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To what extent depend cryptographic protocols on cryptographic primitives? Are there cryptographic protocols that can only be implemented with certain cryptographic primitives?

If the answer is yes, could you give an example of a protocol depending on a primitive?

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    $\begingroup$ One could certainly imagine a protocol that requires a specific property which would indeed make one primitive the obvious (or maybe even only) choice. An example for this may be e-voting and the use of Paillier encryption. $\endgroup$ – SEJPM Jun 22 '16 at 12:15
  • $\begingroup$ It's probably worth asking the OP to clarify what he/she means by crypto protocols/primitives. @juaninf - Could you please give an example of a protocol and/or a primitive, so that we are sure we both use the same terminology? [In any case, though, a question of "to what extent" is hardly answerable]. $\endgroup$ – tum_ Jun 22 '16 at 12:52
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    $\begingroup$ Usually a protocol requires specific properties of the underlying primitives. For instance, a Key Derivation Function requires some kind of PRF. So the underlying primitive needs to be a PRF. There are however multiple primitives that are PRFs.... So if e.g. HMAC-SHA256 is used then the protocol depends on it to be a PRF. But there would be other primitives that could be used. A protocol depending on a single primitive would mean that no other primitives exist that share the same required properties. That's not so likely, especially if you consider time (we may thing up another primitive). $\endgroup$ – Maarten Bodewes Jun 22 '16 at 21:51

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