... Jesús Almansa and Marco Carbone 4th April 2002 { jfa,

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

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

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

5 Key Management A3A3 A1A1 A4A4 A2A2

6 A3A3 A1A1 A4A4 A2A2 TTP

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

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 Pretty Good Privacy (PGP) certification path web of trust

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

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

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

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 Formalism: Graphical Notation Hypothesis and Evidences: hE

17 Formalism: Graphical Notation(2) Σ Belief:

18 Formalism: Graphical Notation(3) Argument:

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

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 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 Formalism: Graphical Notation(5) Confidence Values:

23 Formalism: Graphical Notation(6) Confidence Assignment:

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

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

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

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

29 Principles: P3  f h1h1 h2h2 If

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

31 Principles: P4 h2h2 h1h1 If

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

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

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

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

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

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

41 Confidence Valuation in PGP  f h1h1 h2h2 If

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

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

44 Confidence Valuation in PGP h2h2 h1h1 If

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

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 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.