A Logic of Belief and a A Logic of Belief and a Model Checking Algorithm Model Checking Algorithm

for for Security ProtocolsSecurity Protocols

joint work with Massimo Benerecetti

Fausto GiunchigliaUniversity of Trentofausto@cs.unitn.it

Logics of Beliefs for Logics of Beliefs for Security ProtocolsSecurity Protocols

BAN Logic (Borrows, Abadi & Needham)

Concentrate on beliefs of trustworthy principals and on their evolution as consequence of communication

Logics of Beliefs for Logics of Beliefs for Security ProtocolsSecurity Protocols

BAN Logic (Borrows, Abadi & Needham)

Concentrate on beliefs of trustworthy principals and on their evolution as consequence of communication

Some Extensions

Abadi & Tuttle (AT Logic) Gong, Needham & Yahalom (GNY Logic) Boyd & Mao

Logics of Beliefs for Logics of Beliefs for Security ProtocolsSecurity Protocols

BAN Logic (Borrows, Abadi & Needham)

Concentrate on beliefs of trustworthy principals and on their evolution as consequence of communication

Some Extensions

Abadi & Tuttle (AT Logic) Gong, Needham & Yahalom (GNY Logic) Boyd & Mao

Attempts to automate reasoning in BAN

Kindred & Wing (Theory Building)

The ApproachThe Approach

Define a Logic of Belief and Time

The ApproachThe Approach

Define a Logic of Belief and Time

A Model Checking Algorithm for this logic

The ApproachThe Approach

Define a Logic of Belief and Time

A Model Checking Algorithm for this logic

Built on top of CTL model checking

Define a Logic of Belief and Time

A Model Checking Algorithm for this logic

Built on top of CTL model checking

Integration with existing tools

(e.g. NuSMV)

The ApproachThe Approach

Example: The Andrew ProtocolExample: The Andrew Protocol

1 A B : {NA}KAB

2 B A : {NA,NB}KAB

3 A B : {NB}KAB

4 B A : {KAB,N

B}KAB

Example Property: at the end of the protocol session, A believes that B believes that K’

AB is a "good shared key" for communication between them.

Example: The Andrew ProtocolExample: The Andrew Protocol

1 A B : {NA}KAB

2 B A : {NA,NB}KAB

3 A B : {NB}KAB

4 B A : {KAB,N

B}KAB

1 A B : {NA}KAB

2 B A : {NA,NB}KAB

3 A B : {NB}KAB

4 B A : {KAB,N

B}KAB

Example: Attack to the Andrew Example: Attack to the Andrew Protocol Protocol

1 A B : {NA}KAB

2 B A : {NA,NB}KAB

3 A B : {NB}KAB

4 B A : {KAB,N

B}KAB

1 A B : {NA}Kab

2 B A : {NA,N

B}Kab

3 A B : {NB}KAB

4 I(B) A : {KAB,N

B}KAB

Example: Attack to the Andrew Example: Attack to the Andrew Protocol Protocol

Outline of the TalkOutline of the Talk

Intuitions

Outline of the TalkOutline of the Talk

Intuitions

MultiAgent Temporal Logic (MATL)

MultiAgent Finite State Machine (MAFSM)

The Model Checking Algorithm (MAMC)

Outline of the TalkOutline of the Talk

Intuitions

MultiAgent Temporal Logic (MATL)

MultiAgent Finite State Machine (MAFSM)

The Model Checking Algorithm (MAMC)

Model of the Andrew Protocol in MAFSM

Outline of the TalkOutline of the Talk

Intuitions

MultiAgent Temporal Logic (MATL)

MultiAgent Finite State Machine (MAFSM)

The Model Checking Algorithm (MAMC)

Model of the Andrew Protocol in MAFSM

Conclusion and Future Work

IntuitionsIntuitions

IntuitionsIntuitionsPrincipals have two orthogonal aspects:

Temporal Evolution: when we consider the temporal evolution (CTL), formulae expressing beliefs are treated as atomic propositions.

IntuitionsIntuitionsPrincipals have two orthogonal aspects:

Temporal Evolution: when we consider the temporal evolution (CTL), formulae expressing beliefs are treated as atomic propositions.

Beliefs: "a principal ascribing beliefs to another one" means that it has access to a representation of the second principal as a process.

IntuitionsIntuitionsPrincipals have two orthogonal aspects:

Temporal Evolution: when we consider the temporal evolution (CTL), formulae expressing beliefs are treated as atomic propositions.

Beliefs: "a principal ascribing beliefs to another one" means that it has access to a representation of the second principal as a process.

PrincipalA

PrincipalB

IntuitionsIntuitions

PrincipalA

PrincipalB

A' s Repr. of B

Principals have two orthogonal aspects:

Temporal Evolution: when we consider the temporal evolution (CTL), formulae expressing beliefs are treated as atomic propositions.

Beliefs: "a principal ascribing beliefs to another one" means that it has access to a representation of the second principal as a process.

IntuitionsIntuitions

PrincipalA

PrincipalB

A' s Repr. of B

BB?

Principals have two orthogonal aspects:

Temporal Evolution: when we consider the temporal evolution (CTL), formulae expressing beliefs are treated as atomic propositions.

Beliefs: "a principal ascribing beliefs to another one" means that it has access to a representation of the second principal as a process.

IntuitionsIntuitions

PrincipalA

PrincipalB

A' s Repr. of B

?

BB?

Principals have two orthogonal aspects:

Temporal Evolution: when we consider the temporal evolution (CTL), formulae expressing beliefs are treated as atomic propositions.

Beliefs: "a principal ascribing beliefs to another one" means that it has access to a representation of the second principal as a process.

MultiAgent Temporal LogicMultiAgent Temporal Logic(MATL)(MATL)

.........

BA BB

BBBA BBBBBABBBABA

...

To each level of nesting of beliefs we associate a Representation of a process evolving over time.

MATL: ViewsMATL: Views

.........

BA BB

BBBA BBBBBABBBABA

...

Each Representation is called a View

MATL: ViewsMATL: Views

To each level of nesting of beliefs we associate a Representation of a process evolving over time.

Views represent the beliefs about a principal's evolution during the protocol

View the protocol as seen by the external observer (the analyser's point of view)

View BA 's beliefs about the evolution of principal A.

View BB 's beliefs about the evolution of principal B.

View BABB ('s beliefs about) A's beliefs about the evolution of principal B

....

MATL: ViewsMATL: Views

MATL: ViewsMATL: Views

.

BA BB

BBBA BBBBBABBBABA

.. .. .. ..

* is the set of (possibly empty)

strings of the form BX1···BXn

MATL: Language MATL: Language

We associate to each view a language

The language of each view allows for expressing properties of the process associated with that view

............

BA BB

BBBA BBBBBABBBABA

MATL: LanguageMATL: Language

............

BA BB

BBBA BBBBBABBBABA

BB

MATL: LanguageMATL: Language

............

BA BB

BBBA BBBBBABBBABA

BABB

BB

MATL: LanguageMATL: Language

......

......

BA BB

BBBA BBBBBABBBABA

BABB

BB

BBBA

BA

MATL: LanguageMATL: Language

MATL: LanguageMATL: Language

To each view we associate the smallest CTL language containing:

a finite set of Propositional Atoms

the set of Atoms = {BX| is a formula of BX}

that is the Belief Atoms of the form BX for each

formula of view BX

MATL: LanguageMATL: Language

To each view we associate the smallest CTL language containing:

a finite set of Propositional Atoms

the set of Atoms = {BX| is a formula of BX}

that is the Belief Atoms of the form BX for each

formula of view BX

Example

AG(BABBP) is a formula of view

MATL: LanguageMATL: Language

Definition: Given a family {} of sets of propositional atoms, the family of MATL languages on is the family of CTL languages {}

MATL: LanguageMATL: Language

Definition: Given a family {} of sets of propositional atoms, the family of MATL languages on is the family of CTL languages {}

A MATL formula belonging to is denoted by

Example

AG(BABBP) denotes the formula AG(BABBP) of view

MultiAgent Finite State MachineMultiAgent Finite State Machine(MAFSM)(MAFSM)

MAFSM: IntuitionsMAFSM: Intuitions

Model Checking employs Finite State Machines

We extend the notion of FSM to accommodate beliefs

We associate the Finite State Machine of a process to each view

MAFSM: IntuitionsMAFSM: Intuitions

Model Checking employs Finite State Machines

We extend the notion of FSM to accommodate beliefs

We associate the Finite State Machine of a process to each view

Restriction:

We consider only a finite number of views

MultiAgent Finite State MachineMultiAgent Finite State Machine

.

BA BB

BBBA BBBBBABBBABA

.. .. .. ..

* is the set of (possibly empty)

strings of the form BX1···BXn

MultiAgent Finite State MachineMultiAgent Finite State Machine

.

BA BB

BBBA BBBBBABBBABA

.. .. .. ..

n

MultiAgent Finite State MachineMultiAgent Finite State Machine

.

BA BB

BBBA BBBBBABBBABA

.. .. .. ..

n

n is a finite subset of strings in *

MultiAgent Finite State MachineMultiAgent Finite State MachineWe associate the Finite State Machine of a process to each view in n

BA BB

BA BB BBBA

MultiAgent Finite State MachineMultiAgent Finite State MachineWe associate the Finite State Machine of a process to each view in n

BA BB

BA BB BBBA

Problem: there's a infinite number of Belief Atoms in each view!

Explicit Belief AtomsExplicit Belief Atoms

Solution: chose a finite number of Belief Atoms (Explicit Beliefs Atoms) as state variables of the FSM of a view.

s

s' s''

BX

BX

Explicit Belief AtomsExplicit Belief Atoms

Explicit Belief Atoms induce a Compatibility Relation among states in different views.

s

s' s''

BX

B

X

Implicit Belief AtomsImplicit Belief AtomsImplicit Belief Atoms are the infinite set of Belief Atoms which are not Explicit

BX

BXBX

B

X

Implicit Belief AtomsImplicit Belief AtomsSatisfiability of Implicit Belief Atims in a state is computed via Compatibility Relation

BX

BXBX

BX

Implicit Belief AtomsImplicit Belief Atoms

Explicit Belief Atoms are used to assess the truth of Implicit Belief Atoms

BX

BXBX

Satisfiability of Implicit Belief Atims in a state is computed via Compatibility Relation

BX

MultiAgent Finite State MachineMultiAgent Finite State MachineA MAFSM is a set of FSMs plus compatibility relations induced by Explicit Belief Atoms among them.

BA BB

BA BB BBBA

MAFSM: From Trees to GraphsMAFSM: From Trees to Graphs

The definition of MAFSM as a Tree of FSMs (one for each view):

does not allow for arbitrary nesting of beliefs: “a priori” bound on the length of each branch of the tree.

MAFSM: From Trees to GraphsMAFSM: From Trees to Graphs

The definition of MAFS as a Tree of FSMs (one for each view):

does not allow for arbitrary nesting of beliefs: “a priori” bound on the length of each branch of the tree.

needs a distinct specification of each view even when it is not necessary: often in security protocol we can safely assume that the

protocol is publicly known and each (honest) principal behaviour is completely known to the other principals;

in some cases distinct views of that principal could be modelled by the same process (FSM).

MAFSM: From Trees to GraphsMAFSM: From Trees to Graphs

Solution:

allow for cycles in MAFSM;

a MAFSM becomes a Graph of views

MultiAgent Finite State MachineMultiAgent Finite State Machine

A MAFSM is a set of FSMs plus compatibility relations induced by Explicit Belief Atoms among them.

BBBA

Model Checking AlgorithmModel Checking Algorithm(MAMC)(MAMC)

MultiAgent Model Checking MultiAgent Model Checking AlgorithmAlgorithm

To check the formula in view , the algorithm performs three steps:

recursively descend the tree of views performing Steps 2 and 3 on the sub-formulas inside the BDI atoms at each step.

MultiAgent Model Checking MultiAgent Model Checking AlgorithmAlgorithm

To check the formula in view , the algorithm performs three steps:

recursively descend the tree of views performing Steps 2 and 3 on the sub-formulas inside the BDI atoms at each step.

compute for each state s the BDI atoms occurring in true at s.

MultiAgent Model Checking MultiAgent Model Checking AlgorithmAlgorithm

To check the formula in view , the algorithm performs three steps:

recursively descend the tree of views performing Steps 2 and 3 on the sub-formulas inside the BDI atoms at each step.

compute for each state s the BDI atoms occurring in true at s.

call the standard CTL model checking algorithm (treating BDI atoms as atomic formulas).

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BA

AG (BA BB )

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BAImplicit Belief Atom

AG (BA BB )

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BA

Implicit Belief Atom

AG (BA BB )

BB

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BA

AG (BA BB )

BB

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BA

AG (BA BB )

BB

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BA

AG (BA BB )

BB

AG (BA BB )

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BA

BB

AG (BA BB )

MultiAgent Model Checking AlgorithmMultiAgent Model Checking Algorithm

BB

BA

BB

Model of the Andrew ProtocolModel of the Andrew Protocol

Beliefs in Security ProtocolsBeliefs in Security Protocols

Each Principal is seen as a process able to have Beliefs about other principal

BX means that principal "X believes " to be true

Beliefs in Security ProtocolsBeliefs in Security Protocols

Each Principal is seen as a process able to have Beliefs about other principal

BX means that principal "X believes " to be true

Beliefs evolve over time (as messages are sent/received)

Beliefs in Security ProtocolsBeliefs in Security Protocols

Each Principal is seen as a process able to have Beliefs about other principal

BX means that principal "X believes " to be true

Beliefs evolve over time (as messages are sent/received)

Beliefs can be nested

Example (from BAN)

At the end of the protocol session:

A believes that B believes that K'AB is a "good shared

key" for communication between them.

Beliefs in Security ProtocolsBeliefs in Security Protocols

Each Principal is seen as a process able to have Beliefs about other principal

BX means that principal "X believes " to be true

Beliefs evolve over time (as messages are sent/received)

Beliefs can be nested

Example (from BAN)

At the end of the protocol session:

A believes that B believes that K'AB is a "good shared

key" for communication between them.

recA {K'AB,N'B}KAB BA fresh NA BA BB shk K'AB

Model of the Andrew ProtocolModel of the Andrew Protocol

External Observer a process (the protocol) ascribing beliefs to agents A and B

Agent A a process ascribing beliefs to agent B

Agent B a process ascribing beliefs to agent A

1 A B : {NA}KAB

2 B A : {NA,NB}KAB

3 A B : {NB}KAB

4 B A : {KAB,N

B}KAB

Model of the Andrew ProtocolModel of the Andrew Protocol

All these entities are modeled as processes accessing other agents' representations (views).

External Observer a process (the protocol) ascribing beliefs to agents A and B

Agent A a process ascribing beliefs to agent B

Agent B a process ascribing beliefs to agent A

1 A B : {NA}KAB

2 B A : {NA,NB}KAB

3 A B : {NB}KAB

4 B A : {KAB,N

B}KAB

Model of the Andrew ProtocolModel of the Andrew Protocol

BA BBBA BB BABB

(BBBA , BA) (i.e. BBBA and BA are modelled by the same process)

(BABB , BB) (i.e. BABB and BB are modelled by the same process)

Model of the Andrew ProtocolModel of the Andrew Protocol

To specify a MAFSM we need to specify the following elements:

Propositional Atoms Message variables

Freshness variables

Model of the Andrew ProtocolModel of the Andrew Protocol

To specify a MAFSM we need to specify the following elements:

Propositional Atoms Message variables

Freshness variables

Explicit Belief Atoms

Model of the Andrew ProtocolModel of the Andrew Protocol

To specify a MAFSM we need to specify the following elements:

Propositional Atoms Message variables

Freshness variables

Explicit Belief Atoms

How Atoms’ truth values vary during the protocol execution

Propositional Atoms : Message Propositional Atoms : Message VariablesVariables

We need to model principal sending and receiving messages

Propositional Atoms : Message Propositional Atoms : Message VariablesVariables

We need to model principal sending and receiving messages

Boolean varibles

Propositional Atoms : Message Propositional Atoms : Message VariablesVariables

We need to model principal sending and receiving messages

Boolean varibles

View BA

send {NA}KAB

rec {NA,NB}KAB

... rec {K'AB,N'B}KAB

Propositional Atoms : Message Propositional Atoms : Message VariablesVariables

View BB

rec {NA}KAB

send {NA,NB}KAB

... send {K'AB,N'B}KAB

View BA

send {NA}KAB

rec {NA,NB}KAB

...rec {K'AB,N'B}KAB

We need to model principal sending and receiving messages

Boolean varibles

Propositional Atoms : Message Propositional Atoms : Message VariablesVariables

View

recA {NA}KAB

sendAB {NA,NB}KAB

... sendAB {K'AB,N'B}KAB

View BA

send {NA}KAB

rec {NA,NB}KAB

...rec {K'AB,N'B}KAB

View BB

rec {NA}KAB

send {NA,NB}KAB

...send {K'AB,N'B}KAB

We need to model principal sending and receiving messages

Boolean varibles

Propositional Atoms : Message Propositional Atoms : Message VariablesVariables

Message Variables Evolution

Once they become true they remain stable

View BA

sendB {NA}KAB

rec {NA,NB}KAB

...rec {K'AB,N'B}KAB

View BB

rec {NA}KAB

sendA {NA,NB}KAB

...sendA {K'AB,N'B}KAB

View

recA {NA}KAB

sendAB {NA,NB}KAB

...sendAB {K'AB,N'B}KAB

Propositional Atoms : Message Propositional Atoms : Message VariablesVariables

View BA

sendB {NA}KAB

rec {NA,NB}KAB

...rec {K'AB,N'B}KAB

View BB

rec {NA}KAB

sendA {NA,NB}KAB

...sendA {K'AB,N'B}KAB

View

recA {NA}KAB

sendAB {NA,NB}KAB

...sendAB {K'AB,N'B}KAB

Message Variables Evolution

Once they become true they remain stable

Evolve following the order of messages in the protocol

Example: Evolution of Message Example: Evolution of Message VariablesVariables

send {NA}KAB

rec {NA,NB}KAB

Message variables evolve following the order of messages in the protocol

A has not sent/received any message

Example: Evolution of Message Example: Evolution of Message VariablesVariables

send {NA}KAB

rec {NA,NB}KAB

Message variables evolve following the order of messages in the protocol

A has sent Message 1

send {NA}KAB

rec {NA,NB}KAB

Example: Evolution of Message Example: Evolution of Message VariablesVariables

send {NA}KAB

rec {NA,NB}KAB

Message variables evolve following the order of messages in the protocol

send {NA}KAB

rec {NA,NB}KAB

send {NA}KAB

rec {NA,NB}KAB

A has received Message 2

Propositional Atoms : Freshness Propositional Atoms : Freshness VariablesVariables

We need to express basic properties of messages: freshness

Boolean varibles

View BA

fresh NA

...

fresh{K'AB,N'B}KAB

shk K'AB

Propositional Atoms : Freshness Propositional Atoms : Freshness VariablesVariables

View BA

fresh NB

...

fresh{K'AB,N'B}KAB

shk K'AB

View BA

fresh NA

...

fresh{K'AB,N'B}KAB

shk K'AB

We need to express basic properties of messages: freshness

Boolean varibles

Propositional Atoms : Freshness Propositional Atoms : Freshness VariablesVariables

View BA

fresh NA

…

fresh{K'AB,N'B}KAB

shk K'AB

View

fresh NA

...

fresh{K'AB,N'B}KAB

shk K'AB

View BB

fresh NB

...

fresh{K'AB,N'B}KAB

shk K'AB

We need to express basic properties of messages: freshness

Boolean varibles

Propositional Atoms : Freshness Propositional Atoms : Freshness VariablesVariables

Freshness Variables Evolution

Once they become true they remain stable

View BA

fresh NA

…

fresh{K'AB,N'B}KAB

shk K'AB

View BB

fresh NB

...

fresh{K'AB,N'B}KAB

shk K'AB

View

fresh NA

...

fresh{K'AB,N'B}KAB

shk K'AB

Propositional Atoms : Freshness Propositional Atoms : Freshness VariablesVariables

View BA

fresh NA

...

fresh{K'AB,N'B}KAB

shk K'AB

View BB

fresh NB

...

fresh{K'AB,N'B}KAB

shk K'AB

View

fresh NA

...

fresh{K'AB,N'B}KAB

shk K'AB

Freshness Variables Evolution

Once they become true they remain stable

Must satisfy some additional contraints

Evolution of Freshness VariablesEvolution of Freshness Variables

fresh {NA,NB}KAB fresh NA fresh NB

...

Evolution of Freshness VariablesEvolution of Freshness Variables

BA

fresh {NA,NB}KAB (fresh NA fresh NB) rec{NA,NB}KAB

fresh {K'AB,N'B}KAB (fresh K'AB fresh N'B) rec{K'AB,N'B}KAB

…

fresh {NA,NB}KAB fresh NA fresh NB

...

Evolution of Freshness VariablesEvolution of Freshness Variables

fresh {NA,NB}KAB fresh NA fresh NB

...

BA

fresh {NA,NB}KAB (fresh NA fresh NB) rec{NA,NB}KAB

fresh {K'AB,N'B}KAB (fresh K'AB fresh N'B) rec{K'AB,N'B}KAB..

BB

fresh {K'AB,N'B}KAB (fresh K'AB fresh N'B) rec{K'AB,N'B}KAB

fresh {K'AB,N'B}KAB shk K'AB

...

Explicit Beliefs AtomsExplicit Beliefs Atoms

View BA

BB sendA {K'AB,N'B}KAB

...

We need to express beliefs about (other) principal sending/receiving messages

Boolean varibles

Explicit Beliefs AtomsExplicit Beliefs Atoms

We need to express beliefs about (other) principal sending/receiving messages

Boolean varibles

View BA

BB sendA {K'AB,N'B}KAB

...

View BB

BA sendB {NA}KAB

...

Explicit Belief AtomsExplicit Belief Atoms

We need to express beliefs about (other) principal sending/receiving messages

Boolean varibles

View BA

BB sendA {K'AB,N'B}KAB

...

View BB

BA sendB {NA}KAB

…

View

BA rec {K'AB,N'B}KAB

BB sendA {K'AB,N'B}KAB

...

Explicit Belief AtomsExplicit Belief Atoms

Explicit Belief Atoms Evolution

Once they become true they remain stable

Must satisfy some additional contraints

View

BA rec {K'AB,N'B}KAB

BB sendA {K'AB,N'B}KAB

…

View BA

BB sendA {K'AB,N'B}KAB

...

View BB

BA sendB {NA}KAB

…

Evolution of Explicit Belief AtomsEvolution of Explicit Belief Atoms

recA {K'AB,N'B}KAB BA rec {K'AB,N'B}KAB

…

Evolution of Explicit Belief AtomsEvolution of Explicit Belief Atoms

recA {K'AB,N'B}KAB BA rec {K'AB,N'B}KAB

...

BA

rec {K'AB,N'B}KAB BB sendA {K'AB,N'B}KAB

fresh {K'AB,N'B}KAB BB fresh {K'AB,N'B}KAB

…

Evolution of Explicit Belief AtomsEvolution of Explicit Belief Atoms

recA {K'AB,N'B}KAB BA rec {K'AB,N'B}KAB

...

BA

rec {K'AB,N'B}KAB BB sendA {K'AB,N'B}KAB

fresh {K'AB,N'B}KAB BB fresh {K'AB,N'B}KAB

...

BB

rec {NB}KAB BA sendB {NB}KAB

fresh {NB}KAB BA fresh {NB}KAB

...

Checking the Andrew ProtocolChecking the Andrew Protocol

BB

BA

AG(rec {K'AB,N'B}KAB BA fresh NA BABB shk K'AB)

A security property for the Andrew Protocol

Checking the Andrew ProtocolChecking the Andrew Protocol

BB

BA

BB shk K'AB

shk K'AB

AG(rec {K'AB,N'B}KAB BA fresh NA BABB shk K'AB)

Checking the Andrew ProtocolChecking the Andrew Protocol

BB

BB shk K'AB

shk K'AB

fresh {K'AB,N'B}KAB shk K'AB

AG(rec {K'AB,N'B}KAB BA fresh NA BABB shk K'AB)

BA

Checking the Andrew ProtocolChecking the Andrew Protocol

BB

BB shk K'AB

shk K'AB

rec {K'AB,N'B}KAB BB sendA {K'AB,N'B}KAB

fresh {K'AB,N'B}KAB BB fresh {K'AB,N'B}KAB

(fresh K'AB fresh N'B) rec {K'AB,N'B}KAB fresh {K'AB,N'B}KAB

AG(rec {K'AB,N'B}KAB BA fresh NA BABB shk K'AB)

BA

Checking the Andrew ProtocolChecking the Andrew Protocol

BB

BB shk K'AB

shk K'AB

rec {K'AB,N'B}KAB BB sendA {K'AB,N'B}KAB

fresh {K'AB,N'B}KAB BB fresh {K'AB,N'B}KAB

(fresh K'AB fresh N'B) rec {K'AB,N'B}KAB fresh {K'AB,N'B}KAB

AG(rec {K'AB,N'B}KAB BA fresh NA BABB shk K'AB)

BA

Checking the Andrew ProtocolChecking the Andrew Protocol

BB

BB shk K'AB

shk K'AB

AG(rec {K'AB,N'B}KAB BA fresh NA BABB shk K'AB)

BA

recA {K'AB,N'B}KAB BA rec {K'AB,N'B}KAB

Checking the Andrew ProtocolChecking the Andrew Protocol

BB

BB shk K'AB

shk K'AB

AG(rec {K'AB,N'B}KAB BA fresh NA BABB shk K'AB)

BA

recA {K'AB,N'B}KAB BA rec {K'AB,N'B}KAB

The property doesn’t holdof the Andrew Protocol

ConclusionsConclusions

A Model-Checking based Verification Procedure for Security Protocols

Logic of Beliefs MultiAgent Finite State Machine Model Checking Algorithm

ConclusionsConclusions

A Model-Checking based Verification Procedure for Security Protocols

Logic of Beliefs MultiAgent Finite State Machine Model Checking Algorithm

Future Work Implementation (ongoing work) Experimental Analysis Extension of the logic and comparison with other

logics