Table 1 Explanation of parameters
From: Group signature with time-bound keys and unforgeability of expiry time for smart cities
Parameters | Description | Parameters | Description |
|---|---|---|---|
\(\kappa\) | The security parameter | \(\sigma\) | The signature |
\({\text{BG}}\) | A type-3 bilinear group | \(\pi\) | The proof |
\(P\) | Generator of group \({\mathbb{G}}_{{1}}\) | \(i\) | The user |
\(\hat{P}\) | Generator of group \({\mathbb{G}}_{{2}}\) | \(m\) | The message |
\(gpk\) | Group public key | \(\Pi\) | The non-interactive zero-knowledge proofs system |
\(ik\) | The issuing key | \(\Omega\) | The encryption algorithm |
\(ok\) | The opening key | \(\Sigma\) | The digital signature algorithm |
\(\mathrm{reg}\)Â Â | The user registration table | \(crs\) | Common reference string |
\({\mathcal{R}}_{t}\) | Revoked users at time t | \({(}sk_{{\mathcal{R}}} ,pk_{{\mathcal{R}}} )\) | The key pair from the SPS-EQ algorithm |
\(\, gsk\) | The group signing key | \({ (}sk_{o} ,pk_{o} )\) | The key pair from the encryption algorithm |
\(grt\) | The revocation token | \((sk_{\epsilon } ,pk_{\epsilon } )\) | The key pair from the signature algorithm |
\(info\) | The group information | \((usk{,}upk)\) | The user secret/public key pair |
\(t\) | The current time | \({(}U_{i} ,Q{)}\) | The equivalence classes representative on users |
\(\tau\) | The expiry time | \({(}T_{i} ,Q{)}\) | The equivalence classes representative on time |