Implicit proofs of membership

Smooth hash proof systems have been introduced by Cramer and shoup to build compact efficient cca2 encryption in the standard model. Since then, they found applications in a broad range of protocols from oblivious transfer to authenticated key exchange, passing by witness examples.
In this talk, we will start by a panorama of languages that can be managed by such a primitive and then show how this is enough to instantiate efficiently various primitives.
We will provide examples of such constructions first with vanilla cryptography (elliptic curve, paillier) but also show that post-quantum constructions can be achieved with a non-prohibitive efficiency in both lattice and code based cryptography, widening the range of primitive available under those hypotheses.