Advances, Systems and Applications
Table 2 Notation
From: A threshold hybrid encryption method for integrity audit without trusted center
Notation | Meaning |
|---|---|
\({\mathbb {G}_{1}},{\mathbb {G}_{2}}\) | Two multiplicative cyclic groups with a prime order p |
g,ω | Generators of \({\mathbb {G}_{1}}\) |
e | A bilinear pairing \({e}: {\mathbb {G}_{1}}\times {{\mathbb {G}_{1}}\rightarrow {\mathbb {G}_{2}}}\) |
\(\mathbb {Z}_{p}\) | Residue class ring modulo p |
\(\mathbb {Z}_{p}^{*}\) | Multiplicative group of invertible integers modulo p |
\({\mathbb {F}_{\eta }}\) | A finite field with η prime elements |
\({E\left (\mathbb {F}_{\eta }\right)}\) | An elliptic curve on the finite field \({\mathbb {F}_{\eta }}\) |
Q | The generator of the elliptic curve \({E\left (\mathbb {F}_{\eta }\right)}\) |
N | The number of the managers {P1,P2,…,PN} |
\({\mathbb {F}_{q}}\) | A finite field with a prime number q>N |
t | The preset threshold value of Shamir secret sharing |
H(·) | A hash function:\({\left \{ {0,1} \right \}^{*}} \to {\mathbb {G}_{1}} \) |