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Table 3 Computational overhead among various schemes

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

Schemes Access policy Hidden policy Ciphertext size Test time Decryption time Group order
Nishide et al. [6] AND-gates on multi-values Partially hidden \(2^n[\Vert G_{T}\Vert +(4n+1)\Vert G\Vert ]\) User: super-polynomial User: \((3n+1)e\) p
Li et al. [24] AND-gates on multi-values Partially hidden \(2^n[\Vert G_{T}\Vert +8n\Vert G\Vert ]\) User: super-polynomial user: 4ne p
Lai et al. [25] AND-gates on multi-values Partially hidden \(2^n[\Vert G_{T}\Vert +(4n+2)\Vert G\Vert ]\) user: super-polynomial User: \((n+1)e\) pqr
Cui et al. [28] LSSS Partially hidden \(\Vert G_{T}\Vert +(6n+2)\Vert G\Vert\) User: super-polynomial User: \((6n+1)e\) p
Ours Tree-based structure Secret policy is fully hidden Fog: \((2+2n_1)\Vert G\Vert\) user: \((n_2+2)\Vert G_T\Vert +(4+4n_2)\Vert G\Vert\) Cloud: \(2(n_1+n_2+nn_2+1)e\) Cloud: \((n_1+n_2+6)e\) User: no pairing p
  1. \(\Vert G_{T}\Vert\): the size of group element of \({\mathbb {G}}_T\). \(\Vert G\Vert\): the size of group element of \({\mathbb {G}}_0\)
  2. e, Bilinear pairing; n, number of possible attributes in the access policy; m, number of possible values of each attribute; \(n_1\), number of attributes in the public access policy; \(n_2\), number of attributes in the secret access policy. \(n_1+n_2=n\)
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