eb14b6c07bfd3d1fe4f4a610c17cc44fcfcda695db040e011065000000000000000000",
            "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41",
            ""
        ),
        (
            "d8ed7feed2fe855e6997ad6397f776158573d425031bf085a615784000000000000000000",
            "6f121dcd18c578ab5e229881006007bb6d319b179f11015fe958b9c000000000000000000",
            "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41",
            ""
        ),
        (
            (
                "2a462b156180ea5fe550d3758c764e06fae54e626b5f503265a09df76edbdfbf"
                "a1e6000000000000000000000000"
            ), (
                "1136f41d1879fd4fb9e49e0943a46b6704d77c068ee237c3121f9071cfd3e6a0"
                "0315800000000000000000000000"
            ), (
                "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90"
                "2713E40F51E3B3C214EDFABC451"
            ), (
                "0x2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC"
                "902713E40F51E3B3C214EDFABC451 is (dec) 99999999977^10"
            )
        ),
        (
            (
                "c1ac3800dfb3c6954dea391d206200cf3c47f795bf4a5603b4cb88ae7e574de47"
                "40800000000000000000000000"
            ), (
                "c0d16eda0549ede42fa0deb4635f7b7ce061fadea02ee4d85cba4c4f709603419"
                "3c800000000000000000000000"
            ), (
                "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90"
                "2713E40F51E3B3C214EDFABC451"
            ), ""
        ),
        (
            (
                "19e45bb7633094d272588ad2e43bcb3ee341991c6731b6fa9d47c4018d7ce7bba"
                "5ee800000000000000000000000"
            ), (
                "1e4f83166ae59f6b9cc8fd3e7677ed8bfc01bb99c98bd3eb084246b64c1e18c33"
                "65b800000000000000000000000"
            ), (
                "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90"
                "2713E40F51E3B3C214EDFABC451"
            ), ""
        ),
        (
            (
                "1aa93395fad5f9b7f20b8f9028a054c0bb7c11bb8520e6a95e5a34f06cb70bcdd"
                "01a800000000000000000000000"
            ), (
                "54b45afa5d4310192f8d224634242dd7dcfb342318df3d9bd37b4c614788ba13b"
                "8b000000000000000000000000"
            ), (
                "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E2833EC90"
                "2713E40F51E3B3C214EDFABC451"
            ), ""
        ),
        (
            (
                "544f2628a28cfb5ce0a1b7180ee66b49716f1d9476c466c57f0c4b23089917843"
                "06d48f78686115ee19e25400000000000000000000000000000000"
            ), (
                "677eb31ef8d66c120fa872a60cd47f6e10cbfdf94f90501bd7883cba03d185be0"
                "a0148d1625745e9c4c827300000000000000000000000000000000"
            ), (
                "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1"
                "1DABD6E6144BEF37C6800000000000000000000000000000000051"
            ), (
                "0x8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBF"
                "A11DABD6E6144BEF37C6800000000000000000000000000000000051 is prime,"
                " (dec) 10^143 + 3^4"
            )
        ),
        (
            (
                "76bb3470985174915e9993522aec989666908f9e8cf5cb9f037bf4aee33d8865c"
                "b6464174795d07e30015b80000000000000000000000000000000"
            ), (
                "6aaaf60d5784dcef612d133613b179a317532ecca0eed40b8ad0c01e6d4a6d8c7"
                "9a52af190abd51739009a900000000000000000000000000000000"
            ), (
                "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1"
                "1DABD6E6144BEF37C6800000000000000000000000000000000051"
            ), ""
        ),
        (
            (
                "6cfdd6e60912e441d2d1fc88f421b533f0103a5322ccd3f4db84861643ad63fd6"
                "3d1d8cfbc1d498162786ba00000000000000000000000000000000"
            ), (
                "1177246ec5e93814816465e7f8f248b350d954439d35b2b5d75d917218e7fd5fb"
                "4c2f6d0667f9467fdcf33400000000000000000000000000000000"
            ), (
                "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1"
                "1DABD6E6144BEF37C6800000000000000000000000000000000051"
            ), ""
        ),
        (
            (
                "7a09a0b0f8bbf8057116fb0277a9bdf3a91b5eaa8830d448081510d8973888be5"
                "a9f0ad04facb69aa3715f00000000000000000000000000000000"
            ), (
                "764dec6c05a1c0d87b649efa5fd94c91ea28bffb4725d4ab4b33f1a3e8e3b314d"
                "799020e244a835a145ec9800000000000000000000000000000000"
            ), (
                "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA1"
                "1DABD6E6144BEF37C6800000000000000000000000000000000051"
            ), ""
        )
    ] # type: List[Tuple[str, str, str, str]]

    def __init__(
            self, val_a: str, val_b: str, val_n: str, case_description: str = ""
        ):
        self.case_description = case_description
        self.arg_a = val_a
        self.int_a = bignum_common.hex_to_int(val_a)
        self.arg_b = val_b
        self.int_b = bignum_common.hex_to_int(val_b)
        self.arg_n = val_n
        self.int_n = bignum_common.hex_to_int(val_n)

        limbs_a4 = bignum_common.limbs_mpi(self.int_a, 32)
        limbs_a8 = bignum_common.limbs_mpi(self.int_a, 64)
        self.limbs_b4 = bignum_common.limbs_mpi(self.int_b, 32)
        self.limbs_b8 = bignum_common.limbs_mpi(self.int_b, 64)
        self.limbs_an4 = bignum_common.limbs_mpi(self.int_n, 32)
        self.limbs_an8 = bignum_common.limbs_mpi(self.int_n, 64)

        if limbs_a4 > self.limbs_an4 or limbs_a8 > self.limbs_an8:
            raise Exception("Limbs of input A ({}) exceeds N ({})".format(
                self.arg_a, self.arg_n
            ))

    def arguments(self) -> List[str]:
        return [
            str(self.limbs_an4), str(self.limbs_b4),
            str(self.limbs_an8), str(self.limbs_b8),
            bignum_common.quote_str(self.arg_a),
            bignum_common.quote_str(self.arg_b),
            bignum_common.quote_str(self.arg_n)
        ] + self.result()

    def description(self) -> str:
        if self.case_description != "replay":
            if not self.start_2_mpi4 and self.limbs_an4 > 1:
                tmp = "(start of 2-MPI 4-byte bignums) "
                self.__class__.start_2_mpi4 = True
            elif not self.start_2_mpi8 and self.limbs_an8 > 1:
                tmp = "(start of 2-MPI 8-byte bignums) "
                self.__class__.start_2_mpi8 = True
            else:
                tmp = "(gen) "
            self.case_description = tmp + self.case_description
        return super().description()

    def result(self) -> List[str]:
        """Get the result of the operation."""
        r4 = bignum_common.bound_mpi_limbs(self.limbs_an4, 32)
        i4 = bignum_common.invmod(r4, self.int_n)
        x4 = self.int_a * self.int_b * i4
        x4 = x4 % self.int_n

        r8 = bignum_common.bound_mpi_limbs(self.limbs_an8, 64)
        i8 = bignum_common.invmod(r8, self.int_n)
        x8 = self.int_a * self.int_b * i8
        x8 = x8 % self.int_n
        return [
            "\"{:x}\"".format(x4),
            "\"{:x}\"".format(x8)
        ]

    def set_limbs(
            self, limbs_an4: int, limbs_b4: int, limbs_an8: int, limbs_b8: int
        ) -> None:
        """Set number of limbs for each input.

        Replaces default values set during initialization.
        """
        self.limbs_an4 = limbs_an4
        self.limbs_b4 = limbs_b4
        self.limbs_an8 = limbs_an8
        self.limbs_b8 = limbs_b8

    @classmethod
    def generate_function_tests(cls) -> Iterator[test_case.TestCase]:
        """Generate replay and randomly generated test cases."""
        # Test cases which replay captured invocations during unit test runs.
        for limbs_an4, limbs_b4, limbs_an8, limbs_b8, a, b, n in cls.replay_test_cases:
            cur_op = cls(a, b, n, case_description="replay")
            cur_op.set_limbs(limbs_an4, limbs_b4, limbs_an8, limbs_b8)
            yield cur_op.create_test_case()
        # Random test cases can be generated using mpi_modmul_case_generate()
        # Uses a mixture of primes and odd numbers as N, with four randomly
        # generated cases for each N.
        for a, b, n, description in cls.random_test_cases:
            cur_op = cls(a, b, n, case_description=description)
            yield cur_op.create_test_case()


def mpi_modmul_case_generate() -> None:
    """Generate valid inputs for montmul tests using moduli.

    For each modulus, generates random values for A and B and simple descriptions
    for the test case.
    """
    moduli = [
        ("3", ""), ("7", ""), ("B", ""), ("29", ""), ("FF", ""),
        ("101", ""), ("38B", ""), ("8003", ""), ("10001", ""),
        ("7F7F7", ""), ("800009", ""), ("100002B", ""), ("37EEE9D", ""),
        ("8000000B", ""), ("8CD626B9", ""), ("10000000F", ""),
        ("174876E7E9", "is prime (dec) 99999999977"),
        ("8000000017", ""), ("864CB9076D", ""), ("F7F7F7F7F7", ""),
        ("1000000000F", ""), ("800000000005", ""), ("800795D9BA47", ""),
        ("1000000000015", ""), ("100000000000051", ""), ("ABCDEF0123456789", ""),
        (
            "25A55A46E5DA99C71C7",
            "is the 3rd repunit prime (dec) 11111111111111111111111"
        ),
        ("314DC643FB763F2B8C0E2DE00879", "is (dec)99999999977^3"),
        ("47BF19662275FA2F6845C74942ED1D852E521", "is (dec) 99999999977^4"),
        (
            "97EDD86E4B5C4592C6D32064AC55C888A7245F07CA3CC455E07C931",
            "is (dec) 99999999977^6"
        ),
        (
            "DD15FE80B731872AC104DB37832F7E75A244AA2631BC87885B861E8F20375499",
            "is (dec) 99999999977^7"
        ),
        (
            "141B8EBD9009F84C241879A1F680FACCED355DA36C498F73E96E880CF78EA5F96146380E41",
            "is (dec) 99999999977^8"
        ),
        (
            (
                "2A94608DE88B6D5E9F8920F5ABB06B24CC35AE1FBACC87D075C621C3E283"
                "3EC902713E40F51E3B3C214EDFABC451"
            ),
            "is (dec) 99999999977^10"
        ),
        (
            "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11"
            "DABD6E6144BEF37C6800000000000000000000000000000000051",
            "is prime, (dec) 10^143 + 3^4"
        )
    ] # type: List[Tuple[str, str]]
    primes = [
        "3", "7", "B", "29", "101", "38B", "8003", "10001", "800009",
        "100002B", "37EEE9D", "8000000B", "8CD626B9",
        # From here they require > 1 4-byte MPI
        "10000000F", "174876E7E9", "8000000017", "864CB9076D", "1000000000F",
        "800000000005", "800795D9BA47", "1000000000015", "100000000000051",
        # From here they require > 1 8-byte MPI
        "25A55A46E5DA99C71C7",      # this is 11111111111111111111111 decimal
        # 10^143 + 3^4: (which is prime)
        # 100000000000000000000000000000000000000000000000000000000000000000000000000000
        # 000000000000000000000000000000000000000000000000000000000000000081
        (
            "8335616AED761F1F7F44E6BD49E807B82E3BF2BF11BFA6AF813C808DBF33DBFA11"
            "DABD6E6144BEF37C6800000000000000000000000000000000051"
        )
    ] # type: List[str]
    generated_inputs = []
    for mod, description in moduli:
        n = bignum_common.hex_to_int(mod)
        mod_read = "{:x}".format(n)
        case_count = 3 if n < 5 else 4
        cases = {} # type: Dict[int, int]
        i = 0
        while i < case_count:
            a = random.randint(1, n)
            b = random.randint(1, n)
            if cases.get(a) == b:
                continue
            cases[a] = b
            if description:
                out_description = "0x{} {}".format(mod_read, description)
            elif i == 0 and len(mod) > 1 and mod in primes:
                out_description = "(0x{} is prime)"
            else:
                out_description = ""
            generated_inputs.append(
                ("{:x}".format(a), "{:x}".format(b), mod, out_description)
            )
            i += 1
    print(generated_inputs)