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Table 1 Comparison of CP-ABE schemes with hidden policy

From: Ciphertext-policy attribute-based encryption with hidden sensitive policy from keyword search techniques in smart city

Schemes Access policy Policy hidden Ciphertext size Decryption time Decryption outsourced
Nishide et al. [6] AND-gates on multi-values Partially hidden Linear Deterministic and lineara No
Li et al. [24] AND-gates on multi-values Partially hidden Linear Deterministic and linear No
Lai et al. [25] AND-gates on multi-values Partially hidden Linear Deterministic and linear No
Zhang et al. [26] AND-gates on multi-values Partially hidden Linear Deterministic and linear No
Lai et al. [27] LSSS Partially hidden Linear Opportunistic and linearc No
Cui et al. [28] LSSS Partially hidden Linear Opportunistic and linear No
Lweko et al. [18] Inner product predicates Fully hidden Super-polynomial Opportunistic and linear No
Michalevsky et al. [29] Inner product predicates Fully hidden Super-polynomial Opportunistic and linear No
Khan et al. [30] LSSS with hidden vectors Fully hidden Super-polynomial Opportunistic and linear No
Ours Tree-based structure Public policy is exposed and secret policy is fully hidden Linear Deterministic and constantb Yes
  1. a“Deterministic and linear”: end user needs to test fixed the number of times, usually is one, to look for the correct attributes for successful decryption, and the decryption time scales linearly with the complexity of the access policy.
  2. b“Deterministic and constant”: the test time for the cloud is fixed and the decryption time is constant.
  3. c“Opportunistic and linear”: several tests may be required, which could be super-polynomial when user has many values for each attribute. The decryption time scales linearly with the complexity of the access policy
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