“…Verifiable encryption [1,8], is a protocol between a prover and a verifier such that as a result of the protocol, on input public key E, and value v, the verifier obtains an encryption e of some value s under E such that (w, y) ∈ R. For instance, R could be the relation (w, g w ) ⊂ Z q × G. Generalizing the protocol of Asokan et al [1], Camenisch and Damgård [8] provide a verifiable encryption scheme for a class of relations that, in particular, includes all discrete-logarithm relations that are of relevance in this paper. We denote verifiable encryption similarly as the PK 's, e.g., e := VE(ElGamal, (u, v)){ξ : y = g ξ } denotes the verifiable encryption protocol for the ElGamal scheme, whereby log g y is encrypted in e under public key (u, v).…”