1. Daniel Moran & Marina Yatsina

2. Access control through encryption

3. Publish data in such way that each client can only see the appropriate parts.

4. Access control through encryption example

5. Access control through encryption example safasfdsfdsgdsgdnml gmpodsngnjyjnsbigfs The physician doesn’t see the nurse’s information

6. Protections example nvoidsnfnvodsnvonds foinfbidpadmpnfosbgj The nurse doesn’t see the physician’s information

7. Access control through encryption Publish data in such way that each client can only see the appropriate parts. Alternative to keeping data on servers and relying on them for mediating between data and clients. I’m a nurse I’m a physician

8. Access control through encryption Publish data in such way that each client can only see the appropriate parts. Alternative to keeping data on servers and relying on them for mediating between data and clients. Avoids data duplication. There is only one copy of the data, each client sees the information in it based on the set of keys he posses.

9. Agenda Protections. Security & data Secrecy. Motivation. Basic notations. Formal analysis. Computational analysis. Summary & conclusions. We need them to understand the motivation

10. Agenda Protections. Security & data Secrecy. Motivation. Basic notations. Formal analysis. Computational analysis. Summary & conclusions.

11. Protections example

12. Protections example cont.

13. Protections example cont.

14. Protections XML tree in which nodes are guarded by positive boolean formulas over a set of cryptographic keys.

15. Protections cont. Accessing a node is conditioned by possessing a combination of keys that satisfy the formula that guards the node (and the formulas that guard its ancestors). If you don’t have you can’t access any of the nodes

16. Protections cont. Formally: protection is a function that maps each possible set of keys to the set of nodes that can be accessed using those keys. hospital, physician, administrative

17. Agenda Protections. Security & data Secrecy. Motivation. Basic notations Formal analysis. Computational analysis. Summary & conclusions.

18. Security & data secrecy Adversary is given an arbitrary set of keys.

19. Security & data secrecy cont. The adversary select 2 documents which contain the same information in the nodes he has access too according to his keys.

20. Security & data secrecy cont. The adversary is given a partially encrypted document that corresponds to one of its 2 documents. dsdmhtkinhf

21. Security & data secrecy cont. Security means that the adversary cannot decide which of the 2 documents was used in creation of the partially encrypted document (better than picking randomly). dsdmhtkinhf ? ?

22. Security & data secrecy cont. Security means that the adversary cannot decide which of the 2 documents was used in creation of the partially encrypted document (better than picking randomly). Meaning, partially encrypted document reveals no information on the data in the nodes that should be hidden from the adversary.

23. Agenda Protections. Security & data Secrecy. Motivation. Basic notations. Formal analysis. Computational analysis. Summary & conclusions.

24. Motivation Bridge the gap between the abstract semantic of protections and the use of actual keys and (symmetric) encryption. Establish that if data is hidden according to protection, then it is secret according to the presented definition of secrecy. dsdmhtkinhf ? ?

25. XML Protection Normalized protection Key shares Agenda Protections. Security & data Secrecy. Motivation. Basic notations. Formal analysis. Computational analysis. Summary & conclusions.

26. Basic notations - XML example

27. Basic notations - XML We describe XML tree as follows: For example:

28. Basic notations – Protection Lets recall:

29. Basic notations – Protection cont. We describe protection tree as follows: Explanation in a couple of slides

30. Basic notations – Protection cont. For example:

31. Basic notations – Normalized protection In standard encryption schemes we can encrypt under a single key but not under a boolean combination of keys. Using simple transition we can rewrite any protection into an equivalent normalized protection where all formulas that guard a node are atomic.

32. Basic notations – Normallized protection Lets recall:

33. Basic notations – Normalized protection cont.

34. Basic notations – Key shares We’ve split key into 2 pieces, each piece is called key share. Key shares are pieces of information that together allow the recovery of the key. No proper subset of key shares suffices for computing. We define:

35. Expression Recoverable keys Structure Pattern Pattern-protection semantics Agenda Protections. Security & data Secrecy. Motivation. Basic notations Formal analysis. Computational analysis. Summary & conclusions.

36. Formal analysis - Expression Lets recall:

37. Formal analysis – Expression cont. We describe expressions as follows: For example:

38. Formal analysis – Expression cont. We use expressions for giving a precise definition of how to map normalized protection to a partially encrypted document. safasfdsfdsgdsgdnml gmpodsngnjyjnsbigfs

39. Formal analysis – Expression cont. We describe expressions as follows: are normalized protections

40. Formal analysis – Expression cont. For example:

41. Formal analysis – Recoverable keys A key is recoverable from expression if it occurs in clear (not encrypted) form, or if it’s encrypted under For example: key symbols that occur in E or their shares occur in E

42. Formal analysis – Structure We use structures to describe the structure of the partially encrypted document.

43. Formal analysis – Structure We describe structures as follows:

44. Formal analysis – Structure cont. Lets recall:

45. Formal analysis – Structure cont. Lets recall:

46. Formal analysis – Pattern A pattern represents the information an expression reveilles to the adversary.

47. Formal analysis – Pattern We describe pattern that can be observed in using for decryption keys from as follows:

48. Formal analysis – Pattern cont. Lets recall:

49. Formal analysis – Pattern cont. Lets recall:

50. Formal analysis – Pattern cont. We describe patterns as follows: For example:

51. Formal analysis – Pattern- protection semantics We can transform protections into cryptographic expressions, and use patterns to provide an equivalent semantics for protections. Formally: Let be a normalized protection. For any set of keys and any, it holds that can be accessed iff occurs in.

52. Results Agenda Protections. Security & data Secrecy. Motivation. Basic notations Formal analysis. Computational analysis. Summary & conclusions.

53. Computational analysis - Results We can give concrete interpretation for expressions and patterns as bit-strings. This interpretations is computational because it relies on computations on bit-strings. 10110100011011010110101

54. Computational analysis - Results Expressions and patterns induce distributions on bit- strings. These distributions are obtained by replacing data symbols with bit-strings and implementing encryption and key sharing with actual encryption and secret sharing schemes.

55. Computational analysis - Results Patterns faithfully represent the information that expressions reveal, even when expressions and patterns are mapped to bit strings. Specifically, distribution ensembles associated with and are computationally indistinguishable. 10110100011011010110101

56. Computational analysis - Results If some data is secret according to the abstract semantics of protections, then that data is in fact computationally hidden. However, attacker can still learn a great deal about the length and even the structure of encrypted parts of the document. dsdmhtkinhf ? ?

57. Agenda Protections. Security & data Secrecy. Motivation. Basic notations Formal analysis. Computational analysis. Summary & conclusions.

58. Summary & conclusions We saw justification for encryption-based techniques for enforcing access policies for XML documents. Specifically, we saw that XML data that is secret according to an abstract, symbolic semantics is indeed secret with respect to a strong, computational notion of security.