Jes

1
...

• Jesús Almansa and Marco Carbone

jfa, carbonem _at_brics.dk
4th April 2002
2
Two-Party Communication
unsecured channel
Alice

• Bob

secure channel
Adversary (Passive)
3
Two-Party Communication
unsecured channel
Bob
Alice
secure channel
Adversary (Active)
4
Public-Key Cryptography
unsecured channel
Alice
Bob
Adversary (Active)
5
Key Management
A1
A2
A3
A4
6
Key Management
A1
A2
TTP
A3
A4
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)
Certificates
Trust Relations
Evidences
Conclusions
9
Pretty Good Privacy (PGP)
A widely used software package (Zimmerman)
Stallings notation
10
Pretty Good Privacy (PGP)
11
Pretty Good Privacy (PGP)
Confidence Values
unknown,
no trust,
marginally trusted,
fully trusted
12
Pretty Good Privacy (PGP)
Yes
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

• Hypothesis
• A statement not generally known to be true.

• Piece of Evidence (Assumption)
• A statement we suppose is true.

15
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.

16
Formalism Graphical Notation
Hypothesis and Evidences
17
Formalism Graphical Notation(2)
Belief
18
Formalism Graphical Notation(3)
Argument
19
Formalism Graphical Notation(4)
Validity and Arguments
S
h
20
Formalism Basic Definitions(3)

• Confidence Value
• Degree of certainty for an assumption or
• hypothesis to be true.

• Confidence Assignment
• Entitys initial belief w.r.t. each assumption.

21
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
22
Formalism Graphical Notation(5)
Confidence Values
23
Formalism Graphical Notation(6)
Confidence Assignment
24
Formalism Graphical Notation(7)
Confidence Valuation
(
)
,
e
h
h
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
?
If
?
,
(
)
e
h
then
27
Principles P1 (2)
?
If
,
(
)
e
h
then
28
Principles P2
,
,
(
)
(
)
e
e
then
h
?
h
29
Principles P3
If
f
?
h2
h1
30
Principles P3 (2)
(
)
and
f

then
(
,
,
(
)
)
e
e
h1
h2

31
Principles P4
If
h1
h2
32
Principles P4 (2)
then
,
,
(
)
(
)
?
e
e
h1
h2
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

• 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

35
Modeling PK Certification
Bob
Bob
Carol, K1
Carol, K2
Carol, K1
Alice
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
38
Confidence Valuation in PGP
CertK1,X,K
39
Confidence Valuation in PGP
?
If
?
P1 holds
,
(
)
e
h
then
40
Confidence Valuation in PGP
P2 holds
,
(
)
e
then
h
?
41
Confidence Valuation in PGP
If
f
?
h2
h1
42
Confidence Valuation in PGP
(
)
and
f

then
,
,
(
)
(
)
e
e
h1
h2

43
Confidence Valuation in PGP
P3 does not hold!
Yes
No
44
Confidence Valuation in PGP
If
h1
h2
45
Confidence Valuation in PGP
P4 holds
then
,
,
(
)
(
)
?
e
e
h1
h2
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.