1 Hierarchical Identity-Based Encryption with Constant Size Ciphertext Dan Boneh, Xavier Boyen and Eu-Jin Goh Eurocrypt 2005 投影片製作：張淑慧.

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Presentation transcript:

1 Hierarchical Identity-Based Encryption with Constant Size Ciphertext Dan Boneh, Xavier Boyen and Eu-Jin Goh Eurocrypt 2005 投影片製作：張淑慧

2 Outline Notations Scheme 1: With constant size ciphertext based on Decision BDHE assumption Hybrid Scheme Application Conclusion

3 Bilinear map

4 l-Bilinear Diffie-Hellman Exponent (l-BDHE) Assumption

5 KGC (I1)(I1) (I1,I2)(I1,I2) (I 1,I 2,…,I l ) Level 0 Level 1 Level 2 Level l Hierarchical structure (key generation center)

6 Scheme 1 *A HIBE system with constant size ciphertext * A selective-ID secure Setup KeyGen Encrypt Decrypt

7 Scheme 1 (continuous)

8

9

10 Scheme 1 (continuous)

11 Remark If l+1-BDHE assumption holds, then scheme 1 is selective identity, chosen plaintext (IND-sID-CPA) secure. Chosen ciphertext security: refer to Canetti et al. [10] (Eurocrypt 2004) or Boneh and Katz [7] (RSA-CT 2005) (more efficient) Arbitrary identities: hashing each I i where ID=(I 1,…,I k )

12 Hybrid Scheme :

13 Hybrid Scheme :

14 Hybrid Scheme Setup KeyGen Encrypt Decrypt

15 Hybrid Scheme (continuous)

16 Hybrid Scheme (continuous)

17 Hybrid Scheme (continuous)

18 Hybrid Scheme (continuous)

19 Scheme 1Scheme 2Hybrid scheme ω=1/2 Private key size Ciphertext size

20 Applications Forward secure encryption scheme Forward secure HIBE scheme Broadcast encryption scheme

21 Conclusion Is it possible to propose a HIBE scheme with both private key size O(1) and ciphertext size O(1)? To propose a HIBE scheme with constant size ciphertext based on HDHI assumption is the future research..END.

22 Scheme 1: How to generate d ID by d ID|k-1

23 Scheme 2: ( [1] Eurocrypt 2004 ) Efficient selective identity HIBE based on BDH without random oracles Setup KeyGen Encrypt Decrypt

24 Scheme 2 (continuous)

25 Scheme 2 (continuous)

26 Scheme 2 (continuous)

27 Scheme 2 (continuous)

28 Hybrid Scheme: How to generate private key d ID

29 Hybrid Scheme : How to generate private key d ID (continuous)

30 Hybrid Scheme: An example for encryption

31 q-Bilinear Diffie-Hellman Inversion (q-BDHI) problem