algorithms.py

from __future__ import annotations

import hashlib
import hmac
import json
from abc import ABC, abstractmethod
from typing import TYPE_CHECKING, Any, ClassVar, Literal, NoReturn, cast, overload

from .exceptions import InvalidKeyError
from .types import HashlibHash, JWKDict
from .utils import (
    base64url_decode,
    base64url_encode,
    der_to_raw_signature,
    force_bytes,
    from_base64url_uint,
    is_pem_format,
    is_ssh_key,
    raw_to_der_signature,
    to_base64url_uint,
)

try:
    from cryptography.exceptions import InvalidSignature, UnsupportedAlgorithm
    from cryptography.hazmat.backends import default_backend
    from cryptography.hazmat.primitives import hashes
    from cryptography.hazmat.primitives.asymmetric import padding
    from cryptography.hazmat.primitives.asymmetric.ec import (
        ECDSA,
        SECP256K1,
        SECP256R1,
        SECP384R1,
        SECP521R1,
        EllipticCurve,
        EllipticCurvePrivateKey,
        EllipticCurvePrivateNumbers,
        EllipticCurvePublicKey,
        EllipticCurvePublicNumbers,
    )
    from cryptography.hazmat.primitives.asymmetric.ed448 import (
        Ed448PrivateKey,
        Ed448PublicKey,
    )
    from cryptography.hazmat.primitives.asymmetric.ed25519 import (
        Ed25519PrivateKey,
        Ed25519PublicKey,
    )
    from cryptography.hazmat.primitives.asymmetric.rsa import (
        RSAPrivateKey,
        RSAPrivateNumbers,
        RSAPublicKey,
        RSAPublicNumbers,
        rsa_crt_dmp1,
        rsa_crt_dmq1,
        rsa_crt_iqmp,
        rsa_recover_prime_factors,
    )
    from cryptography.hazmat.primitives.serialization import (
        Encoding,
        NoEncryption,
        PrivateFormat,
        PublicFormat,
        load_pem_private_key,
        load_pem_public_key,
        load_ssh_public_key,
    )

    # pyjwt-964: we use these both for type checking below, as well as for validating the key passed in.
    # in Py >= 3.10, we can replace this with the Union types below
    ALLOWED_RSA_KEY_TYPES = (RSAPrivateKey, RSAPublicKey)
    ALLOWED_EC_KEY_TYPES = (EllipticCurvePrivateKey, EllipticCurvePublicKey)
    ALLOWED_OKP_KEY_TYPES = (
        Ed25519PrivateKey,
        Ed25519PublicKey,
        Ed448PrivateKey,
        Ed448PublicKey,
    )
    ALLOWED_KEY_TYPES = (
        ALLOWED_RSA_KEY_TYPES + ALLOWED_EC_KEY_TYPES + ALLOWED_OKP_KEY_TYPES
    )
    ALLOWED_PRIVATE_KEY_TYPES = (
        RSAPrivateKey,
        EllipticCurvePrivateKey,
        Ed25519PrivateKey,
        Ed448PrivateKey,
    )
    ALLOWED_PUBLIC_KEY_TYPES = (
        RSAPublicKey,
        EllipticCurvePublicKey,
        Ed25519PublicKey,
        Ed448PublicKey,
    )

    has_crypto = True
except ModuleNotFoundError:
    has_crypto = False


if TYPE_CHECKING:
    from typing import TypeAlias

    from cryptography.hazmat.primitives.asymmetric.types import (
        PrivateKeyTypes,
        PublicKeyTypes,
    )

    # Type aliases for convenience in algorithms method signatures
    AllowedRSAKeys: TypeAlias = RSAPrivateKey | RSAPublicKey
    AllowedECKeys: TypeAlias = EllipticCurvePrivateKey | EllipticCurvePublicKey
    AllowedOKPKeys: TypeAlias = (
        Ed25519PrivateKey | Ed25519PublicKey | Ed448PrivateKey | Ed448PublicKey
    )
    AllowedKeys: TypeAlias = AllowedRSAKeys | AllowedECKeys | AllowedOKPKeys
    AllowedPrivateKeys: TypeAlias = (
        RSAPrivateKey | EllipticCurvePrivateKey | Ed25519PrivateKey | Ed448PrivateKey
    )
    AllowedPublicKeys: TypeAlias = (
        RSAPublicKey | EllipticCurvePublicKey | Ed25519PublicKey | Ed448PublicKey
    )


requires_cryptography = {
    "RS256",
    "RS384",
    "RS512",
    "ES256",
    "ES256K",
    "ES384",
    "ES521",
    "ES512",
    "PS256",
    "PS384",
    "PS512",
    "EdDSA",
}


def get_default_algorithms() -> dict[str, Algorithm]:
    """
    Returns the algorithms that are implemented by the library.
    """
    default_algorithms = {
        "none": NoneAlgorithm(),
        "HS256": HMACAlgorithm(HMACAlgorithm.SHA256),
        "HS384": HMACAlgorithm(HMACAlgorithm.SHA384),
        "HS512": HMACAlgorithm(HMACAlgorithm.SHA512),
    }

    if has_crypto:
        default_algorithms.update(
            {
                "RS256": RSAAlgorithm(RSAAlgorithm.SHA256),
                "RS384": RSAAlgorithm(RSAAlgorithm.SHA384),
                "RS512": RSAAlgorithm(RSAAlgorithm.SHA512),
                "ES256": ECAlgorithm(ECAlgorithm.SHA256),
                "ES256K": ECAlgorithm(ECAlgorithm.SHA256),
                "ES384": ECAlgorithm(ECAlgorithm.SHA384),
                "ES521": ECAlgorithm(ECAlgorithm.SHA512),
                "ES512": ECAlgorithm(
                    ECAlgorithm.SHA512
                ),  # Backward compat for #219 fix
                "PS256": RSAPSSAlgorithm(RSAPSSAlgorithm.SHA256),
                "PS384": RSAPSSAlgorithm(RSAPSSAlgorithm.SHA384),
                "PS512": RSAPSSAlgorithm(RSAPSSAlgorithm.SHA512),
                "EdDSA": OKPAlgorithm(),
            }
        )

    return default_algorithms


class Algorithm(ABC):
    """
    The interface for an algorithm used to sign and verify tokens.
    """

    # pyjwt-964: Validate to ensure the key passed in was decoded to the correct cryptography key family
    _crypto_key_types: tuple[type[AllowedKeys], ...] | None = None

    def compute_hash_digest(self, bytestr: bytes) -> bytes:
        """
        Compute a hash digest using the specified algorithm's hash algorithm.

        If there is no hash algorithm, raises a NotImplementedError.
        """
        # lookup self.hash_alg if defined in a way that mypy can understand
        hash_alg = getattr(self, "hash_alg", None)
        if hash_alg is None:
            raise NotImplementedError

        if (
            has_crypto
            and isinstance(hash_alg, type)
            and issubclass(hash_alg, hashes.HashAlgorithm)
        ):
            digest = hashes.Hash(hash_alg(), backend=default_backend())
            digest.update(bytestr)
            return bytes(digest.finalize())
        else:
            return bytes(hash_alg(bytestr).digest())

    def check_crypto_key_type(self, key: PublicKeyTypes | PrivateKeyTypes):
        """Check that the key belongs to the right cryptographic family.

        Note that this method only works when `cryptography` is installed.

        Args:
            key (Any): Potentially a cryptography key
        Raises:
            ValueError: if `cryptography` is not installed, or this method is called by a non-cryptography algorithm
            InvalidKeyError: if the key doesn't match the expected key classes
        """
        if not has_crypto or self._crypto_key_types is None:
            raise ValueError(
                "This method requires the cryptography library, and should only be used by cryptography-based algorithms."
            )

        if not isinstance(key, self._crypto_key_types):
            valid_classes = (cls.__name__ for cls in self._crypto_key_types)
            actual_class = key.__class__.__name__
            self_class = self.__class__.__name__
            raise InvalidKeyError(
                f"Expected one of {valid_classes}, got: {actual_class}. Invalid Key type for {self_class}"
            )

    @abstractmethod
    def prepare_key(self, key: Any) -> Any:
        """
        Performs necessary validation and conversions on the key and returns
        the key value in the proper format for sign() and verify().
        """

    @abstractmethod
    def sign(self, msg: bytes, key: Any) -> bytes:
        """
        Returns a digital signature for the specified message
        using the specified key value.
        """

    @abstractmethod
    def verify(self, msg: bytes, key: Any, sig: bytes) -> bool:
        """
        Verifies that the specified digital signature is valid
        for the specified message and key values.
        """

    @overload
    @staticmethod
    @abstractmethod
    def to_jwk(key_obj, as_dict: Literal[True]) -> JWKDict: ...  # pragma: no cover

    @overload
    @staticmethod
    @abstractmethod
    def to_jwk(key_obj, as_dict: Literal[False] = False) -> str: ...  # pragma: no cover

    @staticmethod
    @abstractmethod
    def to_jwk(key_obj, as_dict: bool = False) -> JWKDict | str:
        """
        Serializes a given key into a JWK
        """

    @staticmethod
    @abstractmethod
    def from_jwk(jwk: str | JWKDict) -> Any:
        """
        Deserializes a given key from JWK back into a key object
        """


class NoneAlgorithm(Algorithm):
    """
    Placeholder for use when no signing or verification
    operations are required.
    """

    def prepare_key(self, key: str | None) -> None:
        if key == "":
            key = None

        if key is not None:
            raise InvalidKeyError('When alg = "none", key value must be None.')

        return key

    def sign(self, msg: bytes, key: None) -> bytes:
        return b""

    def verify(self, msg: bytes, key: None, sig: bytes) -> bool:
        return False

    @staticmethod
    def to_jwk(key_obj: Any, as_dict: bool = False) -> NoReturn:
        raise NotImplementedError()

    @staticmethod
    def from_jwk(jwk: str | JWKDict) -> NoReturn:
        raise NotImplementedError()


class HMACAlgorithm(Algorithm):
    """
    Performs signing and verification operations using HMAC
    and the specified hash function.
    """

    SHA256: ClassVar[HashlibHash] = hashlib.sha256
    SHA384: ClassVar[HashlibHash] = hashlib.sha384
    SHA512: ClassVar[HashlibHash] = hashlib.sha512

    def __init__(self, hash_alg: HashlibHash) -> None:
        self.hash_alg = hash_alg

    def prepare_key(self, key: str | bytes) -> bytes:
        key_bytes = force_bytes(key)

        if is_pem_format(key_bytes) or is_ssh_key(key_bytes):
            raise InvalidKeyError(
                "The specified key is an asymmetric key or x509 certificate and"
                " should not be used as an HMAC secret."
            )

        return key_bytes

    @overload
    @staticmethod
    def to_jwk(
        key_obj: str | bytes, as_dict: Literal[True]
    ) -> JWKDict: ...  # pragma: no cover

    @overload
    @staticmethod
    def to_jwk(
        key_obj: str | bytes, as_dict: Literal[False] = False
    ) -> str: ...  # pragma: no cover

    @staticmethod
    def to_jwk(key_obj: str | bytes, as_dict: bool = False) -> JWKDict | str:
        jwk = {
            "k": base64url_encode(force_bytes(key_obj)).decode(),
            "kty": "oct",
        }

        if as_dict:
            return jwk
        else:
            return json.dumps(jwk)

    @staticmethod
    def from_jwk(jwk: str | JWKDict) -> bytes:
        try:
            if isinstance(jwk, str):
                obj: JWKDict = json.loads(jwk)
            elif isinstance(jwk, dict):
                obj = jwk
            else:
                raise ValueError
        except ValueError:
            raise InvalidKeyError("Key is not valid JSON") from None

        if obj.get("kty") != "oct":
            raise InvalidKeyError("Not an HMAC key")

        return base64url_decode(obj["k"])

    def sign(self, msg: bytes, key: bytes) -> bytes:
        return hmac.new(key, msg, self.hash_alg).digest()

    def verify(self, msg: bytes, key: bytes, sig: bytes) -> bool:
        return hmac.compare_digest(sig, self.sign(msg, key))


if has_crypto:

    class RSAAlgorithm(Algorithm):
        """
        Performs signing and verification operations using
        RSASSA-PKCS-v1_5 and the specified hash function.
        """

        SHA256: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA256
        SHA384: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA384
        SHA512: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA512

        _crypto_key_types = ALLOWED_RSA_KEY_TYPES

        def __init__(self, hash_alg: type[hashes.HashAlgorithm]) -> None:
            self.hash_alg = hash_alg

        def prepare_key(self, key: AllowedRSAKeys | str | bytes) -> AllowedRSAKeys:
            if isinstance(key, self._crypto_key_types):
                return key

            if not isinstance(key, (bytes, str)):
                raise TypeError("Expecting a PEM-formatted key.")

            key_bytes = force_bytes(key)

            try:
                if key_bytes.startswith(b"ssh-rsa"):
                    public_key: PublicKeyTypes = load_ssh_public_key(key_bytes)
                    self.check_crypto_key_type(public_key)
                    return cast(RSAPublicKey, public_key)
                else:
                    private_key: PrivateKeyTypes = load_pem_private_key(
                        key_bytes, password=None
                    )
                    self.check_crypto_key_type(private_key)
                    return cast(RSAPrivateKey, private_key)
            except ValueError:
                try:
                    public_key = load_pem_public_key(key_bytes)
                    self.check_crypto_key_type(public_key)
                    return cast(RSAPublicKey, public_key)
                except (ValueError, UnsupportedAlgorithm):
                    raise InvalidKeyError(
                        "Could not parse the provided public key."
                    ) from None

        @overload
        @staticmethod
        def to_jwk(
            key_obj: AllowedRSAKeys, as_dict: Literal[True]
        ) -> JWKDict: ...  # pragma: no cover

        @overload
        @staticmethod
        def to_jwk(
            key_obj: AllowedRSAKeys, as_dict: Literal[False] = False
        ) -> str: ...  # pragma: no cover

        @staticmethod
        def to_jwk(key_obj: AllowedRSAKeys, as_dict: bool = False) -> JWKDict | str:
            obj: dict[str, Any] | None = None

            if hasattr(key_obj, "private_numbers"):
                # Private key
                numbers = key_obj.private_numbers()

                obj = {
                    "kty": "RSA",
                    "key_ops": ["sign"],
                    "n": to_base64url_uint(numbers.public_numbers.n).decode(),
                    "e": to_base64url_uint(numbers.public_numbers.e).decode(),
                    "d": to_base64url_uint(numbers.d).decode(),
                    "p": to_base64url_uint(numbers.p).decode(),
                    "q": to_base64url_uint(numbers.q).decode(),
                    "dp": to_base64url_uint(numbers.dmp1).decode(),
                    "dq": to_base64url_uint(numbers.dmq1).decode(),
                    "qi": to_base64url_uint(numbers.iqmp).decode(),
                }

            elif hasattr(key_obj, "verify"):
                # Public key
                numbers = key_obj.public_numbers()

                obj = {
                    "kty": "RSA",
                    "key_ops": ["verify"],
                    "n": to_base64url_uint(numbers.n).decode(),
                    "e": to_base64url_uint(numbers.e).decode(),
                }
            else:
                raise InvalidKeyError("Not a public or private key")

            if as_dict:
                return obj
            else:
                return json.dumps(obj)

        @staticmethod
        def from_jwk(jwk: str | JWKDict) -> AllowedRSAKeys:
            try:
                if isinstance(jwk, str):
                    obj = json.loads(jwk)
                elif isinstance(jwk, dict):
                    obj = jwk
                else:
                    raise ValueError
            except ValueError:
                raise InvalidKeyError("Key is not valid JSON") from None

            if obj.get("kty") != "RSA":
                raise InvalidKeyError("Not an RSA key") from None

            if "d" in obj and "e" in obj and "n" in obj:
                # Private key
                if "oth" in obj:
                    raise InvalidKeyError(
                        "Unsupported RSA private key: > 2 primes not supported"
                    )

                other_props = ["p", "q", "dp", "dq", "qi"]
                props_found = [prop in obj for prop in other_props]
                any_props_found = any(props_found)

                if any_props_found and not all(props_found):
                    raise InvalidKeyError(
                        "RSA key must include all parameters if any are present besides d"
                    ) from None

                public_numbers = RSAPublicNumbers(
                    from_base64url_uint(obj["e"]),
                    from_base64url_uint(obj["n"]),
                )

                if any_props_found:
                    numbers = RSAPrivateNumbers(
                        d=from_base64url_uint(obj["d"]),
                        p=from_base64url_uint(obj["p"]),
                        q=from_base64url_uint(obj["q"]),
                        dmp1=from_base64url_uint(obj["dp"]),
                        dmq1=from_base64url_uint(obj["dq"]),
                        iqmp=from_base64url_uint(obj["qi"]),
                        public_numbers=public_numbers,
                    )
                else:
                    d = from_base64url_uint(obj["d"])
                    p, q = rsa_recover_prime_factors(
                        public_numbers.n, d, public_numbers.e
                    )

                    numbers = RSAPrivateNumbers(
                        d=d,
                        p=p,
                        q=q,
                        dmp1=rsa_crt_dmp1(d, p),
                        dmq1=rsa_crt_dmq1(d, q),
                        iqmp=rsa_crt_iqmp(p, q),
                        public_numbers=public_numbers,
                    )

                return numbers.private_key()
            elif "n" in obj and "e" in obj:
                # Public key
                return RSAPublicNumbers(
                    from_base64url_uint(obj["e"]),
                    from_base64url_uint(obj["n"]),
                ).public_key()
            else:
                raise InvalidKeyError("Not a public or private key")

        def sign(self, msg: bytes, key: RSAPrivateKey) -> bytes:
            return key.sign(msg, padding.PKCS1v15(), self.hash_alg())

        def verify(self, msg: bytes, key: RSAPublicKey, sig: bytes) -> bool:
            try:
                key.verify(sig, msg, padding.PKCS1v15(), self.hash_alg())
                return True
            except InvalidSignature:
                return False

    class ECAlgorithm(Algorithm):
        """
        Performs signing and verification operations using
        ECDSA and the specified hash function
        """

        SHA256: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA256
        SHA384: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA384
        SHA512: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA512

        _crypto_key_types = ALLOWED_EC_KEY_TYPES

        def __init__(self, hash_alg: type[hashes.HashAlgorithm]) -> None:
            self.hash_alg = hash_alg

        def prepare_key(self, key: AllowedECKeys | str | bytes) -> AllowedECKeys:
            if isinstance(key, self._crypto_key_types):
                return key

            if not isinstance(key, (bytes, str)):
                raise TypeError("Expecting a PEM-formatted key.")

            key_bytes = force_bytes(key)

            # Attempt to load key. We don't know if it's
            # a Signing Key or a Verifying Key, so we try
            # the Verifying Key first.
            try:
                if key_bytes.startswith(b"ecdsa-sha2-"):
                    public_key: PublicKeyTypes = load_ssh_public_key(key_bytes)
                else:
                    public_key = load_pem_public_key(key_bytes)

                # Explicit check the key to prevent confusing errors from cryptography
                self.check_crypto_key_type(public_key)
                return cast(EllipticCurvePublicKey, public_key)
            except ValueError:
                private_key = load_pem_private_key(key_bytes, password=None)
                self.check_crypto_key_type(private_key)
                return cast(EllipticCurvePrivateKey, private_key)

        def sign(self, msg: bytes, key: EllipticCurvePrivateKey) -> bytes:
            der_sig = key.sign(msg, ECDSA(self.hash_alg()))

            return der_to_raw_signature(der_sig, key.curve)

        def verify(self, msg: bytes, key: AllowedECKeys, sig: bytes) -> bool:
            try:
                der_sig = raw_to_der_signature(sig, key.curve)
            except ValueError:
                return False

            try:
                public_key = (
                    key.public_key()
                    if isinstance(key, EllipticCurvePrivateKey)
                    else key
                )
                public_key.verify(der_sig, msg, ECDSA(self.hash_alg()))
                return True
            except InvalidSignature:
                return False

        @overload
        @staticmethod
        def to_jwk(
            key_obj: AllowedECKeys, as_dict: Literal[True]
        ) -> JWKDict: ...  # pragma: no cover

        @overload
        @staticmethod
        def to_jwk(
            key_obj: AllowedECKeys, as_dict: Literal[False] = False
        ) -> str: ...  # pragma: no cover

        @staticmethod
        def to_jwk(key_obj: AllowedECKeys, as_dict: bool = False) -> JWKDict | str:
            if isinstance(key_obj, EllipticCurvePrivateKey):
                public_numbers = key_obj.public_key().public_numbers()
            elif isinstance(key_obj, EllipticCurvePublicKey):
                public_numbers = key_obj.public_numbers()
            else:
                raise InvalidKeyError("Not a public or private key")

            if isinstance(key_obj.curve, SECP256R1):
                crv = "P-256"
            elif isinstance(key_obj.curve, SECP384R1):
                crv = "P-384"
            elif isinstance(key_obj.curve, SECP521R1):
                crv = "P-521"
            elif isinstance(key_obj.curve, SECP256K1):
                crv = "secp256k1"
            else:
                raise InvalidKeyError(f"Invalid curve: {key_obj.curve}")

            obj: dict[str, Any] = {
                "kty": "EC",
                "crv": crv,
                "x": to_base64url_uint(
                    public_numbers.x,
                    bit_length=key_obj.curve.key_size,
                ).decode(),
                "y": to_base64url_uint(
                    public_numbers.y,
                    bit_length=key_obj.curve.key_size,
                ).decode(),
            }

            if isinstance(key_obj, EllipticCurvePrivateKey):
                obj["d"] = to_base64url_uint(
                    key_obj.private_numbers().private_value,
                    bit_length=key_obj.curve.key_size,
                ).decode()

            if as_dict:
                return obj
            else:
                return json.dumps(obj)

        @staticmethod
        def from_jwk(jwk: str | JWKDict) -> AllowedECKeys:
            try:
                if isinstance(jwk, str):
                    obj = json.loads(jwk)
                elif isinstance(jwk, dict):
                    obj = jwk
                else:
                    raise ValueError
            except ValueError:
                raise InvalidKeyError("Key is not valid JSON") from None

            if obj.get("kty") != "EC":
                raise InvalidKeyError("Not an Elliptic curve key") from None

            if "x" not in obj or "y" not in obj:
                raise InvalidKeyError("Not an Elliptic curve key") from None

            x = base64url_decode(obj.get("x"))
            y = base64url_decode(obj.get("y"))

            curve = obj.get("crv")
            curve_obj: EllipticCurve

            if curve == "P-256":
                if len(x) == len(y) == 32:
                    curve_obj = SECP256R1()
                else:
                    raise InvalidKeyError(
                        "Coords should be 32 bytes for curve P-256"
                    ) from None
            elif curve == "P-384":
                if len(x) == len(y) == 48:
                    curve_obj = SECP384R1()
                else:
                    raise InvalidKeyError(
                        "Coords should be 48 bytes for curve P-384"
                    ) from None
            elif curve == "P-521":
                if len(x) == len(y) == 66:
                    curve_obj = SECP521R1()
                else:
                    raise InvalidKeyError(
                        "Coords should be 66 bytes for curve P-521"
                    ) from None
            elif curve == "secp256k1":
                if len(x) == len(y) == 32:
                    curve_obj = SECP256K1()
                else:
                    raise InvalidKeyError(
                        "Coords should be 32 bytes for curve secp256k1"
                    )
            else:
                raise InvalidKeyError(f"Invalid curve: {curve}")

            public_numbers = EllipticCurvePublicNumbers(
                x=int.from_bytes(x, byteorder="big"),
                y=int.from_bytes(y, byteorder="big"),
                curve=curve_obj,
            )

            if "d" not in obj:
                return public_numbers.public_key()

            d = base64url_decode(obj.get("d"))
            if len(d) != len(x):
                raise InvalidKeyError(
                    "D should be {} bytes for curve {}", len(x), curve
                )

            return EllipticCurvePrivateNumbers(
                int.from_bytes(d, byteorder="big"), public_numbers
            ).private_key()

    class RSAPSSAlgorithm(RSAAlgorithm):
        """
        Performs a signature using RSASSA-PSS with MGF1
        """

        def sign(self, msg: bytes, key: RSAPrivateKey) -> bytes:
            return key.sign(
                msg,
                padding.PSS(
                    mgf=padding.MGF1(self.hash_alg()),
                    salt_length=self.hash_alg().digest_size,
                ),
                self.hash_alg(),
            )

        def verify(self, msg: bytes, key: RSAPublicKey, sig: bytes) -> bool:
            try:
                key.verify(
                    sig,
                    msg,
                    padding.PSS(
                        mgf=padding.MGF1(self.hash_alg()),
                        salt_length=self.hash_alg().digest_size,
                    ),
                    self.hash_alg(),
                )
                return True
            except InvalidSignature:
                return False

    class OKPAlgorithm(Algorithm):
        """
        Performs signing and verification operations using EdDSA

        This class requires ``cryptography>=2.6`` to be installed.
        """

        _crypto_key_types = ALLOWED_OKP_KEY_TYPES

        def __init__(self, **kwargs: Any) -> None:
            pass

        def prepare_key(self, key: AllowedOKPKeys | str | bytes) -> AllowedOKPKeys:
            if not isinstance(key, (str, bytes)):
                self.check_crypto_key_type(key)
                return cast("AllowedOKPKeys", key)

            key_str = key.decode("utf-8") if isinstance(key, bytes) else key
            key_bytes = key.encode("utf-8") if isinstance(key, str) else key

            loaded_key: PublicKeyTypes | PrivateKeyTypes
            if "-----BEGIN PUBLIC" in key_str:
                loaded_key = load_pem_public_key(key_bytes)
            elif "-----BEGIN PRIVATE" in key_str:
                loaded_key = load_pem_private_key(key_bytes, password=None)
            elif key_str[0:4] == "ssh-":
                loaded_key = load_ssh_public_key(key_bytes)
            else:
                raise InvalidKeyError("Not a public or private key")

            # Explicit check the key to prevent confusing errors from cryptography
            self.check_crypto_key_type(loaded_key)
            return cast("AllowedOKPKeys", loaded_key)

        def sign(
            self, msg: str | bytes, key: Ed25519PrivateKey | Ed448PrivateKey
        ) -> bytes:
            """
            Sign a message ``msg`` using the EdDSA private key ``key``
            :param str|bytes msg: Message to sign
            :param Ed25519PrivateKey}Ed448PrivateKey key: A :class:`.Ed25519PrivateKey`
                or :class:`.Ed448PrivateKey` isinstance
            :return bytes signature: The signature, as bytes
            """
            msg_bytes = msg.encode("utf-8") if isinstance(msg, str) else msg
            return key.sign(msg_bytes)

        def verify(
            self, msg: str | bytes, key: AllowedOKPKeys, sig: str | bytes
        ) -> bool:
            """
            Verify a given ``msg`` against a signature ``sig`` using the EdDSA key ``key``

            :param str|bytes sig: EdDSA signature to check ``msg`` against
            :param str|bytes msg: Message to sign
            :param Ed25519PrivateKey|Ed25519PublicKey|Ed448PrivateKey|Ed448PublicKey key:
                A private or public EdDSA key instance
            :return bool verified: True if signature is valid, False if not.
            """
            try:
                msg_bytes = msg.encode("utf-8") if isinstance(msg, str) else msg
                sig_bytes = sig.encode("utf-8") if isinstance(sig, str) else sig

                public_key = (
                    key.public_key()
                    if isinstance(key, (Ed25519PrivateKey, Ed448PrivateKey))
                    else key
                )
                public_key.verify(sig_bytes, msg_bytes)
                return True  # If no exception was raised, the signature is valid.
            except InvalidSignature:
                return False

        @overload
        @staticmethod
        def to_jwk(
            key: AllowedOKPKeys, as_dict: Literal[True]
        ) -> JWKDict: ...  # pragma: no cover

        @overload
        @staticmethod
        def to_jwk(
            key: AllowedOKPKeys, as_dict: Literal[False] = False
        ) -> str: ...  # pragma: no cover

        @staticmethod
        def to_jwk(key: AllowedOKPKeys, as_dict: bool = False) -> JWKDict | str:
            if isinstance(key, (Ed25519PublicKey, Ed448PublicKey)):
                x = key.public_bytes(
                    encoding=Encoding.Raw,
                    format=PublicFormat.Raw,
                )
                crv = "Ed25519" if isinstance(key, Ed25519PublicKey) else "Ed448"

                obj = {
                    "x": base64url_encode(force_bytes(x)).decode(),
                    "kty": "OKP",
                    "crv": crv,
                }

                if as_dict:
                    return obj
                else:
                    return json.dumps(obj)

            if isinstance(key, (Ed25519PrivateKey, Ed448PrivateKey)):
                d = key.private_bytes(
                    encoding=Encoding.Raw,
                    format=PrivateFormat.Raw,
                    encryption_algorithm=NoEncryption(),
                )

                x = key.public_key().public_bytes(
                    encoding=Encoding.Raw,
                    format=PublicFormat.Raw,
                )

                crv = "Ed25519" if isinstance(key, Ed25519PrivateKey) else "Ed448"
                obj = {
                    "x": base64url_encode(force_bytes(x)).decode(),
                    "d": base64url_encode(force_bytes(d)).decode(),
                    "kty": "OKP",
                    "crv": crv,
                }

                if as_dict:
                    return obj
                else:
                    return json.dumps(obj)

            raise InvalidKeyError("Not a public or private key")

        @staticmethod
        def from_jwk(jwk: str | JWKDict) -> AllowedOKPKeys:
            try:
                if isinstance(jwk, str):
                    obj = json.loads(jwk)
                elif isinstance(jwk, dict):
                    obj = jwk
                else:
                    raise ValueError
            except ValueError:
                raise InvalidKeyError("Key is not valid JSON") from None

            if obj.get("kty") != "OKP":
                raise InvalidKeyError("Not an Octet Key Pair")

            curve = obj.get("crv")
            if curve != "Ed25519" and curve != "Ed448":
                raise InvalidKeyError(f"Invalid curve: {curve}")

            if "x" not in obj:
                raise InvalidKeyError('OKP should have "x" parameter')
            x = base64url_decode(obj.get("x"))

            try:
                if "d" not in obj:
                    if curve == "Ed25519":
                        return Ed25519PublicKey.from_public_bytes(x)
                    return Ed448PublicKey.from_public_bytes(x)
                d = base64url_decode(obj.get("d"))
                if curve == "Ed25519":
                    return Ed25519PrivateKey.from_private_bytes(d)
                return Ed448PrivateKey.from_private_bytes(d)
            except ValueError as err:
                raise InvalidKeyError("Invalid key parameter") from err