Efficient verifiable searchable encryption with search and access pattern privacy

Security and Safety of Data in Cloud Computing

Open Access

Table 4.

Efficiency comparison between [16] and our schemes

Schemes	Computation costs			Communation costs		Storage costs
	Setup	Trapdoor	Search	Setup	Search	Cloud server 1
	m(L + 1)T_E	mT_E	(L² + 2L + 3)mT_M + (L² + 4L)	2(L + 1)m\|ℤ_N²\|	(4mL + 8m + 4L + 2)\|ℤ_N²\|	2(L + 1)m\|ℤ_N²\|
Wang et al.’s scheme [16]			mT_A + 4LmT_E + 2LmT_D
SAP-ECKS	m(L + 1)T_R	$m T_{E}'$ $mT_{E}\prime$	(4L + 2)mT_M + (4mL+	2(L + 1)m\|ℝ\|	(L + 1)m\|ℝ\|+(2mL + 2m+	2(L + 1)m\|ℝ\|
			2m − 2L − 1)T_A		2L + 1)\|ℤ_N²\|
SAP-VECKS	m(L + 1)T_R	$2 m T_{E}'$ $2mT_{E}\prime$	(8L + 6)mT_M + (4mL+	2(L + 1)m\|ℝ\|	(2L + 2)m\|ℝ\|+(4mL + 4m+	2(L + 1)m\|ℝ\|
			2m + 8L + 2)T_A		4L + 2)\|ℤ_N²\|

T_E, $T_{E}'$ $T_{E}\prime$ , T_D, T_A, T_M, and T_R represent the time cost of a BCP encryption operation, a Paillier encryption operation, a decryption operation, a homomorphic addition operation, a multiplication operation between a ciphertext and a random number, and a multiplication operatation, respectively. m is the number of keywords in the keyword dictionary. |ℝ| and |ℤ_N²| are the bit lengths of the elements in ℝ and ℤ_N².

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