Advances, Systems and Applications
Table 3 Notations
Symbols | Descriptions |
|---|---|
\(\lambda\) | Security parameter |
\({\mathcal{H}}\) | Hash function \(:\{ 0,1\}^{ * } \to {\mathbb{G}}\) |
\({\mathcal{H}}_{0}\) | Hash function \(:{\mathbb{Z}}_{p}^{k} \to {\mathbb{Z}}_{p}^{*} \times {\mathbb{G}}^{*}\) |
\({\mathcal{H}}_{{1}} \,\) | Hash function \(:{\tilde{\mathbb{G}}}^{n(k + 3)} \to \Theta^{n} \subseteq {\mathbb{Z}}_{p}^{n}\) |
\(e\) | Bilinear groups |
\({\mathbb{G}}{,}{\tilde{\mathbb{G}}}{,}{\mathbb{G}}_{T}\) | Cyclic groups of order \(p\) |
\(\text{g},\hat{\mathrm{g}}, \tilde{\mathrm{g}}\) | Generators:\(\text{g},\hat{\mathrm{g}} \in_{R} \mathbb{G}^{*}, \tilde{g} \in_{R} {\tilde{\mathbb{G}}}\) |
\({\mathcal{I}\ominus } = \{ I_{i} \}_{{i \in [1{, }n]}}\) | The set of \(n\) DOs,\(n = \left| {\mathcal{I}} \right|\) |
\({\mathcal{S}\ominus } = \{ S_{j} \}_{{j \in [1{, }\eta ]}}\) | The set of \(\eta\) RGs,\(\eta = \left| {\mathcal{S}} \right|\) |
\({\mathcal{U}\ominus } = \{ U_{j} \}_{{j \in [1{, }q]}}\) | The set of \(q\) DUs,\(q = \left| {\mathcal{U}} \right|\) |
\({\mathcal{O}\ominus } = \{ {\mathcal{O}\ominus }_{i} \}_{{i \in [1{, }\tau + 1]}}\) | The set of \(\tau + 1\) RGs,\(\tau + 1 = \left| {\mathcal{O}} \right|\) |