| scheme | search time | index | size security | assumption | | Boneh, et al.[46] | nvp | nv(2e+p) | PK-CKA2 | BDH | | Baek, et al.[53](PEKS-1) | nvp | nv(3e+p) | PK-CKA2 | CDH | | Baek, et al.[53](PEKS-2) | nvp | nv(e+2p) | PK-CKA2 | BDH | | Crescenzo and Saraswat[50] | 4nlJ | 4nvlJ | PK-CKA2 | QIP | | Khader[52] | 4nve | 5+3nve | PK-CKA2 | DDH | | Rhee, et al.[54] | nv(e + p) | 2nve+(7+nv)p | PK-CKA2 | BDH, 1-BDHI | | Rhee, et al.[59] | nv(2e + p) | 2nve+nvp | PK-CKA2 | BDH, 1-BDHI |
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