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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 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

  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