1. ... Jesús Almansa and Marco Carbone 4th April 2002 { jfa, carbonem} @brics.dk

2. 2 Two-Party Communication AliceBob Adversary (Passive) unsecured channel secure channel

3. 3 Two-Party Communication Alice Bob Adversary (Active) unsecured channel secure channel

4. 4 Public-Key Cryptography Alice Bob Adversary (Active) unsecured channel

5. 5 Key Management A3A3 A1A1 A4A4 A2A2

6. 6 A3A3 A1A1 A4A4 A2A2 TTP

7. 7 Public-Key Certificate Vouches for the authenticity of the public key bound to the subject entity Usefulness: To prove identity (authenticity of an entity) To avoid denials Good: trust can be used transitively Bad:  all trust placed with one single entity  if TTP is compromised, comm. is insecure

8. 8 Public-Key Infrastructure (PKI) CertificatesTrust Relations Evidences Conclusions associated (confidence) values

9. 9 Pretty Good Privacy (PGP) A widely used software package (Zimmerman) Stalling’s notation: (entity, key) A B pk A signed by pk B

10. 10 Pretty Good Privacy (PGP) certification path web of trust

11. 11 Pretty Good Privacy (PGP) Confidence Values = {unknown, no trust, marginally trusted, fully trusted } pk A is valid if either or pk A

12. 12 Pretty Good Privacy (PGP) Bob Alice Is Bob’s key valid for Alice? : Yes Bob Alice : No

13. 13 Confidence Valuation in a PKI based on Uncertain Evidence (R. Kohlas – U. Maurer) Agenda:  Formalism Basics & Graphical Notation Principles  Modeling Public-Key Certification  Confidence Valuation in PGP  Conclusions

14. 14 Formalism: Basic Definitions Piece of Evidence (Assumption) A statement we suppose is true. Hypothesis A statement not generally known to be true.

15. 15 Formalism: Basic Definitions(2) Argument for h Collection of assumptions from which (along with the belief) h can be derived. Belief Composition of statements taken as a fact.

16. 16 Formalism: Graphical Notation Hypothesis and Evidences: hE

17. 17 Formalism: Graphical Notation(2) Σ Belief:

18. 18 Formalism: Graphical Notation(3) Argument:

19. 19 Formalism: Graphical Notation(4) Validity and Arguments: h Σ

20. 20 Formalism: Basic Definitions(3) Confidence Value Degree of certainty for an assumption or hypothesis to be true. Confidence Assignment Entity’s initial belief w.r.t. each assumption.

21. 21 Formalism: Basic Definitions(4) Reduces a priori information to a single confidence value for the hypothesis Confidence Valuation Function that takes a hypothesis h and a confidence assignment and returns a confidence value for h.

22. 22 Formalism: Graphical Notation(5) Confidence Values:

23. 23 Formalism: Graphical Notation(6) Confidence Assignment:

24. 24 Formalism: Graphical Notation(7) Confidence Valuation: e ()=, hh

25. 25 Confidence Valuation in a PKI based on Uncertain Evidence (R. Kohlas – U. Maurer) Agenda:  Formalism Basics & Graphical Notation Principles  Modeling Public-Key Certification  Confidence Valuation in PGP  Conclusions

26. 26 Principles: P1   e ()=, h h then If

27. 27 Principles: P1 (2)  e ()=, h h then If

28. 28 Principles: P2 then e (), h If   e (), h

29. 29 Principles: P3  f h1h1 h2h2 If

30. 30 Principles: P3 (2) and = f ( ) then e (), h1h1 e ( ), h2h2 =

31. 31 Principles: P4 h2h2 h1h1 If

32. 32 Principles: P4 (2) then e (), h1h1 e (), h2h2 

33. 33 Confidence Valuation in a PKI based on Uncertain Evidence (R. Kohlas – U. Maurer) Agenda:  Formalism Basics & Graphical Notation Principles  Modeling Public-Key Certification  Confidence Valuation in PGP  Conclusions

34. 34 Modeling PK Certification In the particular case of PK Certification: Pairs of entities and keys can be seen like statements The confidence values must be assigned to entities To realize the abstract formalism in a concrete problem: identify pieces of evidence identify possible conclusions define confidence values

35. 35 Modeling PK Certification Alice Bob Carol, K1 Carol, K2 Bob Carol, K1 Alice

36. 36 Confidence Valuation in a PKI based on Uncertain Evidence (R. Kohlas – U. Maurer) Agenda:  Formalism Basics & Graphical Notation Principles  Modeling Public-Key Certification  Confidence Valuation in PGP  Conclusions

37. 37 Confidence Valuation in PGP Statements: Cert K1,X,K2 Aut X,K Trust X,K

38. 38 Confidence Valuation in PGP Cert K1,X,K Aut Y,K1 Trust Y,K1 Aut X,K

39. 39 Confidence Valuation in PGP   e ()=, h h then If P1 holds

40. 40 Confidence Valuation in PGP then e (), h If   e (), h P2 holds

41. 41 Confidence Valuation in PGP  f h1h1 h2h2 If

42. 42 Confidence Valuation in PGP and = f ( ) then e (), h1h1 e (), h2h2 =

43. 43 Confidence Valuation in PGP Bob Alice Is Bob’s key valid for Alice? : Yes Bob Alice : No P3 does not hold!

44. 44 Confidence Valuation in PGP h2h2 h1h1 If

45. 45 Confidence Valuation in PGP then e (), h1h1 e (), h2h2  P4 holds

46. 46 Confidence Valuation in a PKI based on Uncertain Evidence (R. Kohlas – U. Maurer) Agenda:  Formalism Basics & Graphical Notation Principles  Modeling Public-Key Certification  Confidence Valuation in PGP  Conclusions

47. 47 Conclusions Summary Two parts: –Logic –Confidence Valuation Both efficient! What are and how to assign confidence values. In light of what was said, how adequate is it for trust management.