Universally ComposableSymbolic Analysis of

Security ProtocolsJonathan Herzog

(Joint work with Ran Canetti)

7 June 2004

The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions or viewpoints expressed by the author.

Introduction This talk: symbolic analysis can guarantee universally

composable (UC) security Dolev-Yao (symbolic) model

Adversary extremely limited Proofs simple, can even be automated

UC (concrete) framework Complexity- and information-theoretic approach Guarantees strong security and composability properties Requires “hand-crafted” proofs

Symbolic security proofs are sound in UC framework Traditional (symbolic) mutual-authentication definitions suffice Need strengthened notion of symbolic key-exchange

Analysis strategy

Concrete protocol UC security

Symbolic protocol

Symbolic property

Would likeNatural translation for

encryption-based protocols

Simple, automatedMain result of talk:

mutual authenticationand key exchange

Analysis strategy (expanded)

Concrete protocol

UC concretesecurity

Symbolic single-instance protocol

Symbolic property

Single-instanceSetting

Security usingUC encryption

Security for multiple instances

Idealcryptography

UCtheorem

Sim

plify

UC w/jointstate

Prior work Abadi-Rogaway/Abadi-Jürjens

First connection of formal, computational Passive adversary

Micciancio-Warinschi Trace properties (e.g. mutual authentication) No intermediate composition

Complex analysis No composition guarantees

We lift to UC Backes, Pfitzmann, Waidner

UC library of primitives (including symmetric encryption, sigs) Multi-instance Primitive vs. protocol (at level 2)

Overview of talk Describe UC framework Describe Dolev-Yao model

Extended with local outputs Mutual authentication result Key-exchange results

Strengthened symbolic definition Future work

Traditional (non-UC) security

S AP P

F

"Functionality” specifies: what protocol does, what info released to adversary

P

P A∏

P

P A∏

Security: A, S : ViewReal(A) = ViewIdeal(A)Adversary learns only what allowed by F, even in real protocol

Desired: Composition

Q

Q A

Q

Q A

F F F

=

(Higher-levelprotocol)

Achieving Composition

ASP P

F

P

P A Adversary now sets participant input, sees output

Simulator sees neither! Adversary given special name: “environment”

Achieving Composition UC security:

A, S : ViewReal(A) = ViewIdeal(A)

Enforces that protocol messages and protocol outputs are independent

Strongest known (computational) notion of protocol security

The Dolev-Yao model Messages modeled symbolically

Symbols might be compound (crypto operations) Participant hears symbol, replies with symbol

AP1 P2

M1

M2

L

New: local output Not seen by adversary

The Dolev-Yao adversary Adversary maintains set of knowledge:

P1 P2

A

Know

Application of deduction

Dolev-Yao adversary powers

Already in Know Can add to Know

M1, M2 Pair(M1, M2)

Pair(M1, M2) M1 and M2

M, K Enc(M,K)

Enc(M, K), K-1 M

Only four possible deductions:

(Always in Know:• Randomness generated by adversary• Private keys generated by adversary• All public keys)

The Dolev-Yao adversary

AP1 P2

Know

Mutual Authentication UC: need only consider a single (two-party) instance Symbolic condition: Adversary cannot make party Pi

(locally) output (finished Pi Pj)

before both Pi and Pj output (starting Pj Pi)

UC: FMA only sends (success) to participants after both submit (start)

Mutual Authentication Results Theorem: let be a concrete protocol that uses ideal

encryption. Then:DY() achieves mutual auth iff

securely realizes FMA

Cor:let be a concrete protocol that uses concrete (UC) encryption. Then:

DY() achieves mutual auth iff securely realizes FMA

(Note: UC analog to MW04)

Key exchange UC: FKE creates single new key, sends to

requesting participants (but not adversary) Symbolic:

1. Key Agreement: If P1 outputs (Finished P1 P2 K) and P2 outputs (Finished P2 P1 K’) then K = K’.

2. Traditional Dolev-Yao secrecy: If Pi outputs (Finished Pi Pj K), then K can never be in adversary’s set Know

Not strong enough!

Composition and secrecy

Modified protocol still satisfies traditional secrecy Might be insecure when used as sub-protocol

P1 P2Outputs sessionkey: K

{K}K2

K

Traditional secrecy goals fail under composition Session key used in higher-level protocol

Example: let satisfy traditional secrecy for K

Real-or-random (1/3) Need: real-or-random property for session keys

Can think of traditional goal as “computational” Need a stronger “decisional” goal Expressed in Dolev-Yao framework

Let be a protocol Let r be , except that when participant outputs (Finished Pi Pj Kr), Kr added to Know

Let f be , except that when any participant outputs (Finished Pi Pj Kr), fresh key Kf added to adversary set Know

Want: adversary can’t distinguish two protocols

Real-or-random (2/3) Let S be a strategy

Sequence of deductions and transmissions Attempt 1: For any strategy,

Trace(S, r) = Traces(S, f) Problem: Kf not in any traces of r

Attempt 2: Trace(S, r) = Rename(Trace(S, f), Kf Kr)

Sufficient for “if,” too strong for “only if” Two different traces may ‘appear’ the same to adversary

Real-or-random (3/3) Observable part of trace: Abadi-Rogaway pattern

Undecipherable encryptions replaced by “blob” Example:

t = {N1, N2}K1, {N2}K2, K1-1 Pattern(t) = {N1, N2}K1, K2, K1-1

Final condition: for any strategy:

Pattern(Trace(S, r)) =

Pattern(Rename(Trace(S, f), Kf Kr)))

Main results Theorem: let be a concrete protocol that uses (UC)

ideal encryption. Then:

securely realizes FKE iff DY() satisfies1. Key agreement2. Traditional Dolev-Yao secrecy of session key3. Real-or-random

(Note: condition 3 implies 2 for Dolev-Yao message space with equality checks.)

Cor: same for that uses concrete UC encryption

Future work How to prove Dolev-Yao real-or-random?

Needed for UC security Not previously considered in the Dolev-Yao literature Can it be automated? Simpler form?

Similar results for protocols using symmetric encryption, signatures, Diffie-Hellman?

Symbolic representation of other types of tasks Zero-Knowledge from ideal commitment Secure function evaluation from ideal Oblivious Transfer Etc.

Backup-slides

“Simple” protocols Concrete protocols that map naturally to Dolev-Yao framework Two cryptographic operations:

Randomness generation Encryption/decryption

(This talk: asymmetric encryption) Example: Needham-Schroeder-Lowe

P1 P2

{P1, N1}K2

{P2, N1, N2}K1

{N2}K2

UC Key-Exchange Functionality

FKE

(P1 P2)

k {0,1}n

Key P2

P1

(P1 P2)

Key k

P2

(P2 P1)

Key k

(P1 P2)

A

Key P1

(P2 P1)

Key P2

(P2 P1)

Goal of the adversary Recall that the adversary A sees outputs of participants Goal: distinguish real protocol from simulation In protocol execution, output of participants (session key) related to

protocol messages In ideal world, output independent of simulated protocol If there exists a detectable relationship between session key and

protocol messages, adversary can distinguish Example: last message of protocol is {“confirm”}K where K is

session key Can decrypt with participant output from real protocol Can’t in simulated protocol