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Authentication mechanism for low memory, low computing power device

I am looking for an authentication mechanism that works best with low memory, low computing power devices. I came across a paper "A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor ...
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What would make it impossible to deny that decryption of a package has taken place?

I'm part of a team designing a system where a user have to be able to read a certain package, if he has preformed an action or series of actions that makes it legal for him to do so. The tricky part ...