two version of R2R are here HEAD master

author: S. Solomon Darnell 2025-03-28 21:52:21 -0500
committer: S. Solomon Darnell 2025-03-28 21:52:21 -0500
commit: 4a52a71956a8d46fcb7294ac71734504bb09bcc2 (patch)
tree: ee3dc5af3b6313e921cd920906356f5d4febc4ed /.venv/lib/python3.12/site-packages/rsa
parent: cc961e04ba734dd72309fb548a2f97d67d578813 (diff)
download: gn-ai-master.tar.gz
15 files changed, 2806 insertions, 0 deletions
diff --git a/.venv/lib/python3.12/site-packages/rsa/__init__.py b/.venv/lib/python3.12/site-packages/rsa/__init__.py
new file mode 100644
index 00000000..d0185fe9
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/__init__.py
@@ -0,0 +1,60 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+"""RSA module
+
+Module for calculating large primes, and RSA encryption, decryption, signing
+and verification. Includes generating public and private keys.
+
+WARNING: this implementation does not use compression of the cleartext input to
+prevent repetitions, or other common security improvements. Use with care.
+
+"""
+
+from rsa.key import newkeys, PrivateKey, PublicKey
+from rsa.pkcs1 import (
+    encrypt,
+    decrypt,
+    sign,
+    verify,
+    DecryptionError,
+    VerificationError,
+    find_signature_hash,
+    sign_hash,
+    compute_hash,
+)
+
+__author__ = "Sybren Stuvel, Barry Mead and Yesudeep Mangalapilly"
+__date__ = "2022-07-20"
+__version__ = "4.9"
+
+# Do doctest if we're run directly
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+__all__ = [
+    "newkeys",
+    "encrypt",
+    "decrypt",
+    "sign",
+    "verify",
+    "PublicKey",
+    "PrivateKey",
+    "DecryptionError",
+    "VerificationError",
+    "find_signature_hash",
+    "compute_hash",
+    "sign_hash",
+]
diff --git a/.venv/lib/python3.12/site-packages/rsa/asn1.py b/.venv/lib/python3.12/site-packages/rsa/asn1.py
new file mode 100644
index 00000000..b91806fb
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/asn1.py
@@ -0,0 +1,52 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""ASN.1 definitions.
+
+Not all ASN.1-handling code use these definitions, but when it does, they should be here.
+"""
+
+from pyasn1.type import univ, namedtype, tag
+
+
+class PubKeyHeader(univ.Sequence):
+    componentType = namedtype.NamedTypes(
+        namedtype.NamedType("oid", univ.ObjectIdentifier()),
+        namedtype.NamedType("parameters", univ.Null()),
+    )
+
+
+class OpenSSLPubKey(univ.Sequence):
+    componentType = namedtype.NamedTypes(
+        namedtype.NamedType("header", PubKeyHeader()),
+        # This little hack (the implicit tag) allows us to get a Bit String as Octet String
+        namedtype.NamedType(
+            "key",
+            univ.OctetString().subtype(implicitTag=tag.Tag(tagClass=0, tagFormat=0, tagId=3)),
+        ),
+    )
+
+
+class AsnPubKey(univ.Sequence):
+    """ASN.1 contents of DER encoded public key:
+
+    RSAPublicKey ::= SEQUENCE {
+         modulus           INTEGER,  -- n
+         publicExponent    INTEGER,  -- e
+    """
+
+    componentType = namedtype.NamedTypes(
+        namedtype.NamedType("modulus", univ.Integer()),
+        namedtype.NamedType("publicExponent", univ.Integer()),
+    )
diff --git a/.venv/lib/python3.12/site-packages/rsa/cli.py b/.venv/lib/python3.12/site-packages/rsa/cli.py
new file mode 100644
index 00000000..5a6b6506
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/cli.py
@@ -0,0 +1,321 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Commandline scripts.
+
+These scripts are called by the executables defined in setup.py.
+"""
+
+import abc
+import sys
+import typing
+import optparse
+
+import rsa
+import rsa.key
+import rsa.pkcs1
+
+HASH_METHODS = sorted(rsa.pkcs1.HASH_METHODS.keys())
+Indexable = typing.Union[typing.Tuple, typing.List[str]]
+
+
+def keygen() -> None:
+    """Key generator."""
+
+    # Parse the CLI options
+    parser = optparse.OptionParser(
+        usage="usage: %prog [options] keysize",
+        description='Generates a new RSA key pair of "keysize" bits.',
+    )
+
+    parser.add_option(
+        "--pubout",
+        type="string",
+        help="Output filename for the public key. The public key is "
+        "not saved if this option is not present. You can use "
+        "pyrsa-priv2pub to create the public key file later.",
+    )
+
+    parser.add_option(
+        "-o",
+        "--out",
+        type="string",
+        help="Output filename for the private key. The key is "
+        "written to stdout if this option is not present.",
+    )
+
+    parser.add_option(
+        "--form",
+        help="key format of the private and public keys - default PEM",
+        choices=("PEM", "DER"),
+        default="PEM",
+    )
+
+    (cli, cli_args) = parser.parse_args(sys.argv[1:])
+
+    if len(cli_args) != 1:
+        parser.print_help()
+        raise SystemExit(1)
+
+    try:
+        keysize = int(cli_args[0])
+    except ValueError as ex:
+        parser.print_help()
+        print("Not a valid number: %s" % cli_args[0], file=sys.stderr)
+        raise SystemExit(1) from ex
+
+    print("Generating %i-bit key" % keysize, file=sys.stderr)
+    (pub_key, priv_key) = rsa.newkeys(keysize)
+
+    # Save public key
+    if cli.pubout:
+        print("Writing public key to %s" % cli.pubout, file=sys.stderr)
+        data = pub_key.save_pkcs1(format=cli.form)
+        with open(cli.pubout, "wb") as outfile:
+            outfile.write(data)
+
+    # Save private key
+    data = priv_key.save_pkcs1(format=cli.form)
+
+    if cli.out:
+        print("Writing private key to %s" % cli.out, file=sys.stderr)
+        with open(cli.out, "wb") as outfile:
+            outfile.write(data)
+    else:
+        print("Writing private key to stdout", file=sys.stderr)
+        sys.stdout.buffer.write(data)
+
+
+class CryptoOperation(metaclass=abc.ABCMeta):
+    """CLI callable that operates with input, output, and a key."""
+
+    keyname = "public"  # or 'private'
+    usage = "usage: %%prog [options] %(keyname)s_key"
+    description = ""
+    operation = "decrypt"
+    operation_past = "decrypted"
+    operation_progressive = "decrypting"
+    input_help = "Name of the file to %(operation)s. Reads from stdin if " "not specified."
+    output_help = (
+        "Name of the file to write the %(operation_past)s file "
+        "to. Written to stdout if this option is not present."
+    )
+    expected_cli_args = 1
+    has_output = True
+
+    key_class = rsa.PublicKey  # type: typing.Type[rsa.key.AbstractKey]
+
+    def __init__(self) -> None:
+        self.usage = self.usage % self.__class__.__dict__
+        self.input_help = self.input_help % self.__class__.__dict__
+        self.output_help = self.output_help % self.__class__.__dict__
+
+    @abc.abstractmethod
+    def perform_operation(
+        self, indata: bytes, key: rsa.key.AbstractKey, cli_args: Indexable
+    ) -> typing.Any:
+        """Performs the program's operation.
+
+        Implement in a subclass.
+
+        :returns: the data to write to the output.
+        """
+
+    def __call__(self) -> None:
+        """Runs the program."""
+
+        (cli, cli_args) = self.parse_cli()
+
+        key = self.read_key(cli_args[0], cli.keyform)
+
+        indata = self.read_infile(cli.input)
+
+        print(self.operation_progressive.title(), file=sys.stderr)
+        outdata = self.perform_operation(indata, key, cli_args)
+
+        if self.has_output:
+            self.write_outfile(outdata, cli.output)
+
+    def parse_cli(self) -> typing.Tuple[optparse.Values, typing.List[str]]:
+        """Parse the CLI options
+
+        :returns: (cli_opts, cli_args)
+        """
+
+        parser = optparse.OptionParser(usage=self.usage, description=self.description)
+
+        parser.add_option("-i", "--input", type="string", help=self.input_help)
+
+        if self.has_output:
+            parser.add_option("-o", "--output", type="string", help=self.output_help)
+
+        parser.add_option(
+            "--keyform",
+            help="Key format of the %s key - default PEM" % self.keyname,
+            choices=("PEM", "DER"),
+            default="PEM",
+        )
+
+        (cli, cli_args) = parser.parse_args(sys.argv[1:])
+
+        if len(cli_args) != self.expected_cli_args:
+            parser.print_help()
+            raise SystemExit(1)
+
+        return cli, cli_args
+
+    def read_key(self, filename: str, keyform: str) -> rsa.key.AbstractKey:
+        """Reads a public or private key."""
+
+        print("Reading %s key from %s" % (self.keyname, filename), file=sys.stderr)
+        with open(filename, "rb") as keyfile:
+            keydata = keyfile.read()
+
+        return self.key_class.load_pkcs1(keydata, keyform)
+
+    def read_infile(self, inname: str) -> bytes:
+        """Read the input file"""
+
+        if inname:
+            print("Reading input from %s" % inname, file=sys.stderr)
+            with open(inname, "rb") as infile:
+                return infile.read()
+
+        print("Reading input from stdin", file=sys.stderr)
+        return sys.stdin.buffer.read()
+
+    def write_outfile(self, outdata: bytes, outname: str) -> None:
+        """Write the output file"""
+
+        if outname:
+            print("Writing output to %s" % outname, file=sys.stderr)
+            with open(outname, "wb") as outfile:
+                outfile.write(outdata)
+        else:
+            print("Writing output to stdout", file=sys.stderr)
+            sys.stdout.buffer.write(outdata)
+
+
+class EncryptOperation(CryptoOperation):
+    """Encrypts a file."""
+
+    keyname = "public"
+    description = (
+        "Encrypts a file. The file must be shorter than the key " "length in order to be encrypted."
+    )
+    operation = "encrypt"
+    operation_past = "encrypted"
+    operation_progressive = "encrypting"
+
+    def perform_operation(
+        self, indata: bytes, pub_key: rsa.key.AbstractKey, cli_args: Indexable = ()
+    ) -> bytes:
+        """Encrypts files."""
+        assert isinstance(pub_key, rsa.key.PublicKey)
+        return rsa.encrypt(indata, pub_key)
+
+
+class DecryptOperation(CryptoOperation):
+    """Decrypts a file."""
+
+    keyname = "private"
+    description = (
+        "Decrypts a file. The original file must be shorter than "
+        "the key length in order to have been encrypted."
+    )
+    operation = "decrypt"
+    operation_past = "decrypted"
+    operation_progressive = "decrypting"
+    key_class = rsa.PrivateKey
+
+    def perform_operation(
+        self, indata: bytes, priv_key: rsa.key.AbstractKey, cli_args: Indexable = ()
+    ) -> bytes:
+        """Decrypts files."""
+        assert isinstance(priv_key, rsa.key.PrivateKey)
+        return rsa.decrypt(indata, priv_key)
+
+
+class SignOperation(CryptoOperation):
+    """Signs a file."""
+
+    keyname = "private"
+    usage = "usage: %%prog [options] private_key hash_method"
+    description = (
+        "Signs a file, outputs the signature. Choose the hash "
+        "method from %s" % ", ".join(HASH_METHODS)
+    )
+    operation = "sign"
+    operation_past = "signature"
+    operation_progressive = "Signing"
+    key_class = rsa.PrivateKey
+    expected_cli_args = 2
+
+    output_help = (
+        "Name of the file to write the signature to. Written "
+        "to stdout if this option is not present."
+    )
+
+    def perform_operation(
+        self, indata: bytes, priv_key: rsa.key.AbstractKey, cli_args: Indexable
+    ) -> bytes:
+        """Signs files."""
+        assert isinstance(priv_key, rsa.key.PrivateKey)
+
+        hash_method = cli_args[1]
+        if hash_method not in HASH_METHODS:
+            raise SystemExit("Invalid hash method, choose one of %s" % ", ".join(HASH_METHODS))
+
+        return rsa.sign(indata, priv_key, hash_method)
+
+
+class VerifyOperation(CryptoOperation):
+    """Verify a signature."""
+
+    keyname = "public"
+    usage = "usage: %%prog [options] public_key signature_file"
+    description = (
+        "Verifies a signature, exits with status 0 upon success, "
+        "prints an error message and exits with status 1 upon error."
+    )
+    operation = "verify"
+    operation_past = "verified"
+    operation_progressive = "Verifying"
+    key_class = rsa.PublicKey
+    expected_cli_args = 2
+    has_output = False
+
+    def perform_operation(
+        self, indata: bytes, pub_key: rsa.key.AbstractKey, cli_args: Indexable
+    ) -> None:
+        """Verifies files."""
+        assert isinstance(pub_key, rsa.key.PublicKey)
+
+        signature_file = cli_args[1]
+
+        with open(signature_file, "rb") as sigfile:
+            signature = sigfile.read()
+
+        try:
+            rsa.verify(indata, signature, pub_key)
+        except rsa.VerificationError as ex:
+            raise SystemExit("Verification failed.") from ex
+
+        print("Verification OK", file=sys.stderr)
+
+
+encrypt = EncryptOperation()
+decrypt = DecryptOperation()
+sign = SignOperation()
+verify = VerifyOperation()
diff --git a/.venv/lib/python3.12/site-packages/rsa/common.py b/.venv/lib/python3.12/site-packages/rsa/common.py
new file mode 100644
index 00000000..520dfec6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/common.py
@@ -0,0 +1,184 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Common functionality shared by several modules."""
+
+import typing
+
+
+class NotRelativePrimeError(ValueError):
+    def __init__(self, a: int, b: int, d: int, msg: str = "") -> None:
+        super().__init__(msg or "%d and %d are not relatively prime, divider=%i" % (a, b, d))
+        self.a = a
+        self.b = b
+        self.d = d
+
+
+def bit_size(num: int) -> int:
+    """
+    Number of bits needed to represent a integer excluding any prefix
+    0 bits.
+
+    Usage::
+
+        >>> bit_size(1023)
+        10
+        >>> bit_size(1024)
+        11
+        >>> bit_size(1025)
+        11
+
+    :param num:
+        Integer value. If num is 0, returns 0. Only the absolute value of the
+        number is considered. Therefore, signed integers will be abs(num)
+        before the number's bit length is determined.
+    :returns:
+        Returns the number of bits in the integer.
+    """
+
+    try:
+        return num.bit_length()
+    except AttributeError as ex:
+        raise TypeError("bit_size(num) only supports integers, not %r" % type(num)) from ex
+
+
+def byte_size(number: int) -> int:
+    """
+    Returns the number of bytes required to hold a specific long number.
+
+    The number of bytes is rounded up.
+
+    Usage::
+
+        >>> byte_size(1 << 1023)
+        128
+        >>> byte_size((1 << 1024) - 1)
+        128
+        >>> byte_size(1 << 1024)
+        129
+
+    :param number:
+        An unsigned integer
+    :returns:
+        The number of bytes required to hold a specific long number.
+    """
+    if number == 0:
+        return 1
+    return ceil_div(bit_size(number), 8)
+
+
+def ceil_div(num: int, div: int) -> int:
+    """
+    Returns the ceiling function of a division between `num` and `div`.
+
+    Usage::
+
+        >>> ceil_div(100, 7)
+        15
+        >>> ceil_div(100, 10)
+        10
+        >>> ceil_div(1, 4)
+        1
+
+    :param num: Division's numerator, a number
+    :param div: Division's divisor, a number
+
+    :return: Rounded up result of the division between the parameters.
+    """
+    quanta, mod = divmod(num, div)
+    if mod:
+        quanta += 1
+    return quanta
+
+
+def extended_gcd(a: int, b: int) -> typing.Tuple[int, int, int]:
+    """Returns a tuple (r, i, j) such that r = gcd(a, b) = ia + jb"""
+    # r = gcd(a,b) i = multiplicitive inverse of a mod b
+    #      or      j = multiplicitive inverse of b mod a
+    # Neg return values for i or j are made positive mod b or a respectively
+    # Iterateive Version is faster and uses much less stack space
+    x = 0
+    y = 1
+    lx = 1
+    ly = 0
+    oa = a  # Remember original a/b to remove
+    ob = b  # negative values from return results
+    while b != 0:
+        q = a // b
+        (a, b) = (b, a % b)
+        (x, lx) = ((lx - (q * x)), x)
+        (y, ly) = ((ly - (q * y)), y)
+    if lx < 0:
+        lx += ob  # If neg wrap modulo original b
+    if ly < 0:
+        ly += oa  # If neg wrap modulo original a
+    return a, lx, ly  # Return only positive values
+
+
+def inverse(x: int, n: int) -> int:
+    """Returns the inverse of x % n under multiplication, a.k.a x^-1 (mod n)
+
+    >>> inverse(7, 4)
+    3
+    >>> (inverse(143, 4) * 143) % 4
+    1
+    """
+
+    (divider, inv, _) = extended_gcd(x, n)
+
+    if divider != 1:
+        raise NotRelativePrimeError(x, n, divider)
+
+    return inv
+
+
+def crt(a_values: typing.Iterable[int], modulo_values: typing.Iterable[int]) -> int:
+    """Chinese Remainder Theorem.
+
+    Calculates x such that x = a[i] (mod m[i]) for each i.
+
+    :param a_values: the a-values of the above equation
+    :param modulo_values: the m-values of the above equation
+    :returns: x such that x = a[i] (mod m[i]) for each i
+
+
+    >>> crt([2, 3], [3, 5])
+    8
+
+    >>> crt([2, 3, 2], [3, 5, 7])
+    23
+
+    >>> crt([2, 3, 0], [7, 11, 15])
+    135
+    """
+
+    m = 1
+    x = 0
+
+    for modulo in modulo_values:
+        m *= modulo
+
+    for (m_i, a_i) in zip(modulo_values, a_values):
+        M_i = m // m_i
+        inv = inverse(M_i, m_i)
+
+        x = (x + a_i * M_i * inv) % m
+
+    return x
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
diff --git a/.venv/lib/python3.12/site-packages/rsa/core.py b/.venv/lib/python3.12/site-packages/rsa/core.py
new file mode 100644
index 00000000..729123b6
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/core.py
@@ -0,0 +1,53 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Core mathematical operations.
+
+This is the actual core RSA implementation, which is only defined
+mathematically on integers.
+"""
+
+
+def assert_int(var: int, name: str) -> None:
+    if isinstance(var, int):
+        return
+
+    raise TypeError("%s should be an integer, not %s" % (name, var.__class__))
+
+
+def encrypt_int(message: int, ekey: int, n: int) -> int:
+    """Encrypts a message using encryption key 'ekey', working modulo n"""
+
+    assert_int(message, "message")
+    assert_int(ekey, "ekey")
+    assert_int(n, "n")
+
+    if message < 0:
+        raise ValueError("Only non-negative numbers are supported")
+
+    if message > n:
+        raise OverflowError("The message %i is too long for n=%i" % (message, n))
+
+    return pow(message, ekey, n)
+
+
+def decrypt_int(cyphertext: int, dkey: int, n: int) -> int:
+    """Decrypts a cypher text using the decryption key 'dkey', working modulo n"""
+
+    assert_int(cyphertext, "cyphertext")
+    assert_int(dkey, "dkey")
+    assert_int(n, "n")
+
+    message = pow(cyphertext, dkey, n)
+    return message
diff --git a/.venv/lib/python3.12/site-packages/rsa/key.py b/.venv/lib/python3.12/site-packages/rsa/key.py
new file mode 100644
index 00000000..b6b17f91
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/key.py
@@ -0,0 +1,858 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""RSA key generation code.
+
+Create new keys with the newkeys() function. It will give you a PublicKey and a
+PrivateKey object.
+
+Loading and saving keys requires the pyasn1 module. This module is imported as
+late as possible, such that other functionality will remain working in absence
+of pyasn1.
+
+.. note::
+
+    Storing public and private keys via the `pickle` module is possible.
+    However, it is insecure to load a key from an untrusted source.
+    The pickle module is not secure against erroneous or maliciously
+    constructed data. Never unpickle data received from an untrusted
+    or unauthenticated source.
+
+"""
+
+import threading
+import typing
+import warnings
+
+import rsa.prime
+import rsa.pem
+import rsa.common
+import rsa.randnum
+import rsa.core
+
+
+DEFAULT_EXPONENT = 65537
+
+
+T = typing.TypeVar("T", bound="AbstractKey")
+
+
+class AbstractKey:
+    """Abstract superclass for private and public keys."""
+
+    __slots__ = ("n", "e", "blindfac", "blindfac_inverse", "mutex")
+
+    def __init__(self, n: int, e: int) -> None:
+        self.n = n
+        self.e = e
+
+        # These will be computed properly on the first call to blind().
+        self.blindfac = self.blindfac_inverse = -1
+
+        # Used to protect updates to the blinding factor in multi-threaded
+        # environments.
+        self.mutex = threading.Lock()
+
+    @classmethod
+    def _load_pkcs1_pem(cls: typing.Type[T], keyfile: bytes) -> T:
+        """Loads a key in PKCS#1 PEM format, implement in a subclass.
+
+        :param keyfile: contents of a PEM-encoded file that contains
+            the public key.
+        :type keyfile: bytes
+
+        :return: the loaded key
+        :rtype: AbstractKey
+        """
+
+    @classmethod
+    def _load_pkcs1_der(cls: typing.Type[T], keyfile: bytes) -> T:
+        """Loads a key in PKCS#1 PEM format, implement in a subclass.
+
+        :param keyfile: contents of a DER-encoded file that contains
+            the public key.
+        :type keyfile: bytes
+
+        :return: the loaded key
+        :rtype: AbstractKey
+        """
+
+    def _save_pkcs1_pem(self) -> bytes:
+        """Saves the key in PKCS#1 PEM format, implement in a subclass.
+
+        :returns: the PEM-encoded key.
+        :rtype: bytes
+        """
+
+    def _save_pkcs1_der(self) -> bytes:
+        """Saves the key in PKCS#1 DER format, implement in a subclass.
+
+        :returns: the DER-encoded key.
+        :rtype: bytes
+        """
+
+    @classmethod
+    def load_pkcs1(cls: typing.Type[T], keyfile: bytes, format: str = "PEM") -> T:
+        """Loads a key in PKCS#1 DER or PEM format.
+
+        :param keyfile: contents of a DER- or PEM-encoded file that contains
+            the key.
+        :type keyfile: bytes
+        :param format: the format of the file to load; 'PEM' or 'DER'
+        :type format: str
+
+        :return: the loaded key
+        :rtype: AbstractKey
+        """
+
+        methods = {
+            "PEM": cls._load_pkcs1_pem,
+            "DER": cls._load_pkcs1_der,
+        }
+
+        method = cls._assert_format_exists(format, methods)
+        return method(keyfile)
+
+    @staticmethod
+    def _assert_format_exists(
+        file_format: str, methods: typing.Mapping[str, typing.Callable]
+    ) -> typing.Callable:
+        """Checks whether the given file format exists in 'methods'."""
+
+        try:
+            return methods[file_format]
+        except KeyError as ex:
+            formats = ", ".join(sorted(methods.keys()))
+            raise ValueError(
+                "Unsupported format: %r, try one of %s" % (file_format, formats)
+            ) from ex
+
+    def save_pkcs1(self, format: str = "PEM") -> bytes:
+        """Saves the key in PKCS#1 DER or PEM format.
+
+        :param format: the format to save; 'PEM' or 'DER'
+        :type format: str
+        :returns: the DER- or PEM-encoded key.
+        :rtype: bytes
+        """
+
+        methods = {
+            "PEM": self._save_pkcs1_pem,
+            "DER": self._save_pkcs1_der,
+        }
+
+        method = self._assert_format_exists(format, methods)
+        return method()
+
+    def blind(self, message: int) -> typing.Tuple[int, int]:
+        """Performs blinding on the message.
+
+        :param message: the message, as integer, to blind.
+        :param r: the random number to blind with.
+        :return: tuple (the blinded message, the inverse of the used blinding factor)
+
+        The blinding is such that message = unblind(decrypt(blind(encrypt(message))).
+
+        See https://en.wikipedia.org/wiki/Blinding_%28cryptography%29
+        """
+        blindfac, blindfac_inverse = self._update_blinding_factor()
+        blinded = (message * pow(blindfac, self.e, self.n)) % self.n
+        return blinded, blindfac_inverse
+
+    def unblind(self, blinded: int, blindfac_inverse: int) -> int:
+        """Performs blinding on the message using random number 'blindfac_inverse'.
+
+        :param blinded: the blinded message, as integer, to unblind.
+        :param blindfac: the factor to unblind with.
+        :return: the original message.
+
+        The blinding is such that message = unblind(decrypt(blind(encrypt(message))).
+
+        See https://en.wikipedia.org/wiki/Blinding_%28cryptography%29
+        """
+        return (blindfac_inverse * blinded) % self.n
+
+    def _initial_blinding_factor(self) -> int:
+        for _ in range(1000):
+            blind_r = rsa.randnum.randint(self.n - 1)
+            if rsa.prime.are_relatively_prime(self.n, blind_r):
+                return blind_r
+        raise RuntimeError("unable to find blinding factor")
+
+    def _update_blinding_factor(self) -> typing.Tuple[int, int]:
+        """Update blinding factors.
+
+        Computing a blinding factor is expensive, so instead this function
+        does this once, then updates the blinding factor as per section 9
+        of 'A Timing Attack against RSA with the Chinese Remainder Theorem'
+        by Werner Schindler.
+        See https://tls.mbed.org/public/WSchindler-RSA_Timing_Attack.pdf
+
+        :return: the new blinding factor and its inverse.
+        """
+
+        with self.mutex:
+            if self.blindfac < 0:
+                # Compute initial blinding factor, which is rather slow to do.
+                self.blindfac = self._initial_blinding_factor()
+                self.blindfac_inverse = rsa.common.inverse(self.blindfac, self.n)
+            else:
+                # Reuse previous blinding factor.
+                self.blindfac = pow(self.blindfac, 2, self.n)
+                self.blindfac_inverse = pow(self.blindfac_inverse, 2, self.n)
+
+            return self.blindfac, self.blindfac_inverse
+
+
+class PublicKey(AbstractKey):
+    """Represents a public RSA key.
+
+    This key is also known as the 'encryption key'. It contains the 'n' and 'e'
+    values.
+
+    Supports attributes as well as dictionary-like access. Attribute access is
+    faster, though.
+
+    >>> PublicKey(5, 3)
+    PublicKey(5, 3)
+
+    >>> key = PublicKey(5, 3)
+    >>> key.n
+    5
+    >>> key['n']
+    5
+    >>> key.e
+    3
+    >>> key['e']
+    3
+
+    """
+
+    __slots__ = ()
+
+    def __getitem__(self, key: str) -> int:
+        return getattr(self, key)
+
+    def __repr__(self) -> str:
+        return "PublicKey(%i, %i)" % (self.n, self.e)
+
+    def __getstate__(self) -> typing.Tuple[int, int]:
+        """Returns the key as tuple for pickling."""
+        return self.n, self.e
+
+    def __setstate__(self, state: typing.Tuple[int, int]) -> None:
+        """Sets the key from tuple."""
+        self.n, self.e = state
+        AbstractKey.__init__(self, self.n, self.e)
+
+    def __eq__(self, other: typing.Any) -> bool:
+        if other is None:
+            return False
+
+        if not isinstance(other, PublicKey):
+            return False
+
+        return self.n == other.n and self.e == other.e
+
+    def __ne__(self, other: typing.Any) -> bool:
+        return not (self == other)
+
+    def __hash__(self) -> int:
+        return hash((self.n, self.e))
+
+    @classmethod
+    def _load_pkcs1_der(cls, keyfile: bytes) -> "PublicKey":
+        """Loads a key in PKCS#1 DER format.
+
+        :param keyfile: contents of a DER-encoded file that contains the public
+            key.
+        :return: a PublicKey object
+
+        First let's construct a DER encoded key:
+
+        >>> import base64
+        >>> b64der = 'MAwCBQCNGmYtAgMBAAE='
+        >>> der = base64.standard_b64decode(b64der)
+
+        This loads the file:
+
+        >>> PublicKey._load_pkcs1_der(der)
+        PublicKey(2367317549, 65537)
+
+        """
+
+        from pyasn1.codec.der import decoder
+        from rsa.asn1 import AsnPubKey
+
+        (priv, _) = decoder.decode(keyfile, asn1Spec=AsnPubKey())
+        return cls(n=int(priv["modulus"]), e=int(priv["publicExponent"]))
+
+    def _save_pkcs1_der(self) -> bytes:
+        """Saves the public key in PKCS#1 DER format.
+
+        :returns: the DER-encoded public key.
+        :rtype: bytes
+        """
+
+        from pyasn1.codec.der import encoder
+        from rsa.asn1 import AsnPubKey
+
+        # Create the ASN object
+        asn_key = AsnPubKey()
+        asn_key.setComponentByName("modulus", self.n)
+        asn_key.setComponentByName("publicExponent", self.e)
+
+        return encoder.encode(asn_key)
+
+    @classmethod
+    def _load_pkcs1_pem(cls, keyfile: bytes) -> "PublicKey":
+        """Loads a PKCS#1 PEM-encoded public key file.
+
+        The contents of the file before the "-----BEGIN RSA PUBLIC KEY-----" and
+        after the "-----END RSA PUBLIC KEY-----" lines is ignored.
+
+        :param keyfile: contents of a PEM-encoded file that contains the public
+            key.
+        :return: a PublicKey object
+        """
+
+        der = rsa.pem.load_pem(keyfile, "RSA PUBLIC KEY")
+        return cls._load_pkcs1_der(der)
+
+    def _save_pkcs1_pem(self) -> bytes:
+        """Saves a PKCS#1 PEM-encoded public key file.
+
+        :return: contents of a PEM-encoded file that contains the public key.
+        :rtype: bytes
+        """
+
+        der = self._save_pkcs1_der()
+        return rsa.pem.save_pem(der, "RSA PUBLIC KEY")
+
+    @classmethod
+    def load_pkcs1_openssl_pem(cls, keyfile: bytes) -> "PublicKey":
+        """Loads a PKCS#1.5 PEM-encoded public key file from OpenSSL.
+
+        These files can be recognised in that they start with BEGIN PUBLIC KEY
+        rather than BEGIN RSA PUBLIC KEY.
+
+        The contents of the file before the "-----BEGIN PUBLIC KEY-----" and
+        after the "-----END PUBLIC KEY-----" lines is ignored.
+
+        :param keyfile: contents of a PEM-encoded file that contains the public
+            key, from OpenSSL.
+        :type keyfile: bytes
+        :return: a PublicKey object
+        """
+
+        der = rsa.pem.load_pem(keyfile, "PUBLIC KEY")
+        return cls.load_pkcs1_openssl_der(der)
+
+    @classmethod
+    def load_pkcs1_openssl_der(cls, keyfile: bytes) -> "PublicKey":
+        """Loads a PKCS#1 DER-encoded public key file from OpenSSL.
+
+        :param keyfile: contents of a DER-encoded file that contains the public
+            key, from OpenSSL.
+        :return: a PublicKey object
+        """
+
+        from rsa.asn1 import OpenSSLPubKey
+        from pyasn1.codec.der import decoder
+        from pyasn1.type import univ
+
+        (keyinfo, _) = decoder.decode(keyfile, asn1Spec=OpenSSLPubKey())
+
+        if keyinfo["header"]["oid"] != univ.ObjectIdentifier("1.2.840.113549.1.1.1"):
+            raise TypeError("This is not a DER-encoded OpenSSL-compatible public key")
+
+        return cls._load_pkcs1_der(keyinfo["key"][1:])
+
+
+class PrivateKey(AbstractKey):
+    """Represents a private RSA key.
+
+    This key is also known as the 'decryption key'. It contains the 'n', 'e',
+    'd', 'p', 'q' and other values.
+
+    Supports attributes as well as dictionary-like access. Attribute access is
+    faster, though.
+
+    >>> PrivateKey(3247, 65537, 833, 191, 17)
+    PrivateKey(3247, 65537, 833, 191, 17)
+
+    exp1, exp2 and coef will be calculated:
+
+    >>> pk = PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
+    >>> pk.exp1
+    55063
+    >>> pk.exp2
+    10095
+    >>> pk.coef
+    50797
+
+    """
+
+    __slots__ = ("d", "p", "q", "exp1", "exp2", "coef")
+
+    def __init__(self, n: int, e: int, d: int, p: int, q: int) -> None:
+        AbstractKey.__init__(self, n, e)
+        self.d = d
+        self.p = p
+        self.q = q
+
+        # Calculate exponents and coefficient.
+        self.exp1 = int(d % (p - 1))
+        self.exp2 = int(d % (q - 1))
+        self.coef = rsa.common.inverse(q, p)
+
+    def __getitem__(self, key: str) -> int:
+        return getattr(self, key)
+
+    def __repr__(self) -> str:
+        return "PrivateKey(%i, %i, %i, %i, %i)" % (
+            self.n,
+            self.e,
+            self.d,
+            self.p,
+            self.q,
+        )
+
+    def __getstate__(self) -> typing.Tuple[int, int, int, int, int, int, int, int]:
+        """Returns the key as tuple for pickling."""
+        return self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef
+
+    def __setstate__(self, state: typing.Tuple[int, int, int, int, int, int, int, int]) -> None:
+        """Sets the key from tuple."""
+        self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef = state
+        AbstractKey.__init__(self, self.n, self.e)
+
+    def __eq__(self, other: typing.Any) -> bool:
+        if other is None:
+            return False
+
+        if not isinstance(other, PrivateKey):
+            return False
+
+        return (
+            self.n == other.n
+            and self.e == other.e
+            and self.d == other.d
+            and self.p == other.p
+            and self.q == other.q
+            and self.exp1 == other.exp1
+            and self.exp2 == other.exp2
+            and self.coef == other.coef
+        )
+
+    def __ne__(self, other: typing.Any) -> bool:
+        return not (self == other)
+
+    def __hash__(self) -> int:
+        return hash((self.n, self.e, self.d, self.p, self.q, self.exp1, self.exp2, self.coef))
+
+    def blinded_decrypt(self, encrypted: int) -> int:
+        """Decrypts the message using blinding to prevent side-channel attacks.
+
+        :param encrypted: the encrypted message
+        :type encrypted: int
+
+        :returns: the decrypted message
+        :rtype: int
+        """
+
+        # Blinding and un-blinding should be using the same factor
+        blinded, blindfac_inverse = self.blind(encrypted)
+
+        # Instead of using the core functionality, use the Chinese Remainder
+        # Theorem and be 2-4x faster. This the same as:
+        #
+        # decrypted = rsa.core.decrypt_int(blinded, self.d, self.n)
+        s1 = pow(blinded, self.exp1, self.p)
+        s2 = pow(blinded, self.exp2, self.q)
+        h = ((s1 - s2) * self.coef) % self.p
+        decrypted = s2 + self.q * h
+
+        return self.unblind(decrypted, blindfac_inverse)
+
+    def blinded_encrypt(self, message: int) -> int:
+        """Encrypts the message using blinding to prevent side-channel attacks.
+
+        :param message: the message to encrypt
+        :type message: int
+
+        :returns: the encrypted message
+        :rtype: int
+        """
+
+        blinded, blindfac_inverse = self.blind(message)
+        encrypted = rsa.core.encrypt_int(blinded, self.d, self.n)
+        return self.unblind(encrypted, blindfac_inverse)
+
+    @classmethod
+    def _load_pkcs1_der(cls, keyfile: bytes) -> "PrivateKey":
+        """Loads a key in PKCS#1 DER format.
+
+        :param keyfile: contents of a DER-encoded file that contains the private
+            key.
+        :type keyfile: bytes
+        :return: a PrivateKey object
+
+        First let's construct a DER encoded key:
+
+        >>> import base64
+        >>> b64der = 'MC4CAQACBQDeKYlRAgMBAAECBQDHn4npAgMA/icCAwDfxwIDANcXAgInbwIDAMZt'
+        >>> der = base64.standard_b64decode(b64der)
+
+        This loads the file:
+
+        >>> PrivateKey._load_pkcs1_der(der)
+        PrivateKey(3727264081, 65537, 3349121513, 65063, 57287)
+
+        """
+
+        from pyasn1.codec.der import decoder
+
+        (priv, _) = decoder.decode(keyfile)
+
+        # ASN.1 contents of DER encoded private key:
+        #
+        # RSAPrivateKey ::= SEQUENCE {
+        #     version           Version,
+        #     modulus           INTEGER,  -- n
+        #     publicExponent    INTEGER,  -- e
+        #     privateExponent   INTEGER,  -- d
+        #     prime1            INTEGER,  -- p
+        #     prime2            INTEGER,  -- q
+        #     exponent1         INTEGER,  -- d mod (p-1)
+        #     exponent2         INTEGER,  -- d mod (q-1)
+        #     coefficient       INTEGER,  -- (inverse of q) mod p
+        #     otherPrimeInfos   OtherPrimeInfos OPTIONAL
+        # }
+
+        if priv[0] != 0:
+            raise ValueError("Unable to read this file, version %s != 0" % priv[0])
+
+        as_ints = map(int, priv[1:6])
+        key = cls(*as_ints)
+
+        exp1, exp2, coef = map(int, priv[6:9])
+
+        if (key.exp1, key.exp2, key.coef) != (exp1, exp2, coef):
+            warnings.warn(
+                "You have provided a malformed keyfile. Either the exponents "
+                "or the coefficient are incorrect. Using the correct values "
+                "instead.",
+                UserWarning,
+            )
+
+        return key
+
+    def _save_pkcs1_der(self) -> bytes:
+        """Saves the private key in PKCS#1 DER format.
+
+        :returns: the DER-encoded private key.
+        :rtype: bytes
+        """
+
+        from pyasn1.type import univ, namedtype
+        from pyasn1.codec.der import encoder
+
+        class AsnPrivKey(univ.Sequence):
+            componentType = namedtype.NamedTypes(
+                namedtype.NamedType("version", univ.Integer()),
+                namedtype.NamedType("modulus", univ.Integer()),
+                namedtype.NamedType("publicExponent", univ.Integer()),
+                namedtype.NamedType("privateExponent", univ.Integer()),
+                namedtype.NamedType("prime1", univ.Integer()),
+                namedtype.NamedType("prime2", univ.Integer()),
+                namedtype.NamedType("exponent1", univ.Integer()),
+                namedtype.NamedType("exponent2", univ.Integer()),
+                namedtype.NamedType("coefficient", univ.Integer()),
+            )
+
+        # Create the ASN object
+        asn_key = AsnPrivKey()
+        asn_key.setComponentByName("version", 0)
+        asn_key.setComponentByName("modulus", self.n)
+        asn_key.setComponentByName("publicExponent", self.e)
+        asn_key.setComponentByName("privateExponent", self.d)
+        asn_key.setComponentByName("prime1", self.p)
+        asn_key.setComponentByName("prime2", self.q)
+        asn_key.setComponentByName("exponent1", self.exp1)
+        asn_key.setComponentByName("exponent2", self.exp2)
+        asn_key.setComponentByName("coefficient", self.coef)
+
+        return encoder.encode(asn_key)
+
+    @classmethod
+    def _load_pkcs1_pem(cls, keyfile: bytes) -> "PrivateKey":
+        """Loads a PKCS#1 PEM-encoded private key file.
+
+        The contents of the file before the "-----BEGIN RSA PRIVATE KEY-----" and
+        after the "-----END RSA PRIVATE KEY-----" lines is ignored.
+
+        :param keyfile: contents of a PEM-encoded file that contains the private
+            key.
+        :type keyfile: bytes
+        :return: a PrivateKey object
+        """
+
+        der = rsa.pem.load_pem(keyfile, b"RSA PRIVATE KEY")
+        return cls._load_pkcs1_der(der)
+
+    def _save_pkcs1_pem(self) -> bytes:
+        """Saves a PKCS#1 PEM-encoded private key file.
+
+        :return: contents of a PEM-encoded file that contains the private key.
+        :rtype: bytes
+        """
+
+        der = self._save_pkcs1_der()
+        return rsa.pem.save_pem(der, b"RSA PRIVATE KEY")
+
+
+def find_p_q(
+    nbits: int,
+    getprime_func: typing.Callable[[int], int] = rsa.prime.getprime,
+    accurate: bool = True,
+) -> typing.Tuple[int, int]:
+    """Returns a tuple of two different primes of nbits bits each.
+
+    The resulting p * q has exactly 2 * nbits bits, and the returned p and q
+    will not be equal.
+
+    :param nbits: the number of bits in each of p and q.
+    :param getprime_func: the getprime function, defaults to
+        :py:func:`rsa.prime.getprime`.
+
+        *Introduced in Python-RSA 3.1*
+
+    :param accurate: whether to enable accurate mode or not.
+    :returns: (p, q), where p > q
+
+    >>> (p, q) = find_p_q(128)
+    >>> from rsa import common
+    >>> common.bit_size(p * q)
+    256
+
+    When not in accurate mode, the number of bits can be slightly less
+
+    >>> (p, q) = find_p_q(128, accurate=False)
+    >>> from rsa import common
+    >>> common.bit_size(p * q) <= 256
+    True
+    >>> common.bit_size(p * q) > 240
+    True
+
+    """
+
+    total_bits = nbits * 2
+
+    # Make sure that p and q aren't too close or the factoring programs can
+    # factor n.
+    shift = nbits // 16
+    pbits = nbits + shift
+    qbits = nbits - shift
+
+    # Choose the two initial primes
+    p = getprime_func(pbits)
+    q = getprime_func(qbits)
+
+    def is_acceptable(p: int, q: int) -> bool:
+        """Returns True iff p and q are acceptable:
+
+        - p and q differ
+        - (p * q) has the right nr of bits (when accurate=True)
+        """
+
+        if p == q:
+            return False
+
+        if not accurate:
+            return True
+
+        # Make sure we have just the right amount of bits
+        found_size = rsa.common.bit_size(p * q)
+        return total_bits == found_size
+
+    # Keep choosing other primes until they match our requirements.
+    change_p = False
+    while not is_acceptable(p, q):
+        # Change p on one iteration and q on the other
+        if change_p:
+            p = getprime_func(pbits)
+        else:
+            q = getprime_func(qbits)
+
+        change_p = not change_p
+
+    # We want p > q as described on
+    # http://www.di-mgt.com.au/rsa_alg.html#crt
+    return max(p, q), min(p, q)
+
+
+def calculate_keys_custom_exponent(p: int, q: int, exponent: int) -> typing.Tuple[int, int]:
+    """Calculates an encryption and a decryption key given p, q and an exponent,
+    and returns them as a tuple (e, d)
+
+    :param p: the first large prime
+    :param q: the second large prime
+    :param exponent: the exponent for the key; only change this if you know
+        what you're doing, as the exponent influences how difficult your
+        private key can be cracked. A very common choice for e is 65537.
+    :type exponent: int
+
+    """
+
+    phi_n = (p - 1) * (q - 1)
+
+    try:
+        d = rsa.common.inverse(exponent, phi_n)
+    except rsa.common.NotRelativePrimeError as ex:
+        raise rsa.common.NotRelativePrimeError(
+            exponent,
+            phi_n,
+            ex.d,
+            msg="e (%d) and phi_n (%d) are not relatively prime (divider=%i)"
+            % (exponent, phi_n, ex.d),
+        ) from ex
+
+    if (exponent * d) % phi_n != 1:
+        raise ValueError(
+            "e (%d) and d (%d) are not mult. inv. modulo " "phi_n (%d)" % (exponent, d, phi_n)
+        )
+
+    return exponent, d
+
+
+def calculate_keys(p: int, q: int) -> typing.Tuple[int, int]:
+    """Calculates an encryption and a decryption key given p and q, and
+    returns them as a tuple (e, d)
+
+    :param p: the first large prime
+    :param q: the second large prime
+
+    :return: tuple (e, d) with the encryption and decryption exponents.
+    """
+
+    return calculate_keys_custom_exponent(p, q, DEFAULT_EXPONENT)
+
+
+def gen_keys(
+    nbits: int,
+    getprime_func: typing.Callable[[int], int],
+    accurate: bool = True,
+    exponent: int = DEFAULT_EXPONENT,
+) -> typing.Tuple[int, int, int, int]:
+    """Generate RSA keys of nbits bits. Returns (p, q, e, d).
+
+    Note: this can take a long time, depending on the key size.
+
+    :param nbits: the total number of bits in ``p`` and ``q``. Both ``p`` and
+        ``q`` will use ``nbits/2`` bits.
+    :param getprime_func: either :py:func:`rsa.prime.getprime` or a function
+        with similar signature.
+    :param exponent: the exponent for the key; only change this if you know
+        what you're doing, as the exponent influences how difficult your
+        private key can be cracked. A very common choice for e is 65537.
+    :type exponent: int
+    """
+
+    # Regenerate p and q values, until calculate_keys doesn't raise a
+    # ValueError.
+    while True:
+        (p, q) = find_p_q(nbits // 2, getprime_func, accurate)
+        try:
+            (e, d) = calculate_keys_custom_exponent(p, q, exponent=exponent)
+            break
+        except ValueError:
+            pass
+
+    return p, q, e, d
+
+
+def newkeys(
+    nbits: int,
+    accurate: bool = True,
+    poolsize: int = 1,
+    exponent: int = DEFAULT_EXPONENT,
+) -> typing.Tuple[PublicKey, PrivateKey]:
+    """Generates public and private keys, and returns them as (pub, priv).
+
+    The public key is also known as the 'encryption key', and is a
+    :py:class:`rsa.PublicKey` object. The private key is also known as the
+    'decryption key' and is a :py:class:`rsa.PrivateKey` object.
+
+    :param nbits: the number of bits required to store ``n = p*q``.
+    :param accurate: when True, ``n`` will have exactly the number of bits you
+        asked for. However, this makes key generation much slower. When False,
+        `n`` may have slightly less bits.
+    :param poolsize: the number of processes to use to generate the prime
+        numbers. If set to a number > 1, a parallel algorithm will be used.
+        This requires Python 2.6 or newer.
+    :param exponent: the exponent for the key; only change this if you know
+        what you're doing, as the exponent influences how difficult your
+        private key can be cracked. A very common choice for e is 65537.
+    :type exponent: int
+
+    :returns: a tuple (:py:class:`rsa.PublicKey`, :py:class:`rsa.PrivateKey`)
+
+    The ``poolsize`` parameter was added in *Python-RSA 3.1* and requires
+    Python 2.6 or newer.
+
+    """
+
+    if nbits < 16:
+        raise ValueError("Key too small")
+
+    if poolsize < 1:
+        raise ValueError("Pool size (%i) should be >= 1" % poolsize)
+
+    # Determine which getprime function to use
+    if poolsize > 1:
+        from rsa import parallel
+
+        def getprime_func(nbits: int) -> int:
+            return parallel.getprime(nbits, poolsize=poolsize)
+
+    else:
+        getprime_func = rsa.prime.getprime
+
+    # Generate the key components
+    (p, q, e, d) = gen_keys(nbits, getprime_func, accurate=accurate, exponent=exponent)
+
+    # Create the key objects
+    n = p * q
+
+    return (PublicKey(n, e), PrivateKey(n, e, d, p, q))
+
+
+__all__ = ["PublicKey", "PrivateKey", "newkeys"]
+
+if __name__ == "__main__":
+    import doctest
+
+    try:
+        for count in range(100):
+            (failures, tests) = doctest.testmod()
+            if failures:
+                break
+
+            if (count % 10 == 0 and count) or count == 1:
+                print("%i times" % count)
+    except KeyboardInterrupt:
+        print("Aborted")
+    else:
+        print("Doctests done")
diff --git a/.venv/lib/python3.12/site-packages/rsa/parallel.py b/.venv/lib/python3.12/site-packages/rsa/parallel.py
new file mode 100644
index 00000000..ab992480
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/parallel.py
@@ -0,0 +1,96 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Functions for parallel computation on multiple cores.
+
+Introduced in Python-RSA 3.1.
+
+.. note::
+
+    Requires Python 2.6 or newer.
+
+"""
+
+import multiprocessing as mp
+from multiprocessing.connection import Connection
+
+import rsa.prime
+import rsa.randnum
+
+
+def _find_prime(nbits: int, pipe: Connection) -> None:
+    while True:
+        integer = rsa.randnum.read_random_odd_int(nbits)
+
+        # Test for primeness
+        if rsa.prime.is_prime(integer):
+            pipe.send(integer)
+            return
+
+
+def getprime(nbits: int, poolsize: int) -> int:
+    """Returns a prime number that can be stored in 'nbits' bits.
+
+    Works in multiple threads at the same time.
+
+    >>> p = getprime(128, 3)
+    >>> rsa.prime.is_prime(p-1)
+    False
+    >>> rsa.prime.is_prime(p)
+    True
+    >>> rsa.prime.is_prime(p+1)
+    False
+
+    >>> from rsa import common
+    >>> common.bit_size(p) == 128
+    True
+
+    """
+
+    (pipe_recv, pipe_send) = mp.Pipe(duplex=False)
+
+    # Create processes
+    try:
+        procs = [mp.Process(target=_find_prime, args=(nbits, pipe_send)) for _ in range(poolsize)]
+        # Start processes
+        for p in procs:
+            p.start()
+
+        result = pipe_recv.recv()
+    finally:
+        pipe_recv.close()
+        pipe_send.close()
+
+    # Terminate processes
+    for p in procs:
+        p.terminate()
+
+    return result
+
+
+__all__ = ["getprime"]
+
+if __name__ == "__main__":
+    print("Running doctests 1000x or until failure")
+    import doctest
+
+    for count in range(100):
+        (failures, tests) = doctest.testmod()
+        if failures:
+            break
+
+        if count % 10 == 0 and count:
+            print("%i times" % count)
+
+    print("Doctests done")
diff --git a/.venv/lib/python3.12/site-packages/rsa/pem.py b/.venv/lib/python3.12/site-packages/rsa/pem.py
new file mode 100644
index 00000000..eb9c0446
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/pem.py
@@ -0,0 +1,134 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Functions that load and write PEM-encoded files."""
+
+import base64
+import typing
+
+# Should either be ASCII strings or bytes.
+FlexiText = typing.Union[str, bytes]
+
+
+def _markers(pem_marker: FlexiText) -> typing.Tuple[bytes, bytes]:
+    """
+    Returns the start and end PEM markers, as bytes.
+    """
+
+    if not isinstance(pem_marker, bytes):
+        pem_marker = pem_marker.encode("ascii")
+
+    return (
+        b"-----BEGIN " + pem_marker + b"-----",
+        b"-----END " + pem_marker + b"-----",
+    )
+
+
+def _pem_lines(contents: bytes, pem_start: bytes, pem_end: bytes) -> typing.Iterator[bytes]:
+    """Generator over PEM lines between pem_start and pem_end."""
+
+    in_pem_part = False
+    seen_pem_start = False
+
+    for line in contents.splitlines():
+        line = line.strip()
+
+        # Skip empty lines
+        if not line:
+            continue
+
+        # Handle start marker
+        if line == pem_start:
+            if in_pem_part:
+                raise ValueError('Seen start marker "%r" twice' % pem_start)
+
+            in_pem_part = True
+            seen_pem_start = True
+            continue
+
+        # Skip stuff before first marker
+        if not in_pem_part:
+            continue
+
+        # Handle end marker
+        if in_pem_part and line == pem_end:
+            in_pem_part = False
+            break
+
+        # Load fields
+        if b":" in line:
+            continue
+
+        yield line
+
+    # Do some sanity checks
+    if not seen_pem_start:
+        raise ValueError('No PEM start marker "%r" found' % pem_start)
+
+    if in_pem_part:
+        raise ValueError('No PEM end marker "%r" found' % pem_end)
+
+
+def load_pem(contents: FlexiText, pem_marker: FlexiText) -> bytes:
+    """Loads a PEM file.
+
+    :param contents: the contents of the file to interpret
+    :param pem_marker: the marker of the PEM content, such as 'RSA PRIVATE KEY'
+        when your file has '-----BEGIN RSA PRIVATE KEY-----' and
+        '-----END RSA PRIVATE KEY-----' markers.
+
+    :return: the base64-decoded content between the start and end markers.
+
+    @raise ValueError: when the content is invalid, for example when the start
+        marker cannot be found.
+
+    """
+
+    # We want bytes, not text. If it's text, it can be converted to ASCII bytes.
+    if not isinstance(contents, bytes):
+        contents = contents.encode("ascii")
+
+    (pem_start, pem_end) = _markers(pem_marker)
+    pem_lines = [line for line in _pem_lines(contents, pem_start, pem_end)]
+
+    # Base64-decode the contents
+    pem = b"".join(pem_lines)
+    return base64.standard_b64decode(pem)
+
+
+def save_pem(contents: bytes, pem_marker: FlexiText) -> bytes:
+    """Saves a PEM file.
+
+    :param contents: the contents to encode in PEM format
+    :param pem_marker: the marker of the PEM content, such as 'RSA PRIVATE KEY'
+        when your file has '-----BEGIN RSA PRIVATE KEY-----' and
+        '-----END RSA PRIVATE KEY-----' markers.
+
+    :return: the base64-encoded content between the start and end markers, as bytes.
+
+    """
+
+    (pem_start, pem_end) = _markers(pem_marker)
+
+    b64 = base64.standard_b64encode(contents).replace(b"\n", b"")
+    pem_lines = [pem_start]
+
+    for block_start in range(0, len(b64), 64):
+        block = b64[block_start : block_start + 64]
+        pem_lines.append(block)
+
+    pem_lines.append(pem_end)
+    pem_lines.append(b"")
+
+    return b"\n".join(pem_lines)
diff --git a/.venv/lib/python3.12/site-packages/rsa/pkcs1.py b/.venv/lib/python3.12/site-packages/rsa/pkcs1.py
new file mode 100644
index 00000000..b7f54220
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/pkcs1.py
@@ -0,0 +1,485 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Functions for PKCS#1 version 1.5 encryption and signing
+
+This module implements certain functionality from PKCS#1 version 1.5. For a
+very clear example, read http://www.di-mgt.com.au/rsa_alg.html#pkcs1schemes
+
+At least 8 bytes of random padding is used when encrypting a message. This makes
+these methods much more secure than the ones in the ``rsa`` module.
+
+WARNING: this module leaks information when decryption fails. The exceptions
+that are raised contain the Python traceback information, which can be used to
+deduce where in the process the failure occurred. DO NOT PASS SUCH INFORMATION
+to your users.
+"""
+
+import hashlib
+import os
+import sys
+import typing
+from hmac import compare_digest
+
+from . import common, transform, core, key
+
+if typing.TYPE_CHECKING:
+    HashType = hashlib._Hash
+else:
+    HashType = typing.Any
+
+# ASN.1 codes that describe the hash algorithm used.
+HASH_ASN1 = {
+    "MD5": b"\x30\x20\x30\x0c\x06\x08\x2a\x86\x48\x86\xf7\x0d\x02\x05\x05\x00\x04\x10",
+    "SHA-1": b"\x30\x21\x30\x09\x06\x05\x2b\x0e\x03\x02\x1a\x05\x00\x04\x14",
+    "SHA-224": b"\x30\x2d\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x04\x05\x00\x04\x1c",
+    "SHA-256": b"\x30\x31\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x01\x05\x00\x04\x20",
+    "SHA-384": b"\x30\x41\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x02\x05\x00\x04\x30",
+    "SHA-512": b"\x30\x51\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x03\x05\x00\x04\x40",
+}
+
+HASH_METHODS: typing.Dict[str, typing.Callable[[], HashType]] = {
+    "MD5": hashlib.md5,
+    "SHA-1": hashlib.sha1,
+    "SHA-224": hashlib.sha224,
+    "SHA-256": hashlib.sha256,
+    "SHA-384": hashlib.sha384,
+    "SHA-512": hashlib.sha512,
+}
+"""Hash methods supported by this library."""
+
+
+if sys.version_info >= (3, 6):
+    # Python 3.6 introduced SHA3 support.
+    HASH_ASN1.update(
+        {
+            "SHA3-256": b"\x30\x31\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x08\x05\x00\x04\x20",
+            "SHA3-384": b"\x30\x41\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x09\x05\x00\x04\x30",
+            "SHA3-512": b"\x30\x51\x30\x0d\x06\x09\x60\x86\x48\x01\x65\x03\x04\x02\x0a\x05\x00\x04\x40",
+        }
+    )
+
+    HASH_METHODS.update(
+        {
+            "SHA3-256": hashlib.sha3_256,
+            "SHA3-384": hashlib.sha3_384,
+            "SHA3-512": hashlib.sha3_512,
+        }
+    )
+
+
+class CryptoError(Exception):
+    """Base class for all exceptions in this module."""
+
+
+class DecryptionError(CryptoError):
+    """Raised when decryption fails."""
+
+
+class VerificationError(CryptoError):
+    """Raised when verification fails."""
+
+
+def _pad_for_encryption(message: bytes, target_length: int) -> bytes:
+    r"""Pads the message for encryption, returning the padded message.
+
+    :return: 00 02 RANDOM_DATA 00 MESSAGE
+
+    >>> block = _pad_for_encryption(b'hello', 16)
+    >>> len(block)
+    16
+    >>> block[0:2]
+    b'\x00\x02'
+    >>> block[-6:]
+    b'\x00hello'
+
+    """
+
+    max_msglength = target_length - 11
+    msglength = len(message)
+
+    if msglength > max_msglength:
+        raise OverflowError(
+            "%i bytes needed for message, but there is only"
+            " space for %i" % (msglength, max_msglength)
+        )
+
+    # Get random padding
+    padding = b""
+    padding_length = target_length - msglength - 3
+
+    # We remove 0-bytes, so we'll end up with less padding than we've asked for,
+    # so keep adding data until we're at the correct length.
+    while len(padding) < padding_length:
+        needed_bytes = padding_length - len(padding)
+
+        # Always read at least 8 bytes more than we need, and trim off the rest
+        # after removing the 0-bytes. This increases the chance of getting
+        # enough bytes, especially when needed_bytes is small
+        new_padding = os.urandom(needed_bytes + 5)
+        new_padding = new_padding.replace(b"\x00", b"")
+        padding = padding + new_padding[:needed_bytes]
+
+    assert len(padding) == padding_length
+
+    return b"".join([b"\x00\x02", padding, b"\x00", message])
+
+
+def _pad_for_signing(message: bytes, target_length: int) -> bytes:
+    r"""Pads the message for signing, returning the padded message.
+
+    The padding is always a repetition of FF bytes.
+
+    :return: 00 01 PADDING 00 MESSAGE
+
+    >>> block = _pad_for_signing(b'hello', 16)
+    >>> len(block)
+    16
+    >>> block[0:2]
+    b'\x00\x01'
+    >>> block[-6:]
+    b'\x00hello'
+    >>> block[2:-6]
+    b'\xff\xff\xff\xff\xff\xff\xff\xff'
+
+    """
+
+    max_msglength = target_length - 11
+    msglength = len(message)
+
+    if msglength > max_msglength:
+        raise OverflowError(
+            "%i bytes needed for message, but there is only"
+            " space for %i" % (msglength, max_msglength)
+        )
+
+    padding_length = target_length - msglength - 3
+
+    return b"".join([b"\x00\x01", padding_length * b"\xff", b"\x00", message])
+
+
+def encrypt(message: bytes, pub_key: key.PublicKey) -> bytes:
+    """Encrypts the given message using PKCS#1 v1.5
+
+    :param message: the message to encrypt. Must be a byte string no longer than
+        ``k-11`` bytes, where ``k`` is the number of bytes needed to encode
+        the ``n`` component of the public key.
+    :param pub_key: the :py:class:`rsa.PublicKey` to encrypt with.
+    :raise OverflowError: when the message is too large to fit in the padded
+        block.
+
+    >>> from rsa import key, common
+    >>> (pub_key, priv_key) = key.newkeys(256)
+    >>> message = b'hello'
+    >>> crypto = encrypt(message, pub_key)
+
+    The crypto text should be just as long as the public key 'n' component:
+
+    >>> len(crypto) == common.byte_size(pub_key.n)
+    True
+
+    """
+
+    keylength = common.byte_size(pub_key.n)
+    padded = _pad_for_encryption(message, keylength)
+
+    payload = transform.bytes2int(padded)
+    encrypted = core.encrypt_int(payload, pub_key.e, pub_key.n)
+    block = transform.int2bytes(encrypted, keylength)
+
+    return block
+
+
+def decrypt(crypto: bytes, priv_key: key.PrivateKey) -> bytes:
+    r"""Decrypts the given message using PKCS#1 v1.5
+
+    The decryption is considered 'failed' when the resulting cleartext doesn't
+    start with the bytes 00 02, or when the 00 byte between the padding and
+    the message cannot be found.
+
+    :param crypto: the crypto text as returned by :py:func:`rsa.encrypt`
+    :param priv_key: the :py:class:`rsa.PrivateKey` to decrypt with.
+    :raise DecryptionError: when the decryption fails. No details are given as
+        to why the code thinks the decryption fails, as this would leak
+        information about the private key.
+
+
+    >>> import rsa
+    >>> (pub_key, priv_key) = rsa.newkeys(256)
+
+    It works with strings:
+
+    >>> crypto = encrypt(b'hello', pub_key)
+    >>> decrypt(crypto, priv_key)
+    b'hello'
+
+    And with binary data:
+
+    >>> crypto = encrypt(b'\x00\x00\x00\x00\x01', pub_key)
+    >>> decrypt(crypto, priv_key)
+    b'\x00\x00\x00\x00\x01'
+
+    Altering the encrypted information will *likely* cause a
+    :py:class:`rsa.pkcs1.DecryptionError`. If you want to be *sure*, use
+    :py:func:`rsa.sign`.
+
+
+    .. warning::
+
+        Never display the stack trace of a
+        :py:class:`rsa.pkcs1.DecryptionError` exception. It shows where in the
+        code the exception occurred, and thus leaks information about the key.
+        It's only a tiny bit of information, but every bit makes cracking the
+        keys easier.
+
+    >>> crypto = encrypt(b'hello', pub_key)
+    >>> crypto = crypto[0:5] + b'X' + crypto[6:] # change a byte
+    >>> decrypt(crypto, priv_key)
+    Traceback (most recent call last):
+    ...
+    rsa.pkcs1.DecryptionError: Decryption failed
+
+    """
+
+    blocksize = common.byte_size(priv_key.n)
+    encrypted = transform.bytes2int(crypto)
+    decrypted = priv_key.blinded_decrypt(encrypted)
+    cleartext = transform.int2bytes(decrypted, blocksize)
+
+    # Detect leading zeroes in the crypto. These are not reflected in the
+    # encrypted value (as leading zeroes do not influence the value of an
+    # integer). This fixes CVE-2020-13757.
+    if len(crypto) > blocksize:
+        # This is operating on public information, so doesn't need to be constant-time.
+        raise DecryptionError("Decryption failed")
+
+    # If we can't find the cleartext marker, decryption failed.
+    cleartext_marker_bad = not compare_digest(cleartext[:2], b"\x00\x02")
+
+    # Find the 00 separator between the padding and the message
+    sep_idx = cleartext.find(b"\x00", 2)
+
+    # sep_idx indicates the position of the `\x00` separator that separates the
+    # padding from the actual message. The padding should be at least 8 bytes
+    # long (see https://tools.ietf.org/html/rfc8017#section-7.2.2 step 3), which
+    # means the separator should be at least at index 10 (because of the
+    # `\x00\x02` marker that precedes it).
+    sep_idx_bad = sep_idx < 10
+
+    anything_bad = cleartext_marker_bad | sep_idx_bad
+    if anything_bad:
+        raise DecryptionError("Decryption failed")
+
+    return cleartext[sep_idx + 1 :]
+
+
+def sign_hash(hash_value: bytes, priv_key: key.PrivateKey, hash_method: str) -> bytes:
+    """Signs a precomputed hash with the private key.
+
+    Hashes the message, then signs the hash with the given key. This is known
+    as a "detached signature", because the message itself isn't altered.
+
+    :param hash_value: A precomputed hash to sign (ignores message).
+    :param priv_key: the :py:class:`rsa.PrivateKey` to sign with
+    :param hash_method: the hash method used on the message. Use 'MD5', 'SHA-1',
+        'SHA-224', SHA-256', 'SHA-384' or 'SHA-512'.
+    :return: a message signature block.
+    :raise OverflowError: if the private key is too small to contain the
+        requested hash.
+
+    """
+
+    # Get the ASN1 code for this hash method
+    if hash_method not in HASH_ASN1:
+        raise ValueError("Invalid hash method: %s" % hash_method)
+    asn1code = HASH_ASN1[hash_method]
+
+    # Encrypt the hash with the private key
+    cleartext = asn1code + hash_value
+    keylength = common.byte_size(priv_key.n)
+    padded = _pad_for_signing(cleartext, keylength)
+
+    payload = transform.bytes2int(padded)
+    encrypted = priv_key.blinded_encrypt(payload)
+    block = transform.int2bytes(encrypted, keylength)
+
+    return block
+
+
+def sign(message: bytes, priv_key: key.PrivateKey, hash_method: str) -> bytes:
+    """Signs the message with the private key.
+
+    Hashes the message, then signs the hash with the given key. This is known
+    as a "detached signature", because the message itself isn't altered.
+
+    :param message: the message to sign. Can be an 8-bit string or a file-like
+        object. If ``message`` has a ``read()`` method, it is assumed to be a
+        file-like object.
+    :param priv_key: the :py:class:`rsa.PrivateKey` to sign with
+    :param hash_method: the hash method used on the message. Use 'MD5', 'SHA-1',
+        'SHA-224', SHA-256', 'SHA-384' or 'SHA-512'.
+    :return: a message signature block.
+    :raise OverflowError: if the private key is too small to contain the
+        requested hash.
+
+    """
+
+    msg_hash = compute_hash(message, hash_method)
+    return sign_hash(msg_hash, priv_key, hash_method)
+
+
+def verify(message: bytes, signature: bytes, pub_key: key.PublicKey) -> str:
+    """Verifies that the signature matches the message.
+
+    The hash method is detected automatically from the signature.
+
+    :param message: the signed message. Can be an 8-bit string or a file-like
+        object. If ``message`` has a ``read()`` method, it is assumed to be a
+        file-like object.
+    :param signature: the signature block, as created with :py:func:`rsa.sign`.
+    :param pub_key: the :py:class:`rsa.PublicKey` of the person signing the message.
+    :raise VerificationError: when the signature doesn't match the message.
+    :returns: the name of the used hash.
+
+    """
+
+    keylength = common.byte_size(pub_key.n)
+    encrypted = transform.bytes2int(signature)
+    decrypted = core.decrypt_int(encrypted, pub_key.e, pub_key.n)
+    clearsig = transform.int2bytes(decrypted, keylength)
+
+    # Get the hash method
+    method_name = _find_method_hash(clearsig)
+    message_hash = compute_hash(message, method_name)
+
+    # Reconstruct the expected padded hash
+    cleartext = HASH_ASN1[method_name] + message_hash
+    expected = _pad_for_signing(cleartext, keylength)
+
+    if len(signature) != keylength:
+        raise VerificationError("Verification failed")
+
+    # Compare with the signed one
+    if expected != clearsig:
+        raise VerificationError("Verification failed")
+
+    return method_name
+
+
+def find_signature_hash(signature: bytes, pub_key: key.PublicKey) -> str:
+    """Returns the hash name detected from the signature.
+
+    If you also want to verify the message, use :py:func:`rsa.verify()` instead.
+    It also returns the name of the used hash.
+
+    :param signature: the signature block, as created with :py:func:`rsa.sign`.
+    :param pub_key: the :py:class:`rsa.PublicKey` of the person signing the message.
+    :returns: the name of the used hash.
+    """
+
+    keylength = common.byte_size(pub_key.n)
+    encrypted = transform.bytes2int(signature)
+    decrypted = core.decrypt_int(encrypted, pub_key.e, pub_key.n)
+    clearsig = transform.int2bytes(decrypted, keylength)
+
+    return _find_method_hash(clearsig)
+
+
+def yield_fixedblocks(infile: typing.BinaryIO, blocksize: int) -> typing.Iterator[bytes]:
+    """Generator, yields each block of ``blocksize`` bytes in the input file.
+
+    :param infile: file to read and separate in blocks.
+    :param blocksize: block size in bytes.
+    :returns: a generator that yields the contents of each block
+    """
+
+    while True:
+        block = infile.read(blocksize)
+
+        read_bytes = len(block)
+        if read_bytes == 0:
+            break
+
+        yield block
+
+        if read_bytes < blocksize:
+            break
+
+
+def compute_hash(message: typing.Union[bytes, typing.BinaryIO], method_name: str) -> bytes:
+    """Returns the message digest.
+
+    :param message: the signed message. Can be an 8-bit string or a file-like
+        object. If ``message`` has a ``read()`` method, it is assumed to be a
+        file-like object.
+    :param method_name: the hash method, must be a key of
+        :py:const:`rsa.pkcs1.HASH_METHODS`.
+
+    """
+
+    if method_name not in HASH_METHODS:
+        raise ValueError("Invalid hash method: %s" % method_name)
+
+    method = HASH_METHODS[method_name]
+    hasher = method()
+
+    if isinstance(message, bytes):
+        hasher.update(message)
+    else:
+        assert hasattr(message, "read") and hasattr(message.read, "__call__")
+        # read as 1K blocks
+        for block in yield_fixedblocks(message, 1024):
+            hasher.update(block)
+
+    return hasher.digest()
+
+
+def _find_method_hash(clearsig: bytes) -> str:
+    """Finds the hash method.
+
+    :param clearsig: full padded ASN1 and hash.
+    :return: the used hash method.
+    :raise VerificationFailed: when the hash method cannot be found
+    """
+
+    for (hashname, asn1code) in HASH_ASN1.items():
+        if asn1code in clearsig:
+            return hashname
+
+    raise VerificationError("Verification failed")
+
+
+__all__ = [
+    "encrypt",
+    "decrypt",
+    "sign",
+    "verify",
+    "DecryptionError",
+    "VerificationError",
+    "CryptoError",
+]
+
+if __name__ == "__main__":
+    print("Running doctests 1000x or until failure")
+    import doctest
+
+    for count in range(1000):
+        (failures, tests) = doctest.testmod()
+        if failures:
+            break
+
+        if count % 100 == 0 and count:
+            print("%i times" % count)
+
+    print("Doctests done")
diff --git a/.venv/lib/python3.12/site-packages/rsa/pkcs1_v2.py b/.venv/lib/python3.12/site-packages/rsa/pkcs1_v2.py
new file mode 100644
index 00000000..cc2c3170
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/pkcs1_v2.py
@@ -0,0 +1,100 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Functions for PKCS#1 version 2 encryption and signing
+
+This module implements certain functionality from PKCS#1 version 2. Main
+documentation is RFC 2437: https://tools.ietf.org/html/rfc2437
+"""
+
+from rsa import (
+    common,
+    pkcs1,
+    transform,
+)
+
+
+def mgf1(seed: bytes, length: int, hasher: str = "SHA-1") -> bytes:
+    """
+    MGF1 is a Mask Generation Function based on a hash function.
+
+    A mask generation function takes an octet string of variable length and a
+    desired output length as input, and outputs an octet string of the desired
+    length. The plaintext-awareness of RSAES-OAEP relies on the random nature of
+    the output of the mask generation function, which in turn relies on the
+    random nature of the underlying hash.
+
+    :param bytes seed: seed from which mask is generated, an octet string
+    :param int length: intended length in octets of the mask, at most 2^32(hLen)
+    :param str hasher: hash function (hLen denotes the length in octets of the hash
+        function output)
+
+    :return: mask, an octet string of length `length`
+    :rtype: bytes
+
+    :raise OverflowError: when `length` is too large for the specified `hasher`
+    :raise ValueError: when specified `hasher` is invalid
+    """
+
+    try:
+        hash_length = pkcs1.HASH_METHODS[hasher]().digest_size
+    except KeyError as ex:
+        raise ValueError(
+            "Invalid `hasher` specified. Please select one of: {hash_list}".format(
+                hash_list=", ".join(sorted(pkcs1.HASH_METHODS.keys()))
+            )
+        ) from ex
+
+    # If l > 2^32(hLen), output "mask too long" and stop.
+    if length > (2 ** 32 * hash_length):
+        raise OverflowError(
+            "Desired length should be at most 2**32 times the hasher's output "
+            "length ({hash_length} for {hasher} function)".format(
+                hash_length=hash_length,
+                hasher=hasher,
+            )
+        )
+
+    # Looping `counter` from 0 to ceil(l / hLen)-1, build `output` based on the
+    # hashes formed by (`seed` + C), being `C` an octet string of length 4
+    # generated by converting `counter` with the primitive I2OSP
+    output = b"".join(
+        pkcs1.compute_hash(
+            seed + transform.int2bytes(counter, fill_size=4),
+            method_name=hasher,
+        )
+        for counter in range(common.ceil_div(length, hash_length) + 1)
+    )
+
+    # Output the leading `length` octets of `output` as the octet string mask.
+    return output[:length]
+
+
+__all__ = [
+    "mgf1",
+]
+
+if __name__ == "__main__":
+    print("Running doctests 1000x or until failure")
+    import doctest
+
+    for count in range(1000):
+        (failures, tests) = doctest.testmod()
+        if failures:
+            break
+
+        if count % 100 == 0 and count:
+            print("%i times" % count)
+
+    print("Doctests done")
diff --git a/.venv/lib/python3.12/site-packages/rsa/prime.py b/.venv/lib/python3.12/site-packages/rsa/prime.py
new file mode 100644
index 00000000..481c4d77
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/prime.py
@@ -0,0 +1,198 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Numerical functions related to primes.
+
+Implementation based on the book Algorithm Design by Michael T. Goodrich and
+Roberto Tamassia, 2002.
+"""
+
+import rsa.common
+import rsa.randnum
+
+__all__ = ["getprime", "are_relatively_prime"]
+
+
+def gcd(p: int, q: int) -> int:
+    """Returns the greatest common divisor of p and q
+
+    >>> gcd(48, 180)
+    12
+    """
+
+    while q != 0:
+        (p, q) = (q, p % q)
+    return p
+
+
+def get_primality_testing_rounds(number: int) -> int:
+    """Returns minimum number of rounds for Miller-Rabing primality testing,
+    based on number bitsize.
+
+    According to NIST FIPS 186-4, Appendix C, Table C.3, minimum number of
+    rounds of M-R testing, using an error probability of 2 ** (-100), for
+    different p, q bitsizes are:
+      * p, q bitsize: 512; rounds: 7
+      * p, q bitsize: 1024; rounds: 4
+      * p, q bitsize: 1536; rounds: 3
+    See: http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.186-4.pdf
+    """
+
+    # Calculate number bitsize.
+    bitsize = rsa.common.bit_size(number)
+    # Set number of rounds.
+    if bitsize >= 1536:
+        return 3
+    if bitsize >= 1024:
+        return 4
+    if bitsize >= 512:
+        return 7
+    # For smaller bitsizes, set arbitrary number of rounds.
+    return 10
+
+
+def miller_rabin_primality_testing(n: int, k: int) -> bool:
+    """Calculates whether n is composite (which is always correct) or prime
+    (which theoretically is incorrect with error probability 4**-k), by
+    applying Miller-Rabin primality testing.
+
+    For reference and implementation example, see:
+    https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test
+
+    :param n: Integer to be tested for primality.
+    :type n: int
+    :param k: Number of rounds (witnesses) of Miller-Rabin testing.
+    :type k: int
+    :return: False if the number is composite, True if it's probably prime.
+    :rtype: bool
+    """
+
+    # prevent potential infinite loop when d = 0
+    if n < 2:
+        return False
+
+    # Decompose (n - 1) to write it as (2 ** r) * d
+    # While d is even, divide it by 2 and increase the exponent.
+    d = n - 1
+    r = 0
+
+    while not (d & 1):
+        r += 1
+        d >>= 1
+
+    # Test k witnesses.
+    for _ in range(k):
+        # Generate random integer a, where 2 <= a <= (n - 2)
+        a = rsa.randnum.randint(n - 3) + 1
+
+        x = pow(a, d, n)
+        if x == 1 or x == n - 1:
+            continue
+
+        for _ in range(r - 1):
+            x = pow(x, 2, n)
+            if x == 1:
+                # n is composite.
+                return False
+            if x == n - 1:
+                # Exit inner loop and continue with next witness.
+                break
+        else:
+            # If loop doesn't break, n is composite.
+            return False
+
+    return True
+
+
+def is_prime(number: int) -> bool:
+    """Returns True if the number is prime, and False otherwise.
+
+    >>> is_prime(2)
+    True
+    >>> is_prime(42)
+    False
+    >>> is_prime(41)
+    True
+    """
+
+    # Check for small numbers.
+    if number < 10:
+        return number in {2, 3, 5, 7}
+
+    # Check for even numbers.
+    if not (number & 1):
+        return False
+
+    # Calculate minimum number of rounds.
+    k = get_primality_testing_rounds(number)
+
+    # Run primality testing with (minimum + 1) rounds.
+    return miller_rabin_primality_testing(number, k + 1)
+
+
+def getprime(nbits: int) -> int:
+    """Returns a prime number that can be stored in 'nbits' bits.
+
+    >>> p = getprime(128)
+    >>> is_prime(p-1)
+    False
+    >>> is_prime(p)
+    True
+    >>> is_prime(p+1)
+    False
+
+    >>> from rsa import common
+    >>> common.bit_size(p) == 128
+    True
+    """
+
+    assert nbits > 3  # the loop will hang on too small numbers
+
+    while True:
+        integer = rsa.randnum.read_random_odd_int(nbits)
+
+        # Test for primeness
+        if is_prime(integer):
+            return integer
+
+            # Retry if not prime
+
+
+def are_relatively_prime(a: int, b: int) -> bool:
+    """Returns True if a and b are relatively prime, and False if they
+    are not.
+
+    >>> are_relatively_prime(2, 3)
+    True
+    >>> are_relatively_prime(2, 4)
+    False
+    """
+
+    d = gcd(a, b)
+    return d == 1
+
+
+if __name__ == "__main__":
+    print("Running doctests 1000x or until failure")
+    import doctest
+
+    for count in range(1000):
+        (failures, tests) = doctest.testmod()
+        if failures:
+            break
+
+        if count % 100 == 0 and count:
+            print("%i times" % count)
+
+    print("Doctests done")
diff --git a/.venv/lib/python3.12/site-packages/rsa/py.typed b/.venv/lib/python3.12/site-packages/rsa/py.typed
new file mode 100644
index 00000000..bfd62201
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/py.typed
@@ -0,0 +1 @@
+# Marker file for PEP 561.  The rsa package uses inline types.
diff --git a/.venv/lib/python3.12/site-packages/rsa/randnum.py b/.venv/lib/python3.12/site-packages/rsa/randnum.py
new file mode 100644
index 00000000..bb255c57
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/randnum.py
@@ -0,0 +1,95 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Functions for generating random numbers."""
+
+# Source inspired by code by Yesudeep Mangalapilly <yesudeep@gmail.com>
+
+import os
+import struct
+
+from rsa import common, transform
+
+
+def read_random_bits(nbits: int) -> bytes:
+    """Reads 'nbits' random bits.
+
+    If nbits isn't a whole number of bytes, an extra byte will be appended with
+    only the lower bits set.
+    """
+
+    nbytes, rbits = divmod(nbits, 8)
+
+    # Get the random bytes
+    randomdata = os.urandom(nbytes)
+
+    # Add the remaining random bits
+    if rbits > 0:
+        randomvalue = ord(os.urandom(1))
+        randomvalue >>= 8 - rbits
+        randomdata = struct.pack("B", randomvalue) + randomdata
+
+    return randomdata
+
+
+def read_random_int(nbits: int) -> int:
+    """Reads a random integer of approximately nbits bits."""
+
+    randomdata = read_random_bits(nbits)
+    value = transform.bytes2int(randomdata)
+
+    # Ensure that the number is large enough to just fill out the required
+    # number of bits.
+    value |= 1 << (nbits - 1)
+
+    return value
+
+
+def read_random_odd_int(nbits: int) -> int:
+    """Reads a random odd integer of approximately nbits bits.
+
+    >>> read_random_odd_int(512) & 1
+    1
+    """
+
+    value = read_random_int(nbits)
+
+    # Make sure it's odd
+    return value | 1
+
+
+def randint(maxvalue: int) -> int:
+    """Returns a random integer x with 1 <= x <= maxvalue
+
+    May take a very long time in specific situations. If maxvalue needs N bits
+    to store, the closer maxvalue is to (2 ** N) - 1, the faster this function
+    is.
+    """
+
+    bit_size = common.bit_size(maxvalue)
+
+    tries = 0
+    while True:
+        value = read_random_int(bit_size)
+        if value <= maxvalue:
+            break
+
+        if tries % 10 == 0 and tries:
+            # After a lot of tries to get the right number of bits but still
+            # smaller than maxvalue, decrease the number of bits by 1. That'll
+            # dramatically increase the chances to get a large enough number.
+            bit_size -= 1
+        tries += 1
+
+    return value
diff --git a/.venv/lib/python3.12/site-packages/rsa/transform.py b/.venv/lib/python3.12/site-packages/rsa/transform.py
new file mode 100644
index 00000000..76ca8499
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/transform.py
@@ -0,0 +1,72 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Data transformation functions.
+
+From bytes to a number, number to bytes, etc.
+"""
+
+import math
+
+
+def bytes2int(raw_bytes: bytes) -> int:
+    r"""Converts a list of bytes or an 8-bit string to an integer.
+
+    When using unicode strings, encode it to some encoding like UTF8 first.
+
+    >>> (((128 * 256) + 64) * 256) + 15
+    8405007
+    >>> bytes2int(b'\x80@\x0f')
+    8405007
+
+    """
+    return int.from_bytes(raw_bytes, "big", signed=False)
+
+
+def int2bytes(number: int, fill_size: int = 0) -> bytes:
+    """
+    Convert an unsigned integer to bytes (big-endian)::
+
+    Does not preserve leading zeros if you don't specify a fill size.
+
+    :param number:
+        Integer value
+    :param fill_size:
+        If the optional fill size is given the length of the resulting
+        byte string is expected to be the fill size and will be padded
+        with prefix zero bytes to satisfy that length.
+    :returns:
+        Raw bytes (base-256 representation).
+    :raises:
+        ``OverflowError`` when fill_size is given and the number takes up more
+        bytes than fit into the block. This requires the ``overflow``
+        argument to this function to be set to ``False`` otherwise, no
+        error will be raised.
+    """
+
+    if number < 0:
+        raise ValueError("Number must be an unsigned integer: %d" % number)
+
+    bytes_required = max(1, math.ceil(number.bit_length() / 8))
+
+    if fill_size > 0:
+        return number.to_bytes(fill_size, "big")
+
+    return number.to_bytes(bytes_required, "big")
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
diff --git a/.venv/lib/python3.12/site-packages/rsa/util.py b/.venv/lib/python3.12/site-packages/rsa/util.py
new file mode 100644
index 00000000..8a598cca
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/rsa/util.py
@@ -0,0 +1,97 @@
+#  Copyright 2011 Sybren A. Stüvel <sybren@stuvel.eu>
+#
+#  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
+#
+#      https://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.
+
+"""Utility functions."""
+
+import sys
+from optparse import OptionParser
+
+import rsa.key
+
+
+def private_to_public() -> None:
+    """Reads a private key and outputs the corresponding public key."""
+
+    # Parse the CLI options
+    parser = OptionParser(
+        usage="usage: %prog [options]",
+        description="Reads a private key and outputs the "
+        "corresponding public key. Both private and public keys use "
+        "the format described in PKCS#1 v1.5",
+    )
+
+    parser.add_option(
+        "-i",
+        "--input",
+        dest="infilename",
+        type="string",
+        help="Input filename. Reads from stdin if not specified",
+    )
+    parser.add_option(
+        "-o",
+        "--output",
+        dest="outfilename",
+        type="string",
+        help="Output filename. Writes to stdout of not specified",
+    )
+
+    parser.add_option(
+        "--inform",
+        dest="inform",
+        help="key format of input - default PEM",
+        choices=("PEM", "DER"),
+        default="PEM",
+    )
+
+    parser.add_option(
+        "--outform",
+        dest="outform",
+        help="key format of output - default PEM",
+        choices=("PEM", "DER"),
+        default="PEM",
+    )
+
+    (cli, cli_args) = parser.parse_args(sys.argv)
+
+    # Read the input data
+    if cli.infilename:
+        print(
+            "Reading private key from %s in %s format" % (cli.infilename, cli.inform),
+            file=sys.stderr,
+        )
+        with open(cli.infilename, "rb") as infile:
+            in_data = infile.read()
+    else:
+        print("Reading private key from stdin in %s format" % cli.inform, file=sys.stderr)
+        in_data = sys.stdin.read().encode("ascii")
+
+    assert type(in_data) == bytes, type(in_data)
+
+    # Take the public fields and create a public key
+    priv_key = rsa.key.PrivateKey.load_pkcs1(in_data, cli.inform)
+    pub_key = rsa.key.PublicKey(priv_key.n, priv_key.e)
+
+    # Save to the output file
+    out_data = pub_key.save_pkcs1(cli.outform)
+
+    if cli.outfilename:
+        print(
+            "Writing public key to %s in %s format" % (cli.outfilename, cli.outform),
+            file=sys.stderr,
+        )
+        with open(cli.outfilename, "wb") as outfile:
+            outfile.write(out_data)
+    else:
+        print("Writing public key to stdout in %s format" % cli.outform, file=sys.stderr)
+        sys.stdout.write(out_data.decode("ascii"))
author	S. Solomon Darnell	2025-03-28 21:52:21 -0500
committer	S. Solomon Darnell	2025-03-28 21:52:21 -0500
commit	4a52a71956a8d46fcb7294ac71734504bb09bcc2 (patch)
tree	ee3dc5af3b6313e921cd920906356f5d4febc4ed /.venv/lib/python3.12/site-packages/rsa
parent	cc961e04ba734dd72309fb548a2f97d67d578813 (diff)
download	gn-ai-master.tar.gz