Common input: x∈L and identity id∈{0,1}n. Auxiliary input to P: w∈RL(x). Stage 1: P and V runs a generation protocol as (Barak 2001) P←V: $$h \xleftarrow {R} \mathcal {H}_{n}$$ P→V: c1=Com(0n,ρ1) P←V: $$r \xleftarrow {R} \{0,1\}\text {} ^{4n}$$ Stage 2: P runs a WIUA using its auxiliary input w P⇔V: P sends c2 to V and gives a WIUA argument of the statement x∈L or (h,c1,c2,r)∈Λ1, where c2=Com(0n,ρ2). Stage 3: P runs a WIUA again upon receiving the public parameter PP P←V: V invokes the PC.Setupalgorithm to generate (PP,K) and sends PP to P. P⇔V: P sends c3 to V and gives a WIUA argument of the statement x∈L or (h,PP,c2,c3,r)∈Λ2, where c3=Com(0n,ρ3). Stage 4: Vdelegates P to generate the CRS P⇔V: V sends the algorithm$$\hat {\mathcal {P}}_{\textsf {{CRSGen}}}$$ to P and gives a ZK argument of the statement $$(\textsf {PP},c_{3},\hat {\mathcal {P}}_{\textsf {{CRSGen}}}) \in \Lambda$$3, where $$\hat {\mathcal {P}}_{\textsf {{CRSGen}}} =i\mathcal {O}(\mathcal {P}^{c_{3},\textsf {{PP}},\textsf {{K}},\rho _{\textsf {{CRSGen}}}},\rho _{i\mathcal {O}})$$. Stage 5: P runs a WISSP using its auxiliary input w P⇔V: P sends (c4,c5) to V and gives a WISSP argument of the statement that (x,w)∈RL(x) or $$(\textsf {PP},\hat {\mathcal {P}}_{\textsf {{CRSGen}}},c_{5}) \in \Lambda _{4}$$, where $$c_{4}=\textsf {CCACom}_{\textsf {id}}^{1:1}(w,\rho _{4})$$ and c5=Com((PP,κ),ρ5). 