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Concordia University

Design and Analysis of Security Protocols (INSE 7100)

BAN: A Logic of Authentication

Mourad Erhioui

Ahmed Gario

Sami Zhioua

October 27, 2003

Content

1. Introduction

- Syntax

- Logical postulates (rules)

2. Protocol analysis

- Different steps

- Detailed example (Kerberos protocol)

3. Conclusion

- Needham-Shroeder protocol (outline)

- Limitations and advantages

- Conclusion

Introduction

- BAN is the first logic to formally analyze authentication protocols (1990)

- It is named after its inventors : Mike Burrows, Martin Abadi and Roger Needham

- BAN is a belief logic: it concentrates on beliefs of principals and the evolution of these beliefs through the execution of the protocol.

BAN Objectives

- Prove whether a protocol does or does not meet its security goals.

- Make protocols more efficient:

- Does this protocol do anything unnecessary that could be left out without weakening it ?

- Does this protocol encrypt something that could be sent in clear without weakening it ?

A shared key between Alice and Bob is written as : A B

- If Alice believes thatKAB is a good key to communicate with Bob,
- then we write : A | A B.

KAB

KAB

- If Alice believes that S can be trusted to create a good key to communicate with Bob, we write:
- A | S A B

KAB

and we say that ‘A believes that S has a jurisdiction over good keys for A and B’.

Formalism (1)

- If Alice believes a proposition P, we writeA | Pand we say: ‘A believes P’

If Alice sent a message containing the statement P, we write:

- A |~ P and we say: ‘A once said P’

- When a statement P is fresh, we write : #(P) and we say:
- ‘P is fresh’

Formalism (2)

- When Alice receives a message, we write : A Pand we say: ‘A sees P’

Formalism (Summary)

- P | X : PbelievesX

- P X : PseesX

- P |~X : Ponce saidX

- # (P) : Pis fresh

- P X : Phas jurisdiction overX

K

- P Q : Kis a good key for communication between P and Q

K

- P : P has Kas a public key

BAN Logical postulates

P

Means: if P is true, then Q is true

Q

X

If Alice believes X and

, then Alice believes Y

Y

More rules

P | X ,

P | Y

1.

P (X,Y)

P | (X,Y)

5.

P X

P | (X,Y)

2.

K

P | P Q , P {X}K

P | X

6.

P X

P | Q | (X,Y)

3.

P | Q |X

P | # (X)

7.

P | # (X,Y)

P | Q |~ (X,Y)

4.

P | Q |~X

BAN

- BAN cannot be used to prove that a protocol is flawed

- But, when we cannot prove that a protocol is correct, that protocol deserves to be treated with grave suspicion.

Content

1. Introduction

- Syntax

- Logical postulates (rules)

2. Protocol analysis

- Different steps

- Detailed example (Kerberos protocol)

3. Conclusion

- Needham-Shroeder protocol (outline)

- Limitations and advantages

- Conclusion

Message1: A B : {A, }

k

k

k

bs

bs

ab

Kab

Kab

A B

A B

Idealized protocol- BAN Logic transforms each step in a protocol in a idealized form.
- Principal A sends the message to principal B
- It is an informal notation
- Ambiguous presentation
- Obscure in meaning,
- Not appropriate for formal analysis

Message1: A B : {A, }

B {A, }

Idealized protocol

- Transform each protocol into an idealized form
- Omit the parts of the message that do not contribute to the beliefs of the recipient
- Omit clear text communication because it can be forged
- The not encrypted messages will be removed during the steps of idealization
- Only encrypted fields are retained in the idealization

Protocol Analysis

- Derive the idealized protocol from the original one.
- Write assumptions about the initial state.
- Add a logical formulas to the statements of the protocol.
- Use the postulates and rules of the logic to deduce new predicates.

The Kerberos Protocol

S

2: {Ts, L, Kab,B, {Ts, L, Kab,A} Kbs} Kbs

1: A, B

3: {Ts, L, Kab, A} Kbs ,{A, Ta} Kab

A

B

4: { Ta+1} Kab

Message1: A S : A, B

Message2: S A : {Ts, L, Kab, B, {Ts, L, Kab, A} Kbs}Kas

Message3: A B : {Ts, L, Kab, A} Kbs, {A, Ta}Kab

Message4: B A : { Ta+1} Kab

Kab

Kab

Kab

Kab

Kab

A B

A B

A B

A B

A B

Confusion

Idealized protocolMessage1: A S : A, B

Message2: S A : {Ts, L, Kab, B, {Ts, L, Kab, A} Kbs}Kbs

Message3: A B : {Ts, L, Kab, A} Kbs, {A, Ta}Kab

Message4: B A : { Ta+1} Kab

Message2: S A : {Ts, , {Ts, } Kbs }Kas

Message3: A B : {Ts, } Kbs, {Ta, }Kabfrom A

Message4: B A : { Ta, } Kabfrom B

Kas

Kas

Kas

Kas

Kas

A |

B |

B S

B S

A B

A S

A S

S |

S |

K

K

S |

A B

A B

B | (S | )

A | (S | )

Protocol Analysis- Initial assumptions :

A |#(Ta)

B |#(Ts)

B |#(Ta)

Goals of Authentication

- Authentication rests on communication protected by shared session key, so the goals of authentication may be reached between A and B if there is a K such that:
- Authentication between A and B is compete once there is a K such :

K K

A |AB B |AB

- Some authentication protocols achieve this final goal:

K K

A |B |AB B |A |AB

Kab

A |

A B

Goal of authentication- Prove from the postulats of BAN and assumptions, the goal of the protocol

A { }Kas

A |

Kas

S A

A | S A, A {X}k

A | S |~ X

A |#( )

Kab

Kab

Kab

Kab

Kab

Kab

A |#(X), A | S |~ X

__________________________

A | S | X

A B

A B

A B

A B

A B

A B

B | (S | )

A | S | , A | S |

A |

VerificationContent

1. Introduction

- Syntax

- Logical postulates (rules)

2. Protocol analysis

- Different steps

- Detailed example (Kerberos protocol)

3. Conclusion

- Needham-Shroeder protocol (outline)

- Limitations and advantages

- Conclusion

Needham-Schroeder Analysis

- Original version without idealization

S

Message 1 A S: A, B, NA

Message 2 S A:{NA, B, KAB, {KAB, A}KBS} KAS

1

2

Message 3 A B: {KAB, A}KBS

Message 4 B A:{NB}KAB

3

B

A

4

Message 5 A B:{NB – 1}KAB

5

- Corresponding idealized protocol

Kab Kab KabMessage 2 S A: {NA, (AB), # (AB), {AB}Kbs} Kas

Kab Message 3 A B: {AB}Kbs

Kab Message 4 B A: {NB, (AB)}Kab from B

KabMessage 5 A B: {NB, (AB)}Kab from A

Needham-Schroeder Analysis (Con.)

- The original Needham-Schroeder is worth idealization because so much work has been based on it, since too many authentication protocols have been derived from it.
- The goal of this idealization is to see if both principals A & B can be convinced of each other’s presence.

KK

A | A B B | A B and

KK

A | B | A B B | A | A B

Needham-Schroeder Analysis (Con.)

Initial assumptions:

What client trust the server to do

Kab

A | (S | AB)

Kab

B | (S | AB)

Kab

A | (S | #(AB))

Keys already known to the principals

Kas

A |AS

Kbs

B |BS

Kas

S |AS

Kbs

S |BS

Kab

S |AB

A | #(Na) Ka

B | #(Nb)

Kab

S | #(AB)

Kab

B | #(AB)

Needham-Schroeder Analysis (Con.)

- Now we can apply the logical postulate rules to each message with assumptions to see if we can achieve our goal.
- There are too many steps to achieve the goal, unfortunately, there is no enough time to state them.

Conclusions of Analysis

Finally, this has been achieved: The goals of the Needham-Schroeder protocol are that A and B each believe that they share a secret key Kab and they each believe that the other believes it.

K K B | A B A | A B

the final goal has also been achieved:

KK

A | B | A B B | A | A B

BAN finds that this authentication protocol has an extra assumption, which is that B assumes the key it receives from A is fresh

BAN limitations

- Conversion to idealized form
- Lack of ability to state something a principle does not know
- BAN does not catch all protocol flaws.
- - False-positives can result.
- A principal’s beliefs cannot be changed at later stages of the protocol
- - No division of time in protocol run.
- Provides a proof of trust on part of principles, but not a proof of security
- -Final beliefs can be believed only if all original assumptions hold true.
- BAN does not account for improper encryption.

Advantages of BAN Logic

- Huge success for formal methods in cryptography, useful tool.
- BAN Logic successful in uncovering implicit assumptions and weaknesses in a number of protocols
- Vehicle for extensive research in the areas for basis and development of other logic systems.
- BAN’s strengths lie in its simplicity of its logic and its ease of use

Conclusion

- BAN Logic isone of earliest successful attempts at formally reasoning about authentication protocols.
- BAN logic involves idealizing a protocol, identifying initial assumptions, using logical postulates to deduce new predicates and determining if the goals of authentication have been met.
- BAN logic can be used to analyze existing protocols and bring out their flaws.
- As we saw in the Needham Schroeder protocol, BAN logic helped to uncover an extra assumption that the authors themselves did not realize.
- BAN logic has its flaws, but overall it is a welcome success for formal methods in cryptography.

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