diff --git a/pyproject.toml b/pyproject.toml
index c4469c9..f05bcef 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -72,6 +72,7 @@ exclude_lines = [
 ]
 
 [tool.mypy]
+strict = true
 python_version = "3.8"
 files = ["src/joserfc"]
 show_error_codes = true
diff --git a/src/joserfc/jws.py b/src/joserfc/jws.py
index 198744b..f8d7fc3 100644
--- a/src/joserfc/jws.py
+++ b/src/joserfc/jws.py
@@ -227,7 +227,7 @@ def serialize_json(
     if registry is None:
         registry = construct_registry(algorithms)
 
-    def find_key(obj: Any):
+    def find_key(obj: Any) -> Key:
         return guess_key(private_key, obj, True)
 
     _payload = to_bytes(payload)
@@ -271,7 +271,7 @@ def deserialize_json(
     if registry is None:
         registry = construct_registry(algorithms)
 
-    def find_key(obj: Any):
+    def find_key(obj: Any) -> Key:
         return guess_key(public_key, obj)
 
     if "signatures" in value:
diff --git a/src/joserfc/rfc7516/json.py b/src/joserfc/rfc7516/json.py
index b2a7326..4c7e410 100644
--- a/src/joserfc/rfc7516/json.py
+++ b/src/joserfc/rfc7516/json.py
@@ -93,7 +93,8 @@ def extract_flattened_json(data: FlattenedJSONSerialization) -> FlattenedJSONEnc
 
 
 def __extract_segments(
-        data: t.Union[GeneralJSONSerialization, FlattenedJSONSerialization]):  # type: ignore[no-untyped-def]
+        data: t.Union[GeneralJSONSerialization, FlattenedJSONSerialization]
+) -> t.Tuple[t.Dict[str, bytes], t.Dict[str, bytes], t.Optional[bytes]]:
     base64_segments: t.Dict[str, bytes] = {
         "iv": to_bytes(data["iv"]),
         "ciphertext": to_bytes(data["ciphertext"]),
diff --git a/src/joserfc/rfc7516/models.py b/src/joserfc/rfc7516/models.py
index 57181e5..ed44962 100644
--- a/src/joserfc/rfc7516/models.py
+++ b/src/joserfc/rfc7516/models.py
@@ -1,9 +1,10 @@
+from __future__ import annotations
 import os
 import typing as t
 from abc import ABCMeta, abstractmethod
 from ..registry import Header, HeaderRegistryDict
 from ..errors import InvalidKeyTypeError, InvalidKeyLengthError
-from .._keys import Key, ECKey
+from .._keys import Key, ECKey, OctKey
 
 KeyType = t.TypeVar("KeyType")
 
@@ -12,8 +13,8 @@ class Recipient(t.Generic[KeyType]):
     def __init__(
             self,
             parent: t.Union["CompactEncryption", "GeneralJSONEncryption", "FlattenedJSONEncryption"],
-            header: t.Optional[Header] = None,
-            recipient_key: t.Optional[KeyType] = None):
+            header: Header | None = None,
+            recipient_key: KeyType | None = None):
         self.__parent = parent
         self.header = header
         self.recipient_key = recipient_key
@@ -30,7 +31,7 @@ def headers(self) -> Header:
             rv.update(self.header)
         return rv
 
-    def add_header(self, k: str, v: t.Any):
+    def add_header(self, k: str, v: t.Any) -> None:
         if isinstance(self.__parent, CompactEncryption):
             self.__parent.protected.update({k: v})
         elif self.header:
@@ -38,7 +39,7 @@ def add_header(self, k: str, v: t.Any):
         else:
             self.header = {k: v}
 
-    def set_kid(self, kid: str):
+    def set_kid(self, kid: str) -> None:
         self.add_header("kid", kid)
 
 
@@ -46,19 +47,19 @@ class CompactEncryption:
     """An object to represent the JWE Compact Serialization. It is usually returned by
     ``decrypt_compact`` method.
     """
-    def __init__(self, protected: Header, plaintext: t.Optional[bytes] = None):
+    def __init__(self, protected: Header, plaintext: bytes | None = None):
         #: protected header in dict
         self.protected = protected
         #: the plaintext in bytes
         self.plaintext = plaintext
-        self.recipient: t.Optional[Recipient] = None
+        self.recipient: Recipient[t.Any] | None = None
         self.bytes_segments: t.Dict[str, bytes] = {}  # store the decoded segments
         self.base64_segments: t.Dict[str, bytes] = {}  # store the encoded segments
 
     def headers(self) -> Header:
         return self.protected
 
-    def attach_recipient(self, key: Key, header: t.Optional[Header] = None):
+    def attach_recipient(self, key: Key, header: Header | None = None) -> None:
         """Add a recipient to the JWE Compact Serialization. Please add a key that
         comply with the given "alg" value.
 
@@ -71,7 +72,7 @@ def attach_recipient(self, key: Key, header: t.Optional[Header] = None):
         self.recipient = recipient
 
     @property
-    def recipients(self) -> t.List[Recipient]:
+    def recipients(self) -> list[Recipient[t.Any]]:
         if self.recipient is not None:
             return [self.recipient]
         return []
@@ -89,14 +90,14 @@ class BaseJSONEncryption(metaclass=ABCMeta):
     #: an optional additional authenticated data
     aad: t.Optional[bytes]
     #: a list of recipients
-    recipients: t.List[Recipient]
+    recipients: t.List[Recipient[t.Any]]
 
     def __init__(
             self,
             protected: Header,
-            plaintext: t.Optional[bytes] = None,
-            unprotected: t.Optional[Header] = None,
-            aad: t.Optional[bytes] = None):
+            plaintext: bytes | None = None,
+            unprotected: Header | None = None,
+            aad: bytes | None = None):
         self.protected = protected
         self.plaintext = plaintext
         self.unprotected = unprotected
@@ -106,7 +107,7 @@ def __init__(
         self.base64_segments: t.Dict[str, bytes] = {}  # store the encoded segments
 
     @abstractmethod
-    def add_recipient(self, header: t.Optional[Header] = None, key: t.Optional[Key] = None):
+    def add_recipient(self, header: Header | None = None, key: Key | None = None) -> None:
         """Add a recipient to the JWE JSON Serialization. Please add a key that
         comply with the "alg" to this recipient.
 
@@ -131,7 +132,7 @@ class GeneralJSONEncryption(BaseJSONEncryption):
     """
     flattened = False
 
-    def add_recipient(self, header: t.Optional[Header] = None, key: t.Optional[Key] = None):
+    def add_recipient(self, header: Header | None = None, key: Key | None = None) -> None:
         recipient = Recipient(self, header, key)
         self.recipients.append(recipient)
 
@@ -152,7 +153,7 @@ class FlattenedJSONEncryption(BaseJSONEncryption):
     """
     flattened = True
 
-    def add_recipient(self, header: t.Optional[Header] = None, key: t.Optional[Key] = None):
+    def add_recipient(self, header: Header | None = None, key: Key | None = None) -> None:
         self.recipients = [Recipient(self, header, key)]
 
 
@@ -178,7 +179,7 @@ def check_iv(self, iv: bytes) -> bytes:
         return iv
 
     @abstractmethod
-    def encrypt(self, plaintext: bytes, cek: bytes, iv: bytes, aad: bytes) -> t.Tuple[bytes, bytes]:
+    def encrypt(self, plaintext: bytes, cek: bytes, iv: bytes, aad: bytes) -> tuple[bytes, bytes]:
         pass
 
     @abstractmethod
@@ -216,11 +217,11 @@ class KeyManagement:
     def direct_mode(self) -> bool:
         return self.key_size is None
 
-    def check_key_type(self, key: Key):
+    def check_key_type(self, key: Key) -> None:
         if key.key_type not in self.key_types:
             raise InvalidKeyTypeError()
 
-    def prepare_recipient_header(self, recipient: Recipient):
+    def prepare_recipient_header(self, recipient: Recipient[t.Any]) -> None:
         raise NotImplementedError()
 
 
@@ -228,7 +229,7 @@ class JWEDirectEncryption(KeyManagement, metaclass=ABCMeta):
     key_types = ["oct"]
 
     @abstractmethod
-    def compute_cek(self, size: int, recipient: Recipient) -> bytes:
+    def compute_cek(self, size: int, recipient: Recipient[OctKey]) -> bytes:
         pass
 
 
@@ -238,11 +239,11 @@ def direct_mode(self) -> bool:
         return False
 
     @abstractmethod
-    def encrypt_cek(self, cek: bytes, recipient: Recipient) -> bytes:
+    def encrypt_cek(self, cek: bytes, recipient: Recipient[t.Any]) -> bytes:
         pass
 
     @abstractmethod
-    def decrypt_cek(self, recipient: Recipient) -> bytes:
+    def decrypt_cek(self, recipient: Recipient[t.Any]) -> bytes:
         pass
 
 
@@ -254,7 +255,7 @@ class JWEKeyWrapping(KeyManagement, metaclass=ABCMeta):
     def direct_mode(self) -> bool:
         return False
 
-    def check_op_key(self, op_key: bytes):
+    def check_op_key(self, op_key: bytes) -> None:
         if len(op_key) * 8 != self.key_size:
             raise InvalidKeyLengthError(f"A key of size {self.key_size} bits MUST be used")
 
@@ -267,11 +268,11 @@ def unwrap_cek(self, ek: bytes, key: bytes) -> bytes:
         pass
 
     @abstractmethod
-    def encrypt_cek(self, cek: bytes, recipient: Recipient) -> bytes:
+    def encrypt_cek(self, cek: bytes, recipient: Recipient[OctKey]) -> bytes:
         pass
 
     @abstractmethod
-    def decrypt_cek(self, recipient: Recipient) -> bytes:
+    def decrypt_cek(self, recipient: Recipient[OctKey]) -> bytes:
         pass
 
 
@@ -280,7 +281,7 @@ class JWEKeyAgreement(KeyManagement, metaclass=ABCMeta):
     tag_aware: bool = False
     key_wrapping: t.Optional[JWEKeyWrapping]
 
-    def prepare_ephemeral_key(self, recipient: Recipient[ECKey]):
+    def prepare_ephemeral_key(self, recipient: Recipient[ECKey]) -> None:
         recipient_key = recipient.recipient_key
         assert recipient_key is not None
         self.check_key_type(recipient_key)
diff --git a/src/joserfc/rfc7516/registry.py b/src/joserfc/rfc7516/registry.py
index 92e6b1b..cf54e0e 100644
--- a/src/joserfc/rfc7516/registry.py
+++ b/src/joserfc/rfc7516/registry.py
@@ -51,12 +51,12 @@ def __init__(
         self.strict_check_header = strict_check_header
 
     @classmethod
-    def register(cls, model: JWEAlgorithm):
+    def register(cls, model: JWEAlgorithm) -> None:
         cls.algorithms[model.algorithm_location][model.name] = model  # type: ignore
         if model.recommended:
             cls.recommended.append(model.name)
 
-    def check_header(self, header: Header, check_more=False):
+    def check_header(self, header: Header, check_more: bool = False) -> None:
         """Check and validate the fields in header part of a JWS object."""
         check_crit_header(header)
         validate_registry_header(self.header_registry, header)
@@ -77,24 +77,29 @@ def get_alg(self, name: str) -> JWEAlgModel:
 
         :param name: value of the ``alg``, e.g. ``ECDH-ES``, ``A128KW``
         """
-        return self._get_algorithm("alg", name)
+        registry = self.algorithms["alg"]
+        self._check_algorithm(name, registry)
+        return registry[name]
 
     def get_enc(self, name: str) -> JWEEncModel:
         """Get the allowed ("enc") algorithm instance of the given name.
 
         :param name: value of the ``enc``, e.g. ``A128CBC-HS256``, ``A128GCM``
         """
-        return self._get_algorithm("enc", name)
+        registry = self.algorithms["enc"]
+        self._check_algorithm(name, registry)
+        return registry[name]
 
     def get_zip(self, name: str) -> JWEZipModel:
         """Get the allowed ("zip") algorithm instance of the given name.
 
         :param name: value of the ``zip``, e.g. ``DEF``
         """
-        return self._get_algorithm("zip", name)
+        registry = self.algorithms["zip"]
+        self._check_algorithm(name, registry)
+        return registry[name]
 
-    def _get_algorithm(self, location: t.Literal["alg", "enc", "zip"], name: str):
-        registry: t.Dict[str, JWEAlgorithm] = self.algorithms[location]  # type: ignore
+    def _check_algorithm(self, name: str, registry: dict[str, t.Any]) -> None:
         if name not in registry:
             raise ValueError(f'Algorithm of "{name}" is not supported')
 
@@ -105,7 +110,6 @@ def _get_algorithm(self, location: t.Literal["alg", "enc", "zip"], name: str):
 
         if name not in allowed:
             raise ValueError(f'Algorithm of "{name}" is not allowed')
-        return registry[name]
 
 
 default_registry = JWERegistry()
diff --git a/src/joserfc/rfc7517/models.py b/src/joserfc/rfc7517/models.py
index 0643c69..46cce47 100644
--- a/src/joserfc/rfc7517/models.py
+++ b/src/joserfc/rfc7517/models.py
@@ -1,5 +1,6 @@
+from __future__ import annotations
 import typing as t
-from typing import overload
+from collections.abc import KeysView
 from abc import ABCMeta, abstractmethod
 from .types import DictKey, AnyKey, KeyParameters
 from ..registry import (
@@ -82,7 +83,7 @@ class BaseKey(t.Generic[NativePrivateKey, NativePublicKey], metaclass=ABCMeta):
 
     def __init__(
             self,
-            raw_value: t.Union[NativePrivateKey, NativePublicKey],
+            raw_value: NativePrivateKey | NativePublicKey,
             original_value: t.Any,
             parameters: t.Optional[KeyParameters] = None):
         self._raw_value = raw_value
@@ -97,13 +98,13 @@ def __init__(
             self.validate_dict_key(data)
             self._dict_value = data
 
-    def keys(self):
+    def keys(self) -> KeysView[str]:
         return self.dict_value.keys()
 
-    def __getitem__(self, k: str):
+    def __getitem__(self, k: str) -> str | list[str]:
         return self.dict_value[k]
 
-    def get(self, k: str, default=None):
+    def get(self, k: str, default: str | None = None) -> str | list[str] | None:
         return self.dict_value.get(k, default)
 
     def ensure_kid(self) -> None:
@@ -114,17 +115,17 @@ def ensure_kid(self) -> None:
             self._dict_value["kid"] = self.thumbprint()
 
     @property
-    def kid(self) -> t.Optional[str]:
+    def kid(self) -> str | None:
         """The "kid" value of the JSON Web Key."""
-        return self.get("kid")
+        return t.cast(t.Optional[str], self.get("kid"))
 
     @property
-    def alg(self) -> t.Optional[str]:
+    def alg(self) -> str | None:
         """The "alg" value of the JSON Web Key."""
-        return self.get("alg")
+        return t.cast(t.Optional[str], self.get("alg"))
 
     @property
-    def raw_value(self):
+    def raw_value(self) -> t.Any:
         raise NotImplementedError()
 
     @property
@@ -220,13 +221,13 @@ def check_key_op(self, operation: str) -> None:
         if reg.private and not self.is_private:
             raise UnsupportedKeyOperationError(f'Invalid key_op "{operation}" for public key')
 
-    @overload
+    @t.overload
     def get_op_key(self, operation: t.Literal["verify", "encrypt", "wrapKey", "deriveKey"]) -> NativePublicKey: ...
 
-    @overload
+    @t.overload
     def get_op_key(self, operation: t.Literal["sign", "decrypt", "unwrapKey"]) -> NativePrivateKey: ...
 
-    def get_op_key(self, operation: str) -> t.Union[NativePublicKey, NativePrivateKey]:
+    def get_op_key(self, operation: str) -> NativePublicKey | NativePrivateKey:
         self.check_key_op(operation)
         reg = self.operation_registry[operation]
         if reg.private:
@@ -235,7 +236,7 @@ def get_op_key(self, operation: str) -> t.Union[NativePublicKey, NativePrivateKe
         return self.public_key
 
     @classmethod
-    def validate_dict_key(cls, data: DictKey):
+    def validate_dict_key(cls, data: DictKey) -> None:
         cls.binding.validate_dict_key_registry(data, cls.param_registry)
         cls.binding.validate_dict_key_registry(data, cls.value_registry)
         cls.binding.validate_dict_key_use_operations(data)
@@ -257,7 +258,7 @@ def import_key(
     @classmethod
     def generate_key(
             cls: t.Type[GenericKey],
-            size_or_crv,
+            size_or_crv: t.Any,
             parameters: t.Optional[KeyParameters] = None,
             private: bool = True,
             auto_kid: bool = False) -> GenericKey:
@@ -312,5 +313,5 @@ def curve_name(self) -> str:
         pass
 
     @abstractmethod
-    def exchange_derive_key(self, key) -> bytes:
+    def exchange_derive_key(self, key: t.Any) -> bytes:
         pass
diff --git a/src/joserfc/rfc7517/pem.py b/src/joserfc/rfc7517/pem.py
index 6d05e9c..778a2f2 100644
--- a/src/joserfc/rfc7517/pem.py
+++ b/src/joserfc/rfc7517/pem.py
@@ -1,5 +1,5 @@
 from __future__ import annotations
-from typing import Any, Literal
+from typing import Any, Literal, cast
 from abc import ABCMeta, abstractmethod
 from cryptography.hazmat.primitives.serialization import (
     load_pem_private_key,
@@ -73,15 +73,17 @@ def dump_pem_key(
             encryption_algorithm = NoEncryption()
         else:
             encryption_algorithm = BestAvailableEncryption(to_bytes(password))
-        return key.private_bytes(
+        value = key.private_bytes(
             encoding=encoding_enum,
             format=PrivateFormat.PKCS8,
             encryption_algorithm=encryption_algorithm,
         )
-    return key.public_bytes(
-        encoding=encoding_enum,
-        format=PublicFormat.SubjectPublicKeyInfo,
-    )
+    else:
+        value = key.public_bytes(
+            encoding=encoding_enum,
+            format=PublicFormat.SubjectPublicKeyInfo,
+        )
+    return cast(bytes, value)
 
 
 class CryptographyBinding(NativeKeyBinding, metaclass=ABCMeta):
@@ -90,8 +92,10 @@ class CryptographyBinding(NativeKeyBinding, metaclass=ABCMeta):
     @classmethod
     def convert_raw_key_to_dict(cls, raw_key: Any, private: bool) -> DictKey:
         if private:
-            return cls.export_private_key(raw_key)
-        return cls.export_public_key(raw_key)
+            value = cls.export_private_key(raw_key)
+        else:
+            value = cls.export_public_key(raw_key)
+        return cast(DictKey, value)
 
     @classmethod
     def import_from_dict(cls, value: DictKey) -> Any:
@@ -122,20 +126,20 @@ def as_bytes(
 
     @staticmethod
     @abstractmethod
-    def import_private_key(value) -> Any:
+    def import_private_key(value: Any) -> Any:
         pass
 
     @staticmethod
     @abstractmethod
-    def import_public_key(value) -> Any:
+    def import_public_key(value: Any) -> Any:
         pass
 
     @staticmethod
     @abstractmethod
-    def export_private_key(value) -> Any:
+    def export_private_key(value: Any) -> Any:
         pass
 
     @staticmethod
     @abstractmethod
-    def export_public_key(value) -> Any:
+    def export_public_key(value: Any) -> Any:
         pass
diff --git a/src/joserfc/rfc7518/ec_key.py b/src/joserfc/rfc7518/ec_key.py
index 17a35e6..6e71cf3 100644
--- a/src/joserfc/rfc7518/ec_key.py
+++ b/src/joserfc/rfc7518/ec_key.py
@@ -22,7 +22,7 @@
 from ..registry import KeyParameter
 
 ECDictKey = t.TypedDict("ECDictKey", {
-    "crv": t.Literal["P-256", "P-384", "P-521"],
+    "crv": str,
     "x": str,
     "y": str,
     "d": str,  # optional
@@ -56,7 +56,7 @@ def import_private_key(obj: ECDictKey) -> EllipticCurvePrivateKey:
         return private_numbers.private_key(default_backend())
 
     @staticmethod
-    def export_private_key(key: EllipticCurvePrivateKey) -> dict[str, str]:
+    def export_private_key(key: EllipticCurvePrivateKey) -> ECDictKey:
         numbers = key.private_numbers()
         return {
             "crv": CURVES_DSS[key.curve.name],
@@ -76,7 +76,7 @@ def import_public_key(obj: ECDictKey) -> EllipticCurvePublicKey:
         return public_numbers.public_key(default_backend())
 
     @staticmethod
-    def export_public_key(key: EllipticCurvePublicKey) -> dict[str, str]:
+    def export_public_key(key: EllipticCurvePublicKey) -> ECDictKey:
         numbers = key.public_numbers()
         return {
             "crv": CURVES_DSS[numbers.curve.name],
diff --git a/src/joserfc/rfc7797/json.py b/src/joserfc/rfc7797/json.py
index 632413c..a78e1b2 100644
--- a/src/joserfc/rfc7797/json.py
+++ b/src/joserfc/rfc7797/json.py
@@ -11,7 +11,7 @@
     serialize_json as _serialize_json,
     deserialize_json as _deserialize_json,
 )
-from ..jwk import KeyFlexible, guess_key
+from ..jwk import Key, KeyFlexible, guess_key
 from ..util import (
     to_bytes,
     to_str,
@@ -84,7 +84,7 @@ def deserialize_json(
 
     payload_segment = obj.segments["payload"]
 
-    def find_key(d: t.Any):
+    def find_key(d: t.Any) -> Key:
         return guess_key(public_key, d)
 
     assert obj.signature is not None