Possible interesting reading: https://cybersecurity.ieee.org/blog/2016/06/02/design-best-practices-for-an-authentication-system/

Is "What elements should an authentication module include"? a suitable title (summary) for your post? I think the post's body suggestion such a summary (or similar).

Have you tried answering this question yourself? Maybe looked up the word ‘authentication’ on Wikipedia? Possibly followed a link from that article to a publication from NIST (not international, but it's not clear why you specifically want an international organization's take—and at any rate, that publication references other ISO standards you could look at)?

On reread, my previous comment maybe comes off like I'm trying to provoke. What I'm trying to do is suggest that you improve this question by sharing more of what you've looked at and why that doesn't satisfy you, or, if you haven't looked at much, by doing that and then coming back with a more specific question.

The purpose of authentication is to establish the identity of the peer, and the number of ways to do that is infinite. Any software that accomplishes that objective can be categorized as authantication software. Your question is therefore ill-formed. But no competently written piece of software is ever going to receive a private key as input. Keys aren't private if they are communicated.

@EJP --- ill-formed ; just can't be answered ; or can include only answers which are primarily opinion based? About competently written piece of software I agree.

And BTW, I feel as if with a bit of edit what you wrote can actually be a good answer.

@JohnDoes 'Ill-formed' in that it proposes a test via specific requirements when the number of ways to accomplish the task is infinite and need not include any of those proposed.