Table 4 IND-ID-CPA security for IB-DRE

\(\mathbf {Experiment}~\mathsf {Exp}_{\mathcal {IB-DRE},\mathcal {A}}^{\mathsf {ind-id-cpa}}(1^{\lambda }):\)

\((PP,Msk)\overset {\$}{\leftarrow } \mathsf {Setup}_{\mathsf {ID}}(1^{\lambda })\)

\((id_{1st}^{\star },id_{2nd}^{\star },M_{0},M_{1},s)\overset {\$}{\leftarrow }\mathcal {A}^{\mathsf {KeyGen}_{\mathsf {ID}}(PP, Msk,id_{1st},id_{2nd})}(PP)\);

\(b\overset {\$}{\leftarrow }\{0,1\},c^{\star }\overset {\$}{\leftarrow }\mathsf {Enc}_{\mathsf {ID}}(PP,id_{1st}^{\star },id_{2nd}^{\star },M_{b})\);

\(b^{\prime }\overset {\$}{\leftarrow }\mathcal {A}^{\mathsf {KeyGen}_{\mathsf {ID}}(PP,Msk,id_{1st},id_{2nd})\wedge id_{j}\neq id_{j,j=1st,2nd}^{\star }}(c^{\star },s)\);

if b^′=b then return 1 else return 0.