Title: Implicit Proofs of Membership
Abstract: 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.
