diff --git a/lib/jwt/__init__.py b/lib/jwt/__init__.py
index 26c79b24..68d09c1c 100644
--- a/lib/jwt/__init__.py
+++ b/lib/jwt/__init__.py
@@ -19,6 +19,7 @@ from .exceptions import (
     InvalidSignatureError,
     InvalidTokenError,
     MissingRequiredClaimError,
+    PyJWKClientConnectionError,
     PyJWKClientError,
     PyJWKError,
     PyJWKSetError,
@@ -26,7 +27,7 @@ from .exceptions import (
 )
 from .jwks_client import PyJWKClient
 
-__version__ = "2.6.0"
+__version__ = "2.8.0"
 
 __title__ = "PyJWT"
 __description__ = "JSON Web Token implementation in Python"
@@ -65,6 +66,7 @@ __all__ = [
     "InvalidSignatureError",
     "InvalidTokenError",
     "MissingRequiredClaimError",
+    "PyJWKClientConnectionError",
     "PyJWKClientError",
     "PyJWKError",
     "PyJWKSetError",
diff --git a/lib/jwt/algorithms.py b/lib/jwt/algorithms.py
index 93fadf4c..ed187152 100644
--- a/lib/jwt/algorithms.py
+++ b/lib/jwt/algorithms.py
@@ -1,8 +1,14 @@
+from __future__ import annotations
+
 import hashlib
 import hmac
 import json
+import sys
+from abc import ABC, abstractmethod
+from typing import TYPE_CHECKING, Any, ClassVar, NoReturn, Union, cast, overload
 
 from .exceptions import InvalidKeyError
+from .types import HashlibHash, JWKDict
 from .utils import (
     base64url_decode,
     base64url_encode,
@@ -15,14 +21,28 @@ from .utils import (
     to_base64url_uint,
 )
 
+if sys.version_info >= (3, 8):
+    from typing import Literal
+else:
+    from typing_extensions import Literal
+
+
 try:
-    import cryptography.exceptions
     from cryptography.exceptions import InvalidSignature
+    from cryptography.hazmat.backends import default_backend
     from cryptography.hazmat.primitives import hashes
-    from cryptography.hazmat.primitives.asymmetric import ec, padding
+    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,
@@ -56,6 +76,23 @@ try:
 except ModuleNotFoundError:
     has_crypto = False
 
+
+if TYPE_CHECKING:
+    # Type aliases for convenience in algorithms method signatures
+    AllowedRSAKeys = RSAPrivateKey | RSAPublicKey
+    AllowedECKeys = EllipticCurvePrivateKey | EllipticCurvePublicKey
+    AllowedOKPKeys = (
+        Ed25519PrivateKey | Ed25519PublicKey | Ed448PrivateKey | Ed448PublicKey
+    )
+    AllowedKeys = AllowedRSAKeys | AllowedECKeys | AllowedOKPKeys
+    AllowedPrivateKeys = (
+        RSAPrivateKey | EllipticCurvePrivateKey | Ed25519PrivateKey | Ed448PrivateKey
+    )
+    AllowedPublicKeys = (
+        RSAPublicKey | EllipticCurvePublicKey | Ed25519PublicKey | Ed448PublicKey
+    )
+
+
 requires_cryptography = {
     "RS256",
     "RS384",
@@ -72,7 +109,7 @@ requires_cryptography = {
 }
 
 
-def get_default_algorithms():
+def get_default_algorithms() -> dict[str, Algorithm]:
     """
     Returns the algorithms that are implemented by the library.
     """
@@ -106,45 +143,79 @@ def get_default_algorithms():
     return default_algorithms
 
 
-class Algorithm:
+class Algorithm(ABC):
     """
     The interface for an algorithm used to sign and verify tokens.
     """
 
-    def prepare_key(self, key):
+    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())
+
+    @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().
         """
-        raise NotImplementedError
 
-    def sign(self, msg, key):
+    @abstractmethod
+    def sign(self, msg: bytes, key: Any) -> bytes:
         """
         Returns a digital signature for the specified message
         using the specified key value.
         """
-        raise NotImplementedError
 
-    def verify(self, msg, key, sig):
+    @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.
         """
-        raise NotImplementedError
+
+    @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
-    def to_jwk(key_obj):
+    @abstractmethod
+    def to_jwk(key_obj, as_dict: bool = False) -> Union[JWKDict, str]:
         """
-        Serializes a given RSA key into a JWK
+        Serializes a given key into a JWK
         """
-        raise NotImplementedError
 
     @staticmethod
-    def from_jwk(jwk):
+    @abstractmethod
+    def from_jwk(jwk: str | JWKDict) -> Any:
         """
-        Deserializes a given RSA key from JWK back into a PublicKey or PrivateKey object
+        Deserializes a given key from JWK back into a key object
         """
-        raise NotImplementedError
 
 
 class NoneAlgorithm(Algorithm):
@@ -153,7 +224,7 @@ class NoneAlgorithm(Algorithm):
     operations are required.
     """
 
-    def prepare_key(self, key):
+    def prepare_key(self, key: str | None) -> None:
         if key == "":
             key = None
 
@@ -162,12 +233,20 @@ class NoneAlgorithm(Algorithm):
 
         return key
 
-    def sign(self, msg, key):
+    def sign(self, msg: bytes, key: None) -> bytes:
         return b""
 
-    def verify(self, msg, key, sig):
+    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):
     """
@@ -175,38 +254,51 @@ class HMACAlgorithm(Algorithm):
     and the specified hash function.
     """
 
-    SHA256 = hashlib.sha256
-    SHA384 = hashlib.sha384
-    SHA512 = hashlib.sha512
+    SHA256: ClassVar[HashlibHash] = hashlib.sha256
+    SHA384: ClassVar[HashlibHash] = hashlib.sha384
+    SHA512: ClassVar[HashlibHash] = hashlib.sha512
 
-    def __init__(self, hash_alg):
+    def __init__(self, hash_alg: HashlibHash) -> None:
         self.hash_alg = hash_alg
 
-    def prepare_key(self, key):
-        key = force_bytes(key)
+    def prepare_key(self, key: str | bytes) -> bytes:
+        key_bytes = force_bytes(key)
 
-        if is_pem_format(key) or is_ssh_key(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
+        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):
-        return json.dumps(
-            {
-                "k": base64url_encode(force_bytes(key_obj)).decode(),
-                "kty": "oct",
-            }
-        )
+    def to_jwk(key_obj: str | bytes, as_dict: bool = False) -> Union[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):
+    def from_jwk(jwk: str | JWKDict) -> bytes:
         try:
             if isinstance(jwk, str):
-                obj = json.loads(jwk)
+                obj: JWKDict = json.loads(jwk)
             elif isinstance(jwk, dict):
                 obj = jwk
             else:
@@ -219,10 +311,10 @@ class HMACAlgorithm(Algorithm):
 
         return base64url_decode(obj["k"])
 
-    def sign(self, msg, key):
+    def sign(self, msg: bytes, key: bytes) -> bytes:
         return hmac.new(key, msg, self.hash_alg).digest()
 
-    def verify(self, msg, key, sig):
+    def verify(self, msg: bytes, key: bytes, sig: bytes) -> bool:
         return hmac.compare_digest(sig, self.sign(msg, key))
 
 
@@ -234,36 +326,49 @@ if has_crypto:
         RSASSA-PKCS-v1_5 and the specified hash function.
         """
 
-        SHA256 = hashes.SHA256
-        SHA384 = hashes.SHA384
-        SHA512 = hashes.SHA512
+        SHA256: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA256
+        SHA384: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA384
+        SHA512: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA512
 
-        def __init__(self, hash_alg):
+        def __init__(self, hash_alg: type[hashes.HashAlgorithm]) -> None:
             self.hash_alg = hash_alg
 
-        def prepare_key(self, key):
+        def prepare_key(self, key: AllowedRSAKeys | str | bytes) -> AllowedRSAKeys:
             if isinstance(key, (RSAPrivateKey, RSAPublicKey)):
                 return key
 
             if not isinstance(key, (bytes, str)):
                 raise TypeError("Expecting a PEM-formatted key.")
 
-            key = force_bytes(key)
+            key_bytes = force_bytes(key)
 
             try:
-                if key.startswith(b"ssh-rsa"):
-                    key = load_ssh_public_key(key)
+                if key_bytes.startswith(b"ssh-rsa"):
+                    return cast(RSAPublicKey, load_ssh_public_key(key_bytes))
                 else:
-                    key = load_pem_private_key(key, password=None)
+                    return cast(
+                        RSAPrivateKey, load_pem_private_key(key_bytes, password=None)
+                    )
             except ValueError:
-                key = load_pem_public_key(key)
-            return key
+                return cast(RSAPublicKey, load_pem_public_key(key_bytes))
+
+        @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):
-            obj = None
+        def to_jwk(
+            key_obj: AllowedRSAKeys, as_dict: bool = False
+        ) -> Union[JWKDict, str]:
+            obj: dict[str, Any] | None = None
 
-            if getattr(key_obj, "private_numbers", None):
+            if hasattr(key_obj, "private_numbers"):
                 # Private key
                 numbers = key_obj.private_numbers()
 
@@ -280,7 +385,7 @@ if has_crypto:
                     "qi": to_base64url_uint(numbers.iqmp).decode(),
                 }
 
-            elif getattr(key_obj, "verify", None):
+            elif hasattr(key_obj, "verify"):
                 # Public key
                 numbers = key_obj.public_numbers()
 
@@ -293,10 +398,13 @@ if has_crypto:
             else:
                 raise InvalidKeyError("Not a public or private key")
 
-            return json.dumps(obj)
+            if as_dict:
+                return obj
+            else:
+                return json.dumps(obj)
 
         @staticmethod
-        def from_jwk(jwk):
+        def from_jwk(jwk: str | JWKDict) -> AllowedRSAKeys:
             try:
                 if isinstance(jwk, str):
                     obj = json.loads(jwk)
@@ -360,19 +468,17 @@ if has_crypto:
                 return numbers.private_key()
             elif "n" in obj and "e" in obj:
                 # Public key
-                numbers = RSAPublicNumbers(
+                return RSAPublicNumbers(
                     from_base64url_uint(obj["e"]),
                     from_base64url_uint(obj["n"]),
-                )
-
-                return numbers.public_key()
+                ).public_key()
             else:
                 raise InvalidKeyError("Not a public or private key")
 
-        def sign(self, msg, key):
+        def sign(self, msg: bytes, key: RSAPrivateKey) -> bytes:
             return key.sign(msg, padding.PKCS1v15(), self.hash_alg())
 
-        def verify(self, msg, key, sig):
+        def verify(self, msg: bytes, key: RSAPublicKey, sig: bytes) -> bool:
             try:
                 key.verify(sig, msg, padding.PKCS1v15(), self.hash_alg())
                 return True
@@ -385,63 +491,79 @@ if has_crypto:
         ECDSA and the specified hash function
         """
 
-        SHA256 = hashes.SHA256
-        SHA384 = hashes.SHA384
-        SHA512 = hashes.SHA512
+        SHA256: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA256
+        SHA384: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA384
+        SHA512: ClassVar[type[hashes.HashAlgorithm]] = hashes.SHA512
 
-        def __init__(self, hash_alg):
+        def __init__(self, hash_alg: type[hashes.HashAlgorithm]) -> None:
             self.hash_alg = hash_alg
 
-        def prepare_key(self, key):
+        def prepare_key(self, key: AllowedECKeys | str | bytes) -> AllowedECKeys:
             if isinstance(key, (EllipticCurvePrivateKey, EllipticCurvePublicKey)):
                 return key
 
             if not isinstance(key, (bytes, str)):
                 raise TypeError("Expecting a PEM-formatted key.")
 
-            key = force_bytes(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.startswith(b"ecdsa-sha2-"):
-                    key = load_ssh_public_key(key)
+                if key_bytes.startswith(b"ecdsa-sha2-"):
+                    crypto_key = load_ssh_public_key(key_bytes)
                 else:
-                    key = load_pem_public_key(key)
+                    crypto_key = load_pem_public_key(key_bytes)  # type: ignore[assignment]
             except ValueError:
-                key = load_pem_private_key(key, password=None)
+                crypto_key = load_pem_private_key(key_bytes, password=None)  # type: ignore[assignment]
 
             # Explicit check the key to prevent confusing errors from cryptography
-            if not isinstance(key, (EllipticCurvePrivateKey, EllipticCurvePublicKey)):
+            if not isinstance(
+                crypto_key, (EllipticCurvePrivateKey, EllipticCurvePublicKey)
+            ):
                 raise InvalidKeyError(
                     "Expecting a EllipticCurvePrivateKey/EllipticCurvePublicKey. Wrong key provided for ECDSA algorithms"
                 )
 
-            return key
+            return crypto_key
 
-        def sign(self, msg, key):
-            der_sig = key.sign(msg, ec.ECDSA(self.hash_alg()))
+        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, key, sig):
+        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:
-                if isinstance(key, EllipticCurvePrivateKey):
-                    key = key.public_key()
-                key.verify(der_sig, msg, ec.ECDSA(self.hash_alg()))
+                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):
+        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
+        ) -> Union[JWKDict, str]:
             if isinstance(key_obj, EllipticCurvePrivateKey):
                 public_numbers = key_obj.public_key().public_numbers()
             elif isinstance(key_obj, EllipticCurvePublicKey):
@@ -449,18 +571,18 @@ if has_crypto:
             else:
                 raise InvalidKeyError("Not a public or private key")
 
-            if isinstance(key_obj.curve, ec.SECP256R1):
+            if isinstance(key_obj.curve, SECP256R1):
                 crv = "P-256"
-            elif isinstance(key_obj.curve, ec.SECP384R1):
+            elif isinstance(key_obj.curve, SECP384R1):
                 crv = "P-384"
-            elif isinstance(key_obj.curve, ec.SECP521R1):
+            elif isinstance(key_obj.curve, SECP521R1):
                 crv = "P-521"
-            elif isinstance(key_obj.curve, ec.SECP256K1):
+            elif isinstance(key_obj.curve, SECP256K1):
                 crv = "secp256k1"
             else:
                 raise InvalidKeyError(f"Invalid curve: {key_obj.curve}")
 
-            obj = {
+            obj: dict[str, Any] = {
                 "kty": "EC",
                 "crv": crv,
                 "x": to_base64url_uint(public_numbers.x).decode(),
@@ -472,10 +594,13 @@ if has_crypto:
                     key_obj.private_numbers().private_value
                 ).decode()
 
-            return json.dumps(obj)
+            if as_dict:
+                return obj
+            else:
+                return json.dumps(obj)
 
         @staticmethod
-        def from_jwk(jwk):
+        def from_jwk(jwk: str | JWKDict) -> AllowedECKeys:
             try:
                 if isinstance(jwk, str):
                     obj = json.loads(jwk)
@@ -496,24 +621,26 @@ if has_crypto:
             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 = ec.SECP256R1()
+                    curve_obj = SECP256R1()
                 else:
                     raise InvalidKeyError("Coords should be 32 bytes for curve P-256")
             elif curve == "P-384":
                 if len(x) == len(y) == 48:
-                    curve_obj = ec.SECP384R1()
+                    curve_obj = SECP384R1()
                 else:
                     raise InvalidKeyError("Coords should be 48 bytes for curve P-384")
             elif curve == "P-521":
                 if len(x) == len(y) == 66:
-                    curve_obj = ec.SECP521R1()
+                    curve_obj = SECP521R1()
                 else:
                     raise InvalidKeyError("Coords should be 66 bytes for curve P-521")
             elif curve == "secp256k1":
                 if len(x) == len(y) == 32:
-                    curve_obj = ec.SECP256K1()
+                    curve_obj = SECP256K1()
                 else:
                     raise InvalidKeyError(
                         "Coords should be 32 bytes for curve secp256k1"
@@ -521,7 +648,7 @@ if has_crypto:
             else:
                 raise InvalidKeyError(f"Invalid curve: {curve}")
 
-            public_numbers = ec.EllipticCurvePublicNumbers(
+            public_numbers = EllipticCurvePublicNumbers(
                 x=int.from_bytes(x, byteorder="big"),
                 y=int.from_bytes(y, byteorder="big"),
                 curve=curve_obj,
@@ -536,7 +663,7 @@ if has_crypto:
                     "D should be {} bytes for curve {}", len(x), curve
                 )
 
-            return ec.EllipticCurvePrivateNumbers(
+            return EllipticCurvePrivateNumbers(
                 int.from_bytes(d, byteorder="big"), public_numbers
             ).private_key()
 
@@ -545,24 +672,24 @@ if has_crypto:
         Performs a signature using RSASSA-PSS with MGF1
         """
 
-        def sign(self, msg, key):
+        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,
+                    salt_length=self.hash_alg().digest_size,
                 ),
                 self.hash_alg(),
             )
 
-        def verify(self, msg, key, sig):
+        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,
+                        salt_length=self.hash_alg().digest_size,
                     ),
                     self.hash_alg(),
                 )
@@ -577,21 +704,20 @@ if has_crypto:
         This class requires ``cryptography>=2.6`` to be installed.
         """
 
-        def __init__(self, **kwargs):
+        def __init__(self, **kwargs: Any) -> None:
             pass
 
-        def prepare_key(self, key):
+        def prepare_key(self, key: AllowedOKPKeys | str | bytes) -> AllowedOKPKeys:
             if isinstance(key, (bytes, str)):
-                if isinstance(key, str):
-                    key = key.encode("utf-8")
-                str_key = key.decode("utf-8")
+                key_str = key.decode("utf-8") if isinstance(key, bytes) else key
+                key_bytes = key.encode("utf-8") if isinstance(key, str) else key
 
-                if "-----BEGIN PUBLIC" in str_key:
-                    key = load_pem_public_key(key)
-                elif "-----BEGIN PRIVATE" in str_key:
-                    key = load_pem_private_key(key, password=None)
-                elif str_key[0:4] == "ssh-":
-                    key = load_ssh_public_key(key)
+                if "-----BEGIN PUBLIC" in key_str:
+                    key = load_pem_public_key(key_bytes)  # type: ignore[assignment]
+                elif "-----BEGIN PRIVATE" in key_str:
+                    key = load_pem_private_key(key_bytes, password=None)  # type: ignore[assignment]
+                elif key_str[0:4] == "ssh-":
+                    key = load_ssh_public_key(key_bytes)  # type: ignore[assignment]
 
             # Explicit check the key to prevent confusing errors from cryptography
             if not isinstance(
@@ -604,7 +730,9 @@ if has_crypto:
 
             return key
 
-        def sign(self, msg, 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
@@ -612,10 +740,12 @@ if has_crypto:
                 or :class:`.Ed448PrivateKey` isinstance
             :return bytes signature: The signature, as bytes
             """
-            msg = bytes(msg, "utf-8") if type(msg) is not bytes else msg
-            return key.sign(msg)
+            msg_bytes = msg.encode("utf-8") if isinstance(msg, str) else msg
+            return key.sign(msg_bytes)
 
-        def verify(self, msg, key, sig):
+        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``
 
@@ -626,31 +756,48 @@ if has_crypto:
             :return bool verified: True if signature is valid, False if not.
             """
             try:
-                msg = bytes(msg, "utf-8") if type(msg) is not bytes else msg
-                sig = bytes(sig, "utf-8") if type(sig) is not bytes else sig
+                msg_bytes = msg.encode("utf-8") if isinstance(msg, str) else msg
+                sig_bytes = sig.encode("utf-8") if isinstance(sig, str) else sig
 
-                if isinstance(key, (Ed25519PrivateKey, Ed448PrivateKey)):
-                    key = key.public_key()
-                key.verify(sig, msg)
+                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 cryptography.exceptions.InvalidSignature:
+            except InvalidSignature:
                 return False
 
+        @overload
         @staticmethod
-        def to_jwk(key):
+        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) -> Union[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"
-                return json.dumps(
-                    {
-                        "x": base64url_encode(force_bytes(x)).decode(),
-                        "kty": "OKP",
-                        "crv": crv,
-                    }
-                )
+
+                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(
@@ -665,19 +812,22 @@ if has_crypto:
                 )
 
                 crv = "Ed25519" if isinstance(key, Ed25519PrivateKey) else "Ed448"
-                return json.dumps(
-                    {
-                        "x": base64url_encode(force_bytes(x)).decode(),
-                        "d": base64url_encode(force_bytes(d)).decode(),
-                        "kty": "OKP",
-                        "crv": crv,
-                    }
-                )
+                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):
+        def from_jwk(jwk: str | JWKDict) -> AllowedOKPKeys:
             try:
                 if isinstance(jwk, str):
                     obj = json.loads(jwk)
diff --git a/lib/jwt/api_jwk.py b/lib/jwt/api_jwk.py
index aa3dd321..456c7f4d 100644
--- a/lib/jwt/api_jwk.py
+++ b/lib/jwt/api_jwk.py
@@ -2,13 +2,15 @@ from __future__ import annotations
 
 import json
 import time
+from typing import Any
 
-from .algorithms import get_default_algorithms
-from .exceptions import InvalidKeyError, PyJWKError, PyJWKSetError
+from .algorithms import get_default_algorithms, has_crypto, requires_cryptography
+from .exceptions import InvalidKeyError, PyJWKError, PyJWKSetError, PyJWTError
+from .types import JWKDict
 
 
 class PyJWK:
-    def __init__(self, jwk_data, algorithm=None):
+    def __init__(self, jwk_data: JWKDict, algorithm: str | None = None) -> None:
         self._algorithms = get_default_algorithms()
         self._jwk_data = jwk_data
 
@@ -47,37 +49,40 @@ class PyJWK:
             else:
                 raise InvalidKeyError(f"Unsupported kty: {kty}")
 
+        if not has_crypto and algorithm in requires_cryptography:
+            raise PyJWKError(f"{algorithm} requires 'cryptography' to be installed.")
+
         self.Algorithm = self._algorithms.get(algorithm)
 
         if not self.Algorithm:
-            raise PyJWKError(f"Unable to find a algorithm for key: {self._jwk_data}")
+            raise PyJWKError(f"Unable to find an algorithm for key: {self._jwk_data}")
 
         self.key = self.Algorithm.from_jwk(self._jwk_data)
 
     @staticmethod
-    def from_dict(obj, algorithm=None):
+    def from_dict(obj: JWKDict, algorithm: str | None = None) -> "PyJWK":
         return PyJWK(obj, algorithm)
 
     @staticmethod
-    def from_json(data, algorithm=None):
+    def from_json(data: str, algorithm: None = None) -> "PyJWK":
         obj = json.loads(data)
         return PyJWK.from_dict(obj, algorithm)
 
     @property
-    def key_type(self):
+    def key_type(self) -> str | None:
         return self._jwk_data.get("kty", None)
 
     @property
-    def key_id(self):
+    def key_id(self) -> str | None:
         return self._jwk_data.get("kid", None)
 
     @property
-    def public_key_use(self):
+    def public_key_use(self) -> str | None:
         return self._jwk_data.get("use", None)
 
 
 class PyJWKSet:
-    def __init__(self, keys: list[dict]) -> None:
+    def __init__(self, keys: list[JWKDict]) -> None:
         self.keys = []
 
         if not keys:
@@ -89,24 +94,26 @@ class PyJWKSet:
         for key in keys:
             try:
                 self.keys.append(PyJWK(key))
-            except PyJWKError:
+            except PyJWTError:
                 # skip unusable keys
                 continue
 
         if len(self.keys) == 0:
-            raise PyJWKSetError("The JWK Set did not contain any usable keys")
+            raise PyJWKSetError(
+                "The JWK Set did not contain any usable keys. Perhaps 'cryptography' is not installed?"
+            )
 
     @staticmethod
-    def from_dict(obj):
+    def from_dict(obj: dict[str, Any]) -> "PyJWKSet":
         keys = obj.get("keys", [])
         return PyJWKSet(keys)
 
     @staticmethod
-    def from_json(data):
+    def from_json(data: str) -> "PyJWKSet":
         obj = json.loads(data)
         return PyJWKSet.from_dict(obj)
 
-    def __getitem__(self, kid):
+    def __getitem__(self, kid: str) -> "PyJWK":
         for key in self.keys:
             if key.key_id == kid:
                 return key
@@ -118,8 +125,8 @@ class PyJWTSetWithTimestamp:
         self.jwk_set = jwk_set
         self.timestamp = time.monotonic()
 
-    def get_jwk_set(self):
+    def get_jwk_set(self) -> PyJWKSet:
         return self.jwk_set
 
-    def get_timestamp(self):
+    def get_timestamp(self) -> float:
         return self.timestamp
diff --git a/lib/jwt/api_jws.py b/lib/jwt/api_jws.py
index ab8490f9..fa6708cc 100644
--- a/lib/jwt/api_jws.py
+++ b/lib/jwt/api_jws.py
@@ -3,7 +3,7 @@ from __future__ import annotations
 import binascii
 import json
 import warnings
-from typing import Any, Type
+from typing import TYPE_CHECKING, Any
 
 from .algorithms import (
     Algorithm,
@@ -20,11 +20,18 @@ from .exceptions import (
 from .utils import base64url_decode, base64url_encode
 from .warnings import RemovedInPyjwt3Warning
 
+if TYPE_CHECKING:
+    from .algorithms import AllowedPrivateKeys, AllowedPublicKeys
+
 
 class PyJWS:
     header_typ = "JWT"
 
-    def __init__(self, algorithms=None, options=None) -> None:
+    def __init__(
+        self,
+        algorithms: list[str] | None = None,
+        options: dict[str, Any] | None = None,
+    ) -> None:
         self._algorithms = get_default_algorithms()
         self._valid_algs = (
             set(algorithms) if algorithms is not None else set(self._algorithms)
@@ -96,11 +103,12 @@ class PyJWS:
     def encode(
         self,
         payload: bytes,
-        key: str,
+        key: AllowedPrivateKeys | str | bytes,
         algorithm: str | None = "HS256",
         headers: dict[str, Any] | None = None,
-        json_encoder: Type[json.JSONEncoder] | None = None,
+        json_encoder: type[json.JSONEncoder] | None = None,
         is_payload_detached: bool = False,
+        sort_headers: bool = True,
     ) -> str:
         segments = []
 
@@ -133,9 +141,8 @@ class PyJWS:
             # True is the standard value for b64, so no need for it
             del header["b64"]
 
-        # Fix for headers misorder - issue #715
         json_header = json.dumps(
-            header, separators=(",", ":"), cls=json_encoder, sort_keys=True
+            header, separators=(",", ":"), cls=json_encoder, sort_keys=sort_headers
         ).encode()
 
         segments.append(base64url_encode(json_header))
@@ -164,8 +171,8 @@ class PyJWS:
 
     def decode_complete(
         self,
-        jwt: str,
-        key: str = "",
+        jwt: str | bytes,
+        key: AllowedPublicKeys | str | bytes = "",
         algorithms: list[str] | None = None,
         options: dict[str, Any] | None = None,
         detached_payload: bytes | None = None,
@@ -209,13 +216,13 @@ class PyJWS:
 
     def decode(
         self,
-        jwt: str,
-        key: str = "",
+        jwt: str | bytes,
+        key: AllowedPublicKeys | str | bytes = "",
         algorithms: list[str] | None = None,
         options: dict[str, Any] | None = None,
         detached_payload: bytes | None = None,
         **kwargs,
-    ) -> str:
+    ) -> Any:
         if kwargs:
             warnings.warn(
                 "passing additional kwargs to decode() is deprecated "
@@ -228,7 +235,7 @@ class PyJWS:
         )
         return decoded["payload"]
 
-    def get_unverified_header(self, jwt: str | bytes) -> dict:
+    def get_unverified_header(self, jwt: str | bytes) -> dict[str, Any]:
         """Returns back the JWT header parameters as a dict()
 
         Note: The signature is not verified so the header parameters
@@ -239,7 +246,7 @@ class PyJWS:
 
         return headers
 
-    def _load(self, jwt: str | bytes) -> tuple[bytes, bytes, dict, bytes]:
+    def _load(self, jwt: str | bytes) -> tuple[bytes, bytes, dict[str, Any], bytes]:
         if isinstance(jwt, str):
             jwt = jwt.encode("utf-8")
 
@@ -280,13 +287,15 @@ class PyJWS:
     def _verify_signature(
         self,
         signing_input: bytes,
-        header: dict,
+        header: dict[str, Any],
         signature: bytes,
-        key: str = "",
+        key: AllowedPublicKeys | str | bytes = "",
         algorithms: list[str] | None = None,
     ) -> None:
-
-        alg = header.get("alg")
+        try:
+            alg = header["alg"]
+        except KeyError:
+            raise InvalidAlgorithmError("Algorithm not specified")
 
         if not alg or (algorithms is not None and alg not in algorithms):
             raise InvalidAlgorithmError("The specified alg value is not allowed")
@@ -295,16 +304,16 @@ class PyJWS:
             alg_obj = self.get_algorithm_by_name(alg)
         except NotImplementedError as e:
             raise InvalidAlgorithmError("Algorithm not supported") from e
-        key = alg_obj.prepare_key(key)
+        prepared_key = alg_obj.prepare_key(key)
 
-        if not alg_obj.verify(signing_input, key, signature):
+        if not alg_obj.verify(signing_input, prepared_key, signature):
             raise InvalidSignatureError("Signature verification failed")
 
     def _validate_headers(self, headers: dict[str, Any]) -> None:
         if "kid" in headers:
             self._validate_kid(headers["kid"])
 
-    def _validate_kid(self, kid: str) -> None:
+    def _validate_kid(self, kid: Any) -> None:
         if not isinstance(kid, str):
             raise InvalidTokenError("Key ID header parameter must be a string")
 
diff --git a/lib/jwt/api_jwt.py b/lib/jwt/api_jwt.py
index 4bb1ee1f..48d739ad 100644
--- a/lib/jwt/api_jwt.py
+++ b/lib/jwt/api_jwt.py
@@ -3,9 +3,9 @@ from __future__ import annotations
 import json
 import warnings
 from calendar import timegm
-from collections.abc import Iterable, Mapping
+from collections.abc import Iterable
 from datetime import datetime, timedelta, timezone
-from typing import Any, Dict, List, Optional, Type, Union
+from typing import TYPE_CHECKING, Any
 
 from . import api_jws
 from .exceptions import (
@@ -19,15 +19,18 @@ from .exceptions import (
 )
 from .warnings import RemovedInPyjwt3Warning
 
+if TYPE_CHECKING:
+    from .algorithms import AllowedPrivateKeys, AllowedPublicKeys
+
 
 class PyJWT:
-    def __init__(self, options=None):
+    def __init__(self, options: dict[str, Any] | None = None) -> None:
         if options is None:
             options = {}
-        self.options = {**self._get_default_options(), **options}
+        self.options: dict[str, Any] = {**self._get_default_options(), **options}
 
     @staticmethod
-    def _get_default_options() -> Dict[str, Union[bool, List[str]]]:
+    def _get_default_options() -> dict[str, bool | list[str]]:
         return {
             "verify_signature": True,
             "verify_exp": True,
@@ -40,16 +43,17 @@ class PyJWT:
 
     def encode(
         self,
-        payload: Dict[str, Any],
-        key: str,
-        algorithm: Optional[str] = "HS256",
-        headers: Optional[Dict[str, Any]] = None,
-        json_encoder: Optional[Type[json.JSONEncoder]] = None,
+        payload: dict[str, Any],
+        key: AllowedPrivateKeys | str | bytes,
+        algorithm: str | None = "HS256",
+        headers: dict[str, Any] | None = None,
+        json_encoder: type[json.JSONEncoder] | None = None,
+        sort_headers: bool = True,
     ) -> str:
-        # Check that we get a mapping
-        if not isinstance(payload, Mapping):
+        # Check that we get a dict
+        if not isinstance(payload, dict):
             raise TypeError(
-                "Expecting a mapping object, as JWT only supports "
+                "Expecting a dict object, as JWT only supports "
                 "JSON objects as payloads."
             )
 
@@ -60,30 +64,57 @@ class PyJWT:
             if isinstance(payload.get(time_claim), datetime):
                 payload[time_claim] = timegm(payload[time_claim].utctimetuple())
 
-        json_payload = json.dumps(
-            payload, separators=(",", ":"), cls=json_encoder
-        ).encode("utf-8")
+        json_payload = self._encode_payload(
+            payload,
+            headers=headers,
+            json_encoder=json_encoder,
+        )
 
-        return api_jws.encode(json_payload, key, algorithm, headers, json_encoder)
+        return api_jws.encode(
+            json_payload,
+            key,
+            algorithm,
+            headers,
+            json_encoder,
+            sort_headers=sort_headers,
+        )
+
+    def _encode_payload(
+        self,
+        payload: dict[str, Any],
+        headers: dict[str, Any] | None = None,
+        json_encoder: type[json.JSONEncoder] | None = None,
+    ) -> bytes:
+        """
+        Encode a given payload to the bytes to be signed.
+
+        This method is intended to be overridden by subclasses that need to
+        encode the payload in a different way, e.g. compress the payload.
+        """
+        return json.dumps(
+            payload,
+            separators=(",", ":"),
+            cls=json_encoder,
+        ).encode("utf-8")
 
     def decode_complete(
         self,
-        jwt: str,
-        key: str = "",
-        algorithms: Optional[List[str]] = None,
-        options: Optional[Dict[str, Any]] = None,
+        jwt: str | bytes,
+        key: AllowedPublicKeys | str | bytes = "",
+        algorithms: list[str] | None = None,
+        options: dict[str, Any] | None = None,
         # deprecated arg, remove in pyjwt3
-        verify: Optional[bool] = None,
+        verify: bool | None = None,
         # could be used as passthrough to api_jws, consider removal in pyjwt3
-        detached_payload: Optional[bytes] = None,
+        detached_payload: bytes | None = None,
         # passthrough arguments to _validate_claims
         # consider putting in options
-        audience: Optional[Union[str, Iterable[str]]] = None,
-        issuer: Optional[str] = None,
-        leeway: Union[int, float, timedelta] = 0,
+        audience: str | Iterable[str] | None = None,
+        issuer: str | None = None,
+        leeway: float | timedelta = 0,
         # kwargs
-        **kwargs,
-    ) -> Dict[str, Any]:
+        **kwargs: Any,
+    ) -> dict[str, Any]:
         if kwargs:
             warnings.warn(
                 "passing additional kwargs to decode_complete() is deprecated "
@@ -125,12 +156,7 @@ class PyJWT:
             detached_payload=detached_payload,
         )
 
-        try:
-            payload = json.loads(decoded["payload"])
-        except ValueError as e:
-            raise DecodeError(f"Invalid payload string: {e}")
-        if not isinstance(payload, dict):
-            raise DecodeError("Invalid payload string: must be a json object")
+        payload = self._decode_payload(decoded)
 
         merged_options = {**self.options, **options}
         self._validate_claims(
@@ -140,24 +166,40 @@ class PyJWT:
         decoded["payload"] = payload
         return decoded
 
+    def _decode_payload(self, decoded: dict[str, Any]) -> Any:
+        """
+        Decode the payload from a JWS dictionary (payload, signature, header).
+
+        This method is intended to be overridden by subclasses that need to
+        decode the payload in a different way, e.g. decompress compressed
+        payloads.
+        """
+        try:
+            payload = json.loads(decoded["payload"])
+        except ValueError as e:
+            raise DecodeError(f"Invalid payload string: {e}")
+        if not isinstance(payload, dict):
+            raise DecodeError("Invalid payload string: must be a json object")
+        return payload
+
     def decode(
         self,
-        jwt: str,
-        key: str = "",
-        algorithms: Optional[List[str]] = None,
-        options: Optional[Dict[str, Any]] = None,
+        jwt: str | bytes,
+        key: AllowedPublicKeys | str | bytes = "",
+        algorithms: list[str] | None = None,
+        options: dict[str, Any] | None = None,
         # deprecated arg, remove in pyjwt3
-        verify: Optional[bool] = None,
+        verify: bool | None = None,
         # could be used as passthrough to api_jws, consider removal in pyjwt3
-        detached_payload: Optional[bytes] = None,
+        detached_payload: bytes | None = None,
         # passthrough arguments to _validate_claims
         # consider putting in options
-        audience: Optional[Union[str, Iterable[str]]] = None,
-        issuer: Optional[str] = None,
-        leeway: Union[int, float, timedelta] = 0,
+        audience: str | Iterable[str] | None = None,
+        issuer: str | None = None,
+        leeway: float | timedelta = 0,
         # kwargs
-        **kwargs,
-    ) -> Dict[str, Any]:
+        **kwargs: Any,
+    ) -> Any:
         if kwargs:
             warnings.warn(
                 "passing additional kwargs to decode() is deprecated "
@@ -178,7 +220,14 @@ class PyJWT:
         )
         return decoded["payload"]
 
-    def _validate_claims(self, payload, options, audience=None, issuer=None, leeway=0):
+    def _validate_claims(
+        self,
+        payload: dict[str, Any],
+        options: dict[str, Any],
+        audience=None,
+        issuer=None,
+        leeway: float | timedelta = 0,
+    ) -> None:
         if isinstance(leeway, timedelta):
             leeway = leeway.total_seconds()
 
@@ -187,7 +236,7 @@ class PyJWT:
 
         self._validate_required_claims(payload, options)
 
-        now = timegm(datetime.now(tz=timezone.utc).utctimetuple())
+        now = datetime.now(tz=timezone.utc).timestamp()
 
         if "iat" in payload and options["verify_iat"]:
             self._validate_iat(payload, now, leeway)
@@ -202,23 +251,38 @@ class PyJWT:
             self._validate_iss(payload, issuer)
 
         if options["verify_aud"]:
-            self._validate_aud(payload, audience)
+            self._validate_aud(
+                payload, audience, strict=options.get("strict_aud", False)
+            )
 
-    def _validate_required_claims(self, payload, options):
+    def _validate_required_claims(
+        self,
+        payload: dict[str, Any],
+        options: dict[str, Any],
+    ) -> None:
         for claim in options["require"]:
             if payload.get(claim) is None:
                 raise MissingRequiredClaimError(claim)
 
-    def _validate_iat(self, payload, now, leeway):
-        iat = payload["iat"]
+    def _validate_iat(
+        self,
+        payload: dict[str, Any],
+        now: float,
+        leeway: float,
+    ) -> None:
         try:
-            int(iat)
+            iat = int(payload["iat"])
         except ValueError:
             raise InvalidIssuedAtError("Issued At claim (iat) must be an integer.")
         if iat > (now + leeway):
             raise ImmatureSignatureError("The token is not yet valid (iat)")
 
-    def _validate_nbf(self, payload, now, leeway):
+    def _validate_nbf(
+        self,
+        payload: dict[str, Any],
+        now: float,
+        leeway: float,
+    ) -> None:
         try:
             nbf = int(payload["nbf"])
         except ValueError:
@@ -227,7 +291,12 @@ class PyJWT:
         if nbf > (now + leeway):
             raise ImmatureSignatureError("The token is not yet valid (nbf)")
 
-    def _validate_exp(self, payload, now, leeway):
+    def _validate_exp(
+        self,
+        payload: dict[str, Any],
+        now: float,
+        leeway: float,
+    ) -> None:
         try:
             exp = int(payload["exp"])
         except ValueError:
@@ -236,7 +305,13 @@ class PyJWT:
         if exp <= (now - leeway):
             raise ExpiredSignatureError("Signature has expired")
 
-    def _validate_aud(self, payload, audience):
+    def _validate_aud(
+        self,
+        payload: dict[str, Any],
+        audience: str | Iterable[str] | None,
+        *,
+        strict: bool = False,
+    ) -> None:
         if audience is None:
             if "aud" not in payload or not payload["aud"]:
                 return
@@ -251,6 +326,22 @@ class PyJWT:
 
         audience_claims = payload["aud"]
 
+        # In strict mode, we forbid list matching: the supplied audience
+        # must be a string, and it must exactly match the audience claim.
+        if strict:
+            # Only a single audience is allowed in strict mode.
+            if not isinstance(audience, str):
+                raise InvalidAudienceError("Invalid audience (strict)")
+
+            # Only a single audience claim is allowed in strict mode.
+            if not isinstance(audience_claims, str):
+                raise InvalidAudienceError("Invalid claim format in token (strict)")
+
+            if audience != audience_claims:
+                raise InvalidAudienceError("Audience doesn't match (strict)")
+
+            return
+
         if isinstance(audience_claims, str):
             audience_claims = [audience_claims]
         if not isinstance(audience_claims, list):
@@ -262,9 +353,9 @@ class PyJWT:
             audience = [audience]
 
         if all(aud not in audience_claims for aud in audience):
-            raise InvalidAudienceError("Invalid audience")
+            raise InvalidAudienceError("Audience doesn't match")
 
-    def _validate_iss(self, payload, issuer):
+    def _validate_iss(self, payload: dict[str, Any], issuer: Any) -> None:
         if issuer is None:
             return
 
diff --git a/lib/jwt/exceptions.py b/lib/jwt/exceptions.py
index ee201add..8ac6ecf7 100644
--- a/lib/jwt/exceptions.py
+++ b/lib/jwt/exceptions.py
@@ -47,10 +47,10 @@ class InvalidAlgorithmError(InvalidTokenError):
 
 
 class MissingRequiredClaimError(InvalidTokenError):
-    def __init__(self, claim):
+    def __init__(self, claim: str) -> None:
         self.claim = claim
 
-    def __str__(self):
+    def __str__(self) -> str:
         return f'Token is missing the "{self.claim}" claim'
 
 
@@ -64,3 +64,7 @@ class PyJWKSetError(PyJWTError):
 
 class PyJWKClientError(PyJWTError):
     pass
+
+
+class PyJWKClientConnectionError(PyJWKClientError):
+    pass
diff --git a/lib/jwt/help.py b/lib/jwt/help.py
index 0c02eb92..80b0ca56 100644
--- a/lib/jwt/help.py
+++ b/lib/jwt/help.py
@@ -7,8 +7,10 @@ from . import __version__ as pyjwt_version
 
 try:
     import cryptography
+
+    cryptography_version = cryptography.__version__
 except ModuleNotFoundError:
-    cryptography = None
+    cryptography_version = ""
 
 
 def info() -> Dict[str, Dict[str, str]]:
@@ -29,7 +31,7 @@ def info() -> Dict[str, Dict[str, str]]:
     if implementation == "CPython":
         implementation_version = platform.python_version()
     elif implementation == "PyPy":
-        pypy_version_info = getattr(sys, "pypy_version_info")
+        pypy_version_info = sys.pypy_version_info  # type: ignore[attr-defined]
         implementation_version = (
             f"{pypy_version_info.major}."
             f"{pypy_version_info.minor}."
@@ -48,7 +50,7 @@ def info() -> Dict[str, Dict[str, str]]:
             "name": implementation,
             "version": implementation_version,
         },
-        "cryptography": {"version": getattr(cryptography, "__version__", "")},
+        "cryptography": {"version": cryptography_version},
         "pyjwt": {"version": pyjwt_version},
     }
 
diff --git a/lib/jwt/jwk_set_cache.py b/lib/jwt/jwk_set_cache.py
index e8c2a7e0..24325630 100644
--- a/lib/jwt/jwk_set_cache.py
+++ b/lib/jwt/jwk_set_cache.py
@@ -5,11 +5,11 @@ from .api_jwk import PyJWKSet, PyJWTSetWithTimestamp
 
 
 class JWKSetCache:
-    def __init__(self, lifespan: int):
+    def __init__(self, lifespan: int) -> None:
         self.jwk_set_with_timestamp: Optional[PyJWTSetWithTimestamp] = None
         self.lifespan = lifespan
 
-    def put(self, jwk_set: PyJWKSet):
+    def put(self, jwk_set: PyJWKSet) -> None:
         if jwk_set is not None:
             self.jwk_set_with_timestamp = PyJWTSetWithTimestamp(jwk_set)
         else:
@@ -23,7 +23,6 @@ class JWKSetCache:
         return self.jwk_set_with_timestamp.get_jwk_set()
 
     def is_expired(self) -> bool:
-
         return (
             self.jwk_set_with_timestamp is not None
             and self.lifespan > -1
diff --git a/lib/jwt/jwks_client.py b/lib/jwt/jwks_client.py
index b4e98007..f19b10ac 100644
--- a/lib/jwt/jwks_client.py
+++ b/lib/jwt/jwks_client.py
@@ -1,12 +1,13 @@
 import json
 import urllib.request
 from functools import lru_cache
-from typing import Any, List, Optional
+from ssl import SSLContext
+from typing import Any, Dict, List, Optional
 from urllib.error import URLError
 
 from .api_jwk import PyJWK, PyJWKSet
 from .api_jwt import decode_complete as decode_token
-from .exceptions import PyJWKClientError
+from .exceptions import PyJWKClientConnectionError, PyJWKClientError
 from .jwk_set_cache import JWKSetCache
 
 
@@ -18,9 +19,17 @@ class PyJWKClient:
         max_cached_keys: int = 16,
         cache_jwk_set: bool = True,
         lifespan: int = 300,
+        headers: Optional[Dict[str, Any]] = None,
+        timeout: int = 30,
+        ssl_context: Optional[SSLContext] = None,
     ):
+        if headers is None:
+            headers = {}
         self.uri = uri
         self.jwk_set_cache: Optional[JWKSetCache] = None
+        self.headers = headers
+        self.timeout = timeout
+        self.ssl_context = ssl_context
 
         if cache_jwk_set:
             # Init jwt set cache with default or given lifespan.
@@ -41,10 +50,15 @@ class PyJWKClient:
     def fetch_data(self) -> Any:
         jwk_set: Any = None
         try:
-            with urllib.request.urlopen(self.uri) as response:
+            r = urllib.request.Request(url=self.uri, headers=self.headers)
+            with urllib.request.urlopen(
+                r, timeout=self.timeout, context=self.ssl_context
+            ) as response:
                 jwk_set = json.load(response)
-        except URLError as e:
-            raise PyJWKClientError(f'Fail to fetch data from the url, err: "{e}"')
+        except (URLError, TimeoutError) as e:
+            raise PyJWKClientConnectionError(
+                f'Fail to fetch data from the url, err: "{e}"'
+            )
         else:
             return jwk_set
         finally:
@@ -59,6 +73,9 @@ class PyJWKClient:
         if data is None:
             data = self.fetch_data()
 
+        if not isinstance(data, dict):
+            raise PyJWKClientError("The JWKS endpoint did not return a JSON object")
+
         return PyJWKSet.from_dict(data)
 
     def get_signing_keys(self, refresh: bool = False) -> List[PyJWK]:
diff --git a/lib/jwt/types.py b/lib/jwt/types.py
new file mode 100644
index 00000000..7d993520
--- /dev/null
+++ b/lib/jwt/types.py
@@ -0,0 +1,5 @@
+from typing import Any, Callable, Dict
+
+JWKDict = Dict[str, Any]
+
+HashlibHash = Callable[..., Any]
diff --git a/lib/jwt/utils.py b/lib/jwt/utils.py
index 16cae066..81c5ee41 100644
--- a/lib/jwt/utils.py
+++ b/lib/jwt/utils.py
@@ -10,10 +10,10 @@ try:
         encode_dss_signature,
     )
 except ModuleNotFoundError:
-    EllipticCurve = None
+    pass
 
 
-def force_bytes(value: Union[str, bytes]) -> bytes:
+def force_bytes(value: Union[bytes, str]) -> bytes:
     if isinstance(value, str):
         return value.encode("utf-8")
     elif isinstance(value, bytes):
@@ -22,16 +22,15 @@ def force_bytes(value: Union[str, bytes]) -> bytes:
         raise TypeError("Expected a string value")
 
 
-def base64url_decode(input: Union[str, bytes]) -> bytes:
-    if isinstance(input, str):
-        input = input.encode("ascii")
+def base64url_decode(input: Union[bytes, str]) -> bytes:
+    input_bytes = force_bytes(input)
 
-    rem = len(input) % 4
+    rem = len(input_bytes) % 4
 
     if rem > 0:
-        input += b"=" * (4 - rem)
+        input_bytes += b"=" * (4 - rem)
 
-    return base64.urlsafe_b64decode(input)
+    return base64.urlsafe_b64decode(input_bytes)
 
 
 def base64url_encode(input: bytes) -> bytes:
@@ -50,11 +49,8 @@ def to_base64url_uint(val: int) -> bytes:
     return base64url_encode(int_bytes)
 
 
-def from_base64url_uint(val: Union[str, bytes]) -> int:
-    if isinstance(val, str):
-        val = val.encode("ascii")
-
-    data = base64url_decode(val)
+def from_base64url_uint(val: Union[bytes, str]) -> int:
+    data = base64url_decode(force_bytes(val))
     return int.from_bytes(data, byteorder="big")
 
 
@@ -78,7 +74,7 @@ def bytes_from_int(val: int) -> bytes:
     return val.to_bytes(byte_length, "big", signed=False)
 
 
-def der_to_raw_signature(der_sig: bytes, curve: EllipticCurve) -> bytes:
+def der_to_raw_signature(der_sig: bytes, curve: "EllipticCurve") -> bytes:
     num_bits = curve.key_size
     num_bytes = (num_bits + 7) // 8
 
@@ -87,7 +83,7 @@ def der_to_raw_signature(der_sig: bytes, curve: EllipticCurve) -> bytes:
     return number_to_bytes(r, num_bytes) + number_to_bytes(s, num_bytes)
 
 
-def raw_to_der_signature(raw_sig: bytes, curve: EllipticCurve) -> bytes:
+def raw_to_der_signature(raw_sig: bytes, curve: "EllipticCurve") -> bytes:
     num_bits = curve.key_size
     num_bytes = (num_bits + 7) // 8
 
@@ -97,7 +93,7 @@ def raw_to_der_signature(raw_sig: bytes, curve: EllipticCurve) -> bytes:
     r = bytes_to_number(raw_sig[:num_bytes])
     s = bytes_to_number(raw_sig[num_bytes:])
 
-    return encode_dss_signature(r, s)
+    return bytes(encode_dss_signature(r, s))
 
 
 # Based on https://github.com/hynek/pem/blob/7ad94db26b0bc21d10953f5dbad3acfdfacf57aa/src/pem/_core.py#L224-L252
diff --git a/requirements.txt b/requirements.txt
index 755f9a21..0ac5222b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -31,7 +31,7 @@ paho-mqtt==1.6.1
 plexapi==4.13.4
 portend==3.1.0
 profilehooks==1.12.0
-PyJWT==2.6.0
+PyJWT==2.8.0
 pyparsing==3.0.9
 python-dateutil==2.8.2
 python-twitter==3.5