    def _verify_signature(
        self,
        signing_input: bytes,
        header: dict[str, Any],
        signature: bytes,
        key: AllowedPublicKeys | PyJWK | str | bytes = "",
        algorithms: Sequence[str] | None = None,
        options: SigOptions | None = None,
    ) -> None:
        effective_options = options if options is not None else self.options

        if algorithms is None and isinstance(key, PyJWK):
            algorithms = [key.algorithm_name]
        try:
            alg = header["alg"]
        except KeyError:
            raise InvalidAlgorithmError("Algorithm not specified") from None

        if not alg or (algorithms is not None and alg not in algorithms):
            raise InvalidAlgorithmError("The specified alg value is not allowed")

        if isinstance(key, PyJWK):
            # The PyJWK has a fixed algorithm bound at construction time.
            # Verification must use that algorithm, not whatever the token
            # header advertises, otherwise the caller's allow-list check
            # above degenerates into a string compare with no behavioural
            # effect on which algorithm actually verifies the signature.
            if alg != key.algorithm_name:
                raise InvalidAlgorithmError(
                    f"Token algorithm {alg!r} does not match the key's "
                    f"algorithm {key.algorithm_name!r}"
                )
            alg_obj = key.Algorithm
            prepared_key = alg_obj.prepare_key(key.key)
        else:
            try:
                alg_obj = self.get_algorithm_by_name(alg)
            except NotImplementedError as e:
                raise InvalidAlgorithmError("Algorithm not supported") from e
            prepared_key = alg_obj.prepare_key(key)

        key_length_msg = alg_obj.check_key_length(prepared_key)
        if key_length_msg:
            if effective_options.get("enforce_minimum_key_length", False):
                raise InvalidKeyError(key_length_msg)
            else:
                warnings.warn(key_length_msg, InsecureKeyLengthWarning, stacklevel=4)

        if not alg_obj.verify(signing_input, prepared_key, signature):
            raise InvalidSignatureError("Signature verification failed")
Warm-up
