Basic authentication is a method to send credentials from the client to the proxy|server (like NTLM or Kerberos). Setting the method does not control what channel (http|https) these credentials are sent.
If you want the credentials to be sent over a secure channel you have to change the type of authentication you're doing (explicit proxy auth to auth server with https).
For more info, see the following community thread about this:
This article discusses how one would implement the authentication server:
Thanks very much! I'll reconfigure our proxy