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I was taught only GGM based PRF construction in class. It's very inefficient. I am just curious about various PRF constructions from standard assumptions. Please provide a few PRF constructions from various assumptions.

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  • $\begingroup$ Well, one standard assumption is that the SHA-256 compression function is a PRF, from which we can conclude that HMAC-SHA256 is a PRF (and a reasonably efficient one at that), but maybe you meant to restrict the domain of ‘standard assumptions’? $\endgroup$ – Squeamish Ossifrage Apr 26 at 18:44
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The most common efficient PRFs from specific assumptions are:

The Naor-Reingold PRF, which is based on the decision Diffie-Hellman assumption (DDH), and

The BPR PRF, which is based on the learning with error assumption (LWE).

Perhaps slightly less well-known is the NRR PRF, which is based on the hardness of factoring.

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