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Table 2 Comparisons with revocable IBE schemes

From: Server-aided immediate and robust user revocation mechanism for SM9

 (Boneh and Franklin 2001)(Boldyreva et al. 2008)(Libert and Vergnaud 2009)(Seo and Emura 2013)(Li et al. 2013)(Qin et al. 2015)Ours
Revocation ModeIndirectIndirectIndirectIndirectDirectIndirectDirect
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 Cost1Exp12Exp4 logNExp3 logNExp6Exp3Exp1Exp
Encryption Cost2Exp + 1P7 logNExp5Exp + 2P5Exp3Exp5Exp3Exp
Decryption Cost1Exp + 1P2Exp + 4P1Exp + 3P3P4P3P1P
Key Update Cost(Nr)Exp\(7r\log {\frac {N}{r}}\)Exp4\(r\log {\frac {N}{r}}\)Exp3\(r\log {\frac {N}{r}}\)Exp3(Nr)Exp\(3r\log {\frac {N}{r}}\)ExpnExp
  1. Exp and P denote a module exponentiation and a pairing computation, respectively. N,r and n indicate the numbers of users, revoked users and ciphertexts stored in the server, respectively