The REST way to do this is, as indicated in the links that you provide, to authenticate each request and NOT to conduct sessions.
As for authentication with username / password for each request, it is safe if you can use ... secure level (https); else, the pair is sent as plaintext and detected.
Another option is to use something like AWS for this (Amazon links here and here , for example). Here for other explanations: buzzmedia and samritchie
OAuth may be an option, but I have no experience with it.
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