Encryption

1. Encryption Public-Key, Identity-Based, Attribute-Based

2. I. Public keyencryptionandsecurityconcepts Eve Use encryption to prevent eavesdropping and achieve confidentiality.

3. Public keyencryption • Bob • generates pair of public key pkB and secret key skB • makes pkB public • decrypts with skB • Alice • encrypts messagem with pkB • sends encrypted message/ciphertextc

4. Public-keyencryptionschemes

5. Negligiblefunctions

6. Security concepts • Security concepts must specify • goals of adversary • resources of adversary • additional information available to adversary. • adversaries should learn almost nothing about plaintext given a ciphertext • adversaries will be probabilistic polynomial time algorithms. • adversaries known complete specifications of encryption schemes (Kerckhoff’s principle) • additional information formalized with chosen plaintext and chosen ciphertext attacks

7. The CPA game

8. The CPA game

9. CPA security

10. The CCA game

11. CCA security Observation CPA security does not imply CCA security.

12. PKC andreality Certification Authority (CA)

13. Certificatesandcertificationauthorities • require significant organizational and technical overhead • require complex data management • their complexity can become a threat to security

14. Public key vs. identity-basedencryption • PKE requires special pairs of keys, not all bit strings can be public keys • in IBE every bit string or identity can be public key • identities can already be certified, e.g. passport numbers • may simplify necessary infrastructure • IBE introduced in 1984 by A. Shamir • first fully functional realization in 2001 by Boneh, Franklin • can be generalized to attribute-based encryption

15. Identity-basedenryption Private Key Generator

16. Identity-basedenryption

17. Identity-basedenryption Private Key Generator

18. Security concepts • Security concepts must specify • goals of adversary • resources of adversary • additional information available to adversary. • adversaries should learn almost nothing about plaintext given a ciphertext • adversaries will be probabilistic polynomial time algorithms. • adversaries known complete specifications of encryption schemes (Kerckhoff’s principle) • additional information formalized with chosen plaintext and chosen ciphertext attacks

19. IBE security – additional requirements • adversaries should learn almost nothing about plaintext given a ciphertext • adversaries will be probabilistic polynomial time algorithms. • adversaries known complete specifications of encryption schemes (Kerckhoff’s principle) • additional information formalized with chosen plaintext and chosen ciphertext attacks • adversary may know private keys to many identities Challenge Exponentially (in n) many private keys depend on master secret msk of polynomial (in n) length.

20. The CPA game

21. The CCA game

22. IBE security

23. Power of PKG • PKG is • very powerful • attractive target for attacks • Possible solutions • secure protocols • distributed realization Private Key Generator

24. PKG via secureprotocols Private Key Generator

25. Distributed PKG

26. Boneh-Franklin IBE andpairings • uses one basic primitive – bilinear pairings • concrete realization with groups on elliptic curves • examples are Weil, Tate, Eta, Ate pairing • but can be described with generic pairings • share this feature with most techniques in IBC

27. Boneh-Franklin IBE andpairings

28. SimplifiedBoneh-Franklin IBE

29. Boneh-Franklin IBE - correctness

30. Boneh-Franklin IBE

31. Boneh-Franklin IBE - correctness