Abstraction and refinement in protocol derivation
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Abstraction and Refinement in Protocol Derivation. Anupam Datta Ante Derek John C. Mitchell Dusko Pavlovic Stanford University Kestrel Institute CSFW June 28, 2004. Project Goals. Protocol derivation Build security protocols by combining and refining parts from basic protocols.

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Abstraction and Refinement in Protocol Derivation

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Abstraction and Refinement in Protocol Derivation

Anupam DattaAnte Derek

John C. Mitchell Dusko Pavlovic

Stanford University Kestrel Institute

CSFW June 28, 2004


Project Goals

  • Protocol derivation

    • Build security protocols by combining and refining parts from basic protocols.

  • Proof of correctness

    • Prove protocols correct using logic that follows steps of derivation.


Outline

  • Background

    • Derivation System[CSFW03]

    • Compositional Logic[CSFW01,CSFW03]

  • Abstraction and Refinement

    • Methods

    • Applications

  • Conclusions and Future Work


Example

  • Construct protocol with properties:

    • Shared secret

    • Authenticated

    • Identity Protection

  • Design requirements forIKE, JFK, IKEv2(IPSec key exchange protocol)


Component 1

Diffie Hellman

  • Shared secret (with someone)

    • A deduces:

      Knows(Y, gab) (Y = A) ۷ Knows(Y,b)

  • Authenticated

  • Identity Protection

A  B: ga

B  A: gb


Component 2

Challenge-Response

  • Shared secret

  • Authenticated

    • A deduces: Received (B, msg1) Λ Sent (B, msg2)

  • Identity Protection

A  B: m, A

B  A: n, sigB {m, n, A}

A  B: sigA {m, n, B}


Composition

m := ga

n := gb

ISO-9798-3

  • Shared secret: gab

  • Authenticated

  • Identity Protection

A  B: ga, A

B  A: gb, sigB {ga, gb, A}

A  B: sigA {ga, gb, B}


Refinement

Encrypt Signatures

  • Shared secret: gab

  • Authenticated

  • Identity Protection

A  B: ga, A

B  A: gb, EK {sigB {ga, gb, A}}

A  B: EK {sigA {ga, gb, B}}


Outline

  • Background

    • Derivation System

    • Compositional Logic

  • Abstraction and Refinement

    • Methods

    • Applications

  • Conclusions and Future Work


Challenge-Response: Proof Idea

m, A

n, sigB {m, n, A}

A

B

sigA {m, n, B}

  • Alice reasons: if Bob is honest, then:

    • only Bob can generate his signature. [protocol independent]

    • if Bob generates a signature of the form sigB {m, n, A},

      • he sends it as part of msg 2 of the protocol and

      • he must have received msg1 from Alice. [protocol specific]

  • Alice deduces:Received (B, msg1) Λ Sent (B, msg2)


Formalism

  • Cord calculus

    • Protocol programming language

  • Protocol logic

    • Expressing protocol properties

  • Proof system

    • Proving protocol properties

Symbolic (“Dolev-Yao”) model


Challenge-Response as Cords

m, A

n, sigB {m, n, A}

A

B

sigA {m, n, B}

RespCR(B) = [

receive Y, B, y, Y;

new n;

send B, Y, n, sigB{y, n, Y};

receive Y, B, sigY{y, n, B};

]

InitCR(A, X) = [

new m;

send A, X, m, A;

receive X, A, x, sigX{m, x, A};

send A, X, sigA{m, x, X};

]


Correctness of CR

InitCR(A, X) = [

new m;

send A, X, {m, A};

receive X, A, {x, sigX{m, x, A}};

send A, X, sigA{m, x, X}};

]

RespCR(B) = [

receive Y, B, {y, Y};

new n;

send B, Y, {n, sigB{y, n, Y}};

receive Y, B, sigY{y, n, B}};

]

CR |- [ InitCR(A, B) ] A Honest(B)  ActionsInOrder(

Send(A, {A,B,m}),

Receive(B, {A,B,m}),

Send(B, {B,A,{n, sigB {m, n, A}}}),

Receive(A, {B,A,{n, sigB {m, n, A}}})

)


Proof System

  • Sample Axioms:

    • Reasoning about possession:

      • Has(A, {m}K)  Has(A, K)  Has(A, m)

      • Has(A, {m,n})  Has(A, m)  Has(A, n)

    • Reasoning about crypto primitives:

      • Honest(X)  Decrypt(Y, encX{m})  X=Y

      • Honest(X)  Verify(Y, sigX{m}) 

         m’ (Send(X, m’)  Contains(m’, sigX{m})

  • Protocol-specific Rule:Honesty/Invariance rule

  • Soundness Theorem:

    Every provable formula is valid


Outline

  • Background

    • Derivation System

    • Compositional Logic

  • Abstraction and Refinement

    • Methods

    • Applications

  • Conclusions and Future Work


Protocol Templates

  • Protocols with function variables instead of specific cryptographic operations

  • Idea: One template can be instantiated to many protocols

  • Advantages:

    • proof reuse

    • design principles/patterns


Example

Challenge-Response Template

A  B: m

B  A: n, F(B,A,n,m)

A  B: G(A,B,n,m)

Abstraction

A  B: m

B  A: n,EKAB(n,m,B)

A  B: EKAB(n,m)

A  B: m

B  A: n,HKAB(n,m,B)

A  B: HKAB(n,m,A)

A  B: m

B  A: n, sigB(n,m,A)

A  B: sigA(n,m,B)

ISO-9798-2

SKID3

ISO-9798-3

Instantiations


Extending Formalism

  • Language Extensions: Add function variables to term language for cords and logic (HOL)

  • Semantics:Q |= φ  σQ |= σφ, for all substitutions σ eliminating all function variables

  • Soundness Theorem: Every provable formula is valid


Abstraction-Instantiation Method(1)

  • Characterizing protocol concepts

    • Step 1: Under hypotheses about function variables and invariants, prove security property of template

    • Step 2: Instantiate function variables to cryptographic operations and prove hypotheses.

  • Benefit:

    • Proof reuse


Example

Challenge-Response Template

A  B: m

B  A: n, F(B,A,n,m)

A  B: G(A,B,n,m)

  • Step 1:

    • Hypotheses: Function F(B,A,n,m) can be computed only by B or A,…

    • Property: Mutual authentication

  • Step 2:

    • Instantiate F() to signature, keyed hash, encryption (ISO-9798-2,3, SKID3)

    • Satisfies hypotheses => Guarantees mutual authentication


Proof Structure

Discharge hypothesis

axiom

hypothesis

Proof reuse

Instance

Template


Abstraction-Instantiation Method(2)

  • Combining protocol templates

    If protocol P is a hypotheses-respecting instance of two different templates, then it has the properties of both.

  • Benefits:

    • Modular proofs of properties

    • Formalization of protocol refinements


Refinement Example Revisited

Encrypt Signatures

Two templates:

  • Template 1: authentication + shared secret

    (Preserves existing properties; proof reused)

  • Template 2: identity protection (encryption)

    (Adds new property)

A  B: ga, A

B  A: gb, EK {sigB {ga, gb, A}}

A  B: EK {sigA {ga, gb, B}}


Authenticated key exchange

AKE1

AKE2

A  B: ga, A

B  A: gb, F(B,A,gb,ga)

A  B: G(A,B,ga,gb)

A  B: ga

B  A: gb, F(B,gb,ga), F’(B,gab)

A  B: G(A,ga, gb), G’(A,gab)

ISO-9798-3, JFKi

STS, JFKr, IKEv2, SIGMA

  • Shared secret

  • Stronger authentication

  • Identity protection for B

  • Non-repudiation

  • Shared secret

  • Weaker authentication

  • Identity protection for A

  • Repudiability

H. Krawczyk: The Cryptography of the IPSec and IKE Protocols [CRYPTO’03]


More examples…

  • Authenticated Key Exchange:

    • Template for JFKr, STS, IKE, IKEv2

  • Key Computation:

    • Template for Diffie-Hellman, UM, MTI/A, MQV

  • Combining these templates


Synthesis: STS-MQV

protect

identities

symmetric

hash

STSPH

DH

STSP

RFK

STS

authenticate

cookie

MTI/A

MTIC

MTIRFK

MTICPH

MTICP

key

conf.

UM

UMC

UMCPH

UMRFK

UMCP

MQV

MQVRFK

MQVCPH

MQVC

MQVCP


Conclusions

  • Abstraction-Instantiation using protocol templates:

    • Single proof for similar protocols from common template

    • Multiple protocol properties from different templates

  • Logical foundation:

    • Add function variables to protocol language and logic

  • Applications:

    • CR template: ISO-9798-2,3, SKID3

    • Identity protection refinement in JFK

    • Design principles: IKEv2, JFKi, JFKr, ISO, STS, SIGMA, IKE

    • Synthesis: DH-MQV + STS-JFKr


Future Work

  • Done:

    • Derivation idea successfully applied to large set of protocol examples

    • Rigorous treatment of composition, refinement in protocol logic

  • Work In Progress:

    • Tool support for derivation system and logic

    • Formalization of protocol transformations

    • More applications


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