Table 1 Notations
Symbol | Comment |
|---|---|
F p | The finite field with cardinality p |
E | An EC equation by weierstrass |
E(Fp) | An EC-group over Fp |
P, Q | EC-points \(\in\) E(Fp) |
P + Q | The sum of P and Q |
[k]P | The k-th multiple of a point P |
\(x_{P}\) (or) \(y_{P}\) | The x and y coordinates of point P respectively |
P | The base point of E(Fp) |
N | The order of P. Usually, N is a large prime number of bit length ≥ 224 |
M i | The ith member of the group, \(1 \le i \le n,\) where n the total group members |
M n | The last member of the group is the group controller (GC) |
C i | The ith cluster, \(1 \le i \le r,\) where r = number of clusters |
\(x_{{s_{i} }}\) | The CKs of \(C_{i} ,\;1 \le i \le r\) |
CK i | The ith updated CK for new cluster, \(1 \le i \le r\) |
\(M_{{i_{j} }}\) | The jth member of ith cluster, \(1 \le i \le r,\;1 \le j \le n\) |
\(M_{{i_{l} }}\) | The CH of ith cluster and the last member of that cluster |
\(x_{i}\) | The Mi’s private key, an integer belongs to [1,N − 1] |
\(x \leftarrow \left[ {N - 1} \right]\) | Pick an integer \(x \in \left[ {N - 1} \right]\) |
X i | The Mi’s public key |
\(x_{{K_{i,j} }}\) | ECDH common key between ith member Mi and jth member Mj |