From: Server-aided immediate and robust user revocation mechanism for SM9
 | Ours | ||||||
---|---|---|---|---|---|---|---|
Revocation Mode | Indirect | Indirect | Indirect | Indirect | Direct | Indirect | Direct |
Server | - | - | - | - | Semi-trusted | Untrusted | Semi-trusted |
Master Public Key Size | \(2|\mathbb {G}|\) | \(6|\mathbb {G}|\) | \((6 + \log {N})|\mathbb {G}|\) | \((6 + \log {N})|\mathbb {G}|\) | \(3|\mathbb {G}|\) | \((6 + \log {N})|\mathbb {G}|\) | \(4|\mathbb {G}|\) |
Secret Key Size | \(|\mathbb {G}|\) | \(2\log {N}|\mathbb {G}|\) | \(\log {N}(2|\mathbb {G}| + |\mathbb {Z}_{p}|)\) | \(2\log {N}|\mathbb {G}|\) | \(4|\mathbb {G}|\) | \(2|\mathbb {G}|\) | \(|\mathbb {G}|\) |
Ciphertext Size | \(|\mathbb {G}|\) | \(3|\mathbb {G}| + |\mathbb {G}_{T}|\) | \(3|\mathbb {G}| + 2|\mathbb {G}_{T}|\) | \(3|\mathbb {G}| + |\mathbb {G}_{T}|\) | \(3|\mathbb {G}|\) | \(3|\mathbb {G}| + |\mathbb {G}_{T}|\) | \(|\mathbb {G}|\) |
Key Update Size | \((N - r)|\mathbb {G}|\) | \(2r\log {\frac {N}{r}}|\mathbb {G}|\) | \(r\log {\frac {N}{r}}(2|\mathbb {G}| + |\mathbb {Z}_{p}|)\) | \(2r\log {\frac {N}{r}}|\mathbb {G}|\) | \(2(N-r)|\mathbb {G}|\) | \(2r\log {\frac {N}{r}}|\mathbb {G}|\) | 0 |
Key Generation Cost | 1Exp | 12Exp | 4 logNExp | 3 logNExp | 6Exp | 3Exp | 1Exp |
Encryption Cost | 2Exp + 1P | 7 logNExp | 5Exp + 2P | 5Exp | 3Exp | 5Exp | 3Exp |
Decryption Cost | 1Exp + 1P | 2Exp + 4P | 1Exp + 3P | 3P | 4P | 3P | 1P |
Key Update Cost | (N−r)Exp | \(7r\log {\frac {N}{r}}\)Exp | 4\(r\log {\frac {N}{r}}\)Exp | 3\(r\log {\frac {N}{r}}\)Exp | 3(N−r)Exp | \(3r\log {\frac {N}{r}}\)Exp | nExp |