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

3. 3 Bilinear map

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

5. 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. 6 Scheme 1 *A HIBE system with constant size ciphertext * A selective-ID secure Setup KeyGen Encrypt Decrypt

7. 7 Scheme 1 (continuous)

8. 8

9. 9

10. 10 Scheme 1 (continuous)

11. 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. 12 Hybrid Scheme :

13. 13 Hybrid Scheme :

14. 14 Hybrid Scheme Setup KeyGen Encrypt Decrypt

15. 15 Hybrid Scheme (continuous)

16. 16 Hybrid Scheme (continuous)

17. 17 Hybrid Scheme (continuous)

18. 18 Hybrid Scheme (continuous)

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

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

21. 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. 22 Scheme 1: How to generate d ID by d ID|k-1

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

24. 24 Scheme 2 (continuous)

25. 25 Scheme 2 (continuous)

26. 26 Scheme 2 (continuous)

27. 27 Scheme 2 (continuous)

28. 28 Hybrid Scheme: How to generate private key d ID

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

30. 30 Hybrid Scheme: An example for encryption

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