Item

Description

$G_1$

a cyclic additive group with order p

$G_2$

a cyclic multiplicative group with order p

e

a bilinear pairing in which $e:G_1\times G_1\to G_2$

$H_1\left(x\right)$

hash function in which $H_1\left(x\right)={\left\{0,1\right\}}^{*}\to G_1^{*}$

$H_2\left(x\right)$

hash function in which $H_2\left(x\right)=G_2\to Z_p^{*}$

$N_{\mathcal{F}}$

Founder nodes

N_i

Identification of node i

SK_i

Private key of node i

PK_i

Public key of node i

MSK

Master private key of system

MPK

Master public key of system

MSK_i

Share of master private key hold by node i