First of all, if you do not know that using SSL is too expensive for you, use SSL. Security runs until performance is optimized.
Now about passing usernames and passwords: usually you have an βAPI access tokenβ or the like. This is not actually a username / password, but when someone has this, they are given the opportunity to make API requests. They may have limited or unlimited legal force. You can even make a token a signature - the user signs the request using some key, and you confirm the signature.
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