requirements.txt:

cryptography
requests

Authentication.py:

import json
import requests
import time
from base64 import b64encode
from cryptography.hazmat.primitives import hashes, serialization
from cryptography.hazmat.primitives.asymmetric import padding, utils
from cryptography.hazmat.backends import default_backend

class Authenticate:
    def __init__(self, request_body: dict, private_key: str):
        self.url = 'https://api.transip.nl/v6/auth'
        self.request_body = request_body
        self.private_key = private_key

    def sign(self) -> str:
        key_object = serialization.load_pem_private_key(
            self.private_key.encode('utf-8'),
            password=None,
            backend=default_backend()
        )

        signature = key_object.sign(
            json.dumps(self.request_body).encode('utf-8'),
            padding.PKCS1v15(),
            hashes.SHA512()
        )

        return b64encode(signature).decode('utf-8')

    def authenticate(self) -> str:
        headers = {'Signature': self.sign()}
        response = requests.post(self.url, json=self.request_body, headers=headers)
        return response.text

if __name__ == '__main__':
    """ RESULT: {"token":"...."} """
    request_body = {
        "login": "test-user",
        "nonce": str(time.time()),
        "read_only": False,
        "expiration_time": "30 minutes",
        "label": "add description",
        "global_key": True
    }
    private_key = """
-----BEGIN PRIVATE KEY-----
your-key==
-----END PRIVATE KEY-----"""

    authorize = Authenticate(request_body, private_key)
    result = authorize.authenticate()
    print(result)