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Advances, Systems and Applications

Table 1 Notations

From: An improved secure designated server public key searchable encryption scheme with multi-ciphertext indistinguishability

Notation Description
(PkO,SkO) Data owner’ keys
(PkR,SkR) Receiver’ keys
(PkS,SkS) Server’keys
κ Security parameter
Cw Keyword ciphertext
\(T_{w^{\prime }}\) Search trapdoor
\(\mathcal {C},\mathcal {A}\) Challenger and adversary
\(\mathcal {O}\) Oracles
g,h,g1 Generators of group G1
G1,G2 Multiplicative cyclic groups with order q
q A large prime number
H1 A hash function \(H_{1}:G_{1} \rightarrow Z_{q}^{*}\)
H2 A hash function \(H_{2}:\{0,1\}^{*} \rightarrow Z_{q}^{*}\)
pp A global parameter
E The time cost of one modular exponentiation
Hp The time cost of one Hash-to-point operation
P The time cost of one pairing operation
M The time cost of one multiplication operation
H The time cost of one hash function operation
\(\vert \mathbb {G}_{1} \vert \) the bit length of an element in \(\mathbb {G}_{1}\)
\(\vert \mathbb {G}_{2} \vert \) the bit length of an element in \(\mathbb {G}_{2}\)
|q| the bit length of an element in \(\mathbb {Z}_{q}\)