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

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

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

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

Key Management A1 A2 A3 A4

Key Management A1 A2 TTP A3 A4

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

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

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

certification path web of trust Pretty Good Privacy (PGP)

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

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

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

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

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

E h Formalism: Graphical Notation Hypothesis and Evidences:

Σ Formalism: Graphical Notation(2) Belief:

Formalism: Graphical Notation(3) Argument:

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

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.

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

Formalism: Graphical Notation(5) Confidence Values:

Formalism: Graphical Notation(6) Confidence Assignment:

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

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

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

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

Principles: P3 If f  h2 h1

Principles: P3 (2) ( ) and f = then ( , , ( ) ) e e h1 = h2

Principles: P4 If h1 h2

Principles: P4 (2) then , , ( ) ( )  e e h1 h2

Modeling PK Certification • To realize the abstract formalism in a concrete problem: • identify pieces of evidence • identify possible conclusions • define confidence values • 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

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

AutX,K TrustX,K CertK1,X,K2 Confidence Valuation in PGP Statements:

AutY,K1 AutX,K TrustY,K1 Confidence Valuation in PGP CertK1,X,K

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

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

Confidence Valuation in PGP If f  h2 h1

Confidence Valuation in PGP ( ) and f = then , , ( ) ( ) e e h1 = h2

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

Confidence Valuation in PGP If h1 h2

Confidence Valuation in PGP P4 holds then , , ( ) ( )  e e h1 h2

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.

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