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

EURASIP Journal on Wireless Communications and Networking

Table 3 Computational overhead among various schemes

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

\(\Vert G_{T}\Vert\): the size of group element of \({\mathbb {G}}_T\). \(\Vert G\Vert\): the size of group element of \({\mathbb {G}}_0\)
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. \(n_1+n_2=n\)