universally composable symbolic analysis of cryptographic protocols ran canetti and jonathan herzog...

Universally ComposableSymbolic Analysis of

Cryptographic Protocols

Ran Canetti and Jonathan Herzog

6 March 2006

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.

Universally ComposableAutomated Analysis of

Cryptographic Protocols

Ran Canetti and Jonathan Herzog

6 March 2006

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.

Overview

This talk: symbolic analysis can guarantee universally composable (UC) key exchange • (Paper also includes mutual authentication)

Symbolic (Dolev-Yao) model: high-level framework• Messages treated symbolically; adversary extremely limited• Despite (general) undecidability, proofs can be automated

Result: symbolic proofs are computationally sound (UC) • For some protocols • For strengthened symbolic definition of secrecy

With UC theorems, suffices to analyze single session• Implies decidability!

Needham-Schroeder-Lowe protocol

(Prev: A, B get other’s public encryption keys)

A BEKB(A || Na)

EKA(Na || Nb || B)

EKB(Nb)

K

K

Version 1: K = Na Version 2: K = Nb

Which one is secure?

Two approaches to analysis

Standard (computational) approach: reduce attacks to weakness of encryption

Alternate approach: apply methods of the symbolic model• Originally proposed by Dolev & Yao (1983)

• Cryptography without: probability, security parameter, etc.

• Messages are parse trees Countable symbols for keys (K, K’,…), names (A, B,…)

and nonces (N, N’, Na, Nb, …) Encryption ( EK(M) ) pairing ( M || N ) are constructors

• Participants send/receive messages Output some key-symbol

The symbolic adversary Explicitly enumerated powers

• Interact with countable number of participants• Knowledge of all public values, non-secret keys• Limited set of re-write rules:

M1, M2 M1 || M2

M1 || M2 M1, M2

M, K EK(M)

EK(M), K-1 M

‘Traditional’ symbolic secrecy

Conventional goal for symbolic secrecy proofs:“If A or B output K, then no sequence of

interactions/rewrites can result in K” Undecidable in general [EG, HT, DLMS] but:

• Decidable with bounds [DLMS, RT]• Also, general case can be automatically verified in practice

Demo 1: analysis of both NSLv1, NSLv2

So what? • Symbolic model has weak adversary, strong assumptions• We want computational properties!• …But can we harness these automated tools?

What we’d like

Concrete protocol

Computationalkey-exchange

Symbolic protocol

Symbolickey-exchange

Would like

Natural translation forlarge class of protocols

Simple, automated‘Soundness’

(need only be done once)

Some previous work

General area: [AR]: soundness for indistinguishability

• Passive adversary [MW, BPW]: soundness for general trace properties

• Includes mutual authentication; active adversary

Many, many others

Key-exchange in particular (independent work): [BPW]: (later) [CW]: soundness for key-exchange

• Traditional symbolic secrecy implies (weak) computational secrecy

Limitations of ‘traditional’ secrecy

Big question:Can ‘traditional’ symbolic secrecy imply standard

computational definitions of secrecy?

Unfortunately, no Counter-example:

• Demo: NSLv2 satisfies traditional secrecy

• Cannot provide real-or-random secrecy in standard models

• Falls prey to the ‘Rackoff’ attack

The ‘Rackoff attack’ (on NSLv2)

A BEKB( A || Na)

EKA( Na || Nb || B )

EKB(Nb)

AdvK =? Nb

EKB(K)

K if K = Nb

O.W.

?

Achieving soundness

Soundness requires new symbolic definition of secrecy

[BPW]: ‘traditional’ secrecy + ‘non-use’• Thm: new definition implies secrecy (in their framework)• But: must analyze infinite concurrent sessions and all resulting

protocols

Here: ‘traditional’ secrecy + symbolic real-or-random• Non-interference property; close to ‘strong secrecy’ [B]• Thm: new definition equivalent to UC secrecy• Demonstrably automatable (Demo 2)• Suffices to consider single session!

(Infinite concurrency results from joint-state UC theorems)• Implies decidability (forthcoming)

Decidability (not in paper)

Traditional secrecy

Symbolic

real-or-random

Unbounded sessions

Undecidable[EG, HT, DLMS]

Undecidable[B]

Bounded sessions Decidable(NP-complete)

[DLMS, RT]

Decidable(NP-complete)

Proof overview (soundness)

Multi-session KE(CCA-2 crypto)

Symbolickey-exchange

Single session UC KE(ideal crypto)

Multi-session UC KE(ideal crypto)

UC w/ joint state

[CR](Info-theor.)

UC theorem

Construct simulator• Information-theoretic• Must strengthen notion of UC public-key encryption

Intermediate step: trace properties (as in [MW,BPW])• Every activity-trace of UC adversary could also be produced by symbolic adversary• Rephrase: UC adversary no more powerful than symbolic adversary

Summary & future work

Result: symbolic proofs are computationally sound (UC) • For some protocols

• For strengthened symbolic definition of secrecy

With UC theorems, suffices to analyze single session• Implies decidability!

Additional primitives • Have public-key encryption, signatures [P]

• Would like symmetric encryption, MACs, PRFs…

Symbolic representation of other goals• Commitment schemes, ZK, MPC…

Backup slides

Two challenges

1. Traditional secrecy is undecidable for:• Unbounded message sizes [EG, HT] or

• Unbounded number of concurrent sessions(Decidable when both are bounded) [DLMS]

2. Traditional secrecy is unsound• Cannot imply standard security definitions for

computational key exchange

• Example: NSLv2 (Demo)

Prior work: BPW

New symbolic definition

Implies UC key exchange

(Public-key & symmetric encryption, signatures)

Theory Practice

Our work

New symbolic definition:

‘real-or-random’

Equiv. to UC key exchange

(Public-key encryption [CH], signatures [P])

UC suffices to examine single protocol run

Automated verification!

+ Finite system

Decidability?

Theory Practice

Demo 3: UC security for NSLv1

Our work: solving the challenges

Soundness: requires new symbolic definition of secrecy• Ours: purely symbolic expression of ‘real-or-random’ security

• Result: new symbolic definition equivalent to UC key exchange

UC theorems: sufficient to examine single protocol in isolation

• Thus, bounded numbers of concurrent sessions

• Automated verification of our new definition is decidable!… Probably

Summary

Summary: • Symbolic key-exchange sound in UC model

• Computational crypto can now harness symbolic tools

• Now have the best of both worlds: security and automation!

Future work

Secure key-exchange: UC

?P P

AK K

Answer: yes, it matters• Negative result [CH]: traditional symbolic secrecy does

not imply universally composable key exchange

Secure key-exchange: UC

?P P

A

Adversary gets key when output by participants• Does this matter? (Demo 2)

K K

F

S?

Secure key-exchange [CW]

P P

A

Adversary interacts with participants• Afterward, receives real key, random key• Protocol secure if adversary unable to distinguish

NSLv1, NSLv2 satisfy symbolic def of secrecy• Therefore, NSLv1, NSLv2 meet this definition as well

K, K’

KE

?P P

A

F

S

Adversary unable to distinguish real/ideal worlds• Effectively: real or random keys• Adversary gets candidate key at end of protocol• NSL1, NSL2 secure by this defn.

Analysis strategy

Concrete protocol

UC key-exchangefunctionality

Dolev-Yao protocol

Dolev-Yaokey-exchange

Would like

Natural translation forlarge class of protocols

Simple, automatedMain result of talk

(Need only be done once)

“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)

X

The Dolev-Yao model Participants, adversary take turns Participant turn:

AP1 P2

M1

M2

L

Local output:Not seen by adversary

The Dolev-Yao adversary Adversary turn:

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

Always in Know:Randomness generated by adversaryPrivate keys generated by adversaryAll public keys

The Dolev-Yao adversary

AP1 P2

Know

M

Dolev-Yao key exchange Assume that last step of (successful) protocol execution

is local output of (Finished Pi Pj K)

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 enough!

Goal of the environment

Recall that the environment Z 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, environment 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

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) Attempt 1: Let Traces() be traces adversary can induce

on . Then:

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

Attempt 2:

Traces(r) = Rename(Traces(f), Kf Kr) Problem: Two different traces may “look” the same

• Example protocol: If participant receives session key, encrypts “yes” under own (secret) key. Otherwise, encrypts “no” instead

• Traces different, but adversary can’t tell

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:

Pattern(Traces(r)) =

Pattern(Rename(Traces(f), Kf Kr)))

Main results Let key-exchange in the Dolev-Yao model be:

• Key agreement• Traditional Dolev-Yao secrecy of session key• Real-or-random

Let be a simple protocol that uses UC asymmetric encryption. Then:

DY() satisfies Dolev-Yao key exchangeiff

UC() securely realizes FKE

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?

Weaker forms of DY real-or-random Similar results for symmetric encryption and

signatures