On Recycling Encryption Schemes

or

Achieving Resistance to Cache Attacks via Low Bandwidth Encryption

Weizmann Institute of Science

Moni Naor

Crypto in the Clouds, August 2009, MIT

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Adversarial ModelsSTANDARD MODEL: Abstract models of computation

Interactive Turing machines Private memory, randomness ...

Well-defined adversarial access Can model powerful attacks

REAL LIFE: Physical implementations leak information Adversarial access not always captured by

abstract models

Ek(m)

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Adversarial Models

Ek(m)

Attacks - standard model: Chosen-plaintext attacks Chosen-ciphertext attacks Composition Self-referential encryption Circular encryption ....

Attacks outside standard model: Timing attacks [Kocher 96] Fault detection [BDL 97, BS 97] Power analysis [KJJ 99] Cache attacks [OST 05] Memory attacks [HSHCPCFAF 08] ...

Osvik, Tromer and Shamir

Lampson 1973Tenex Password with page faults

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Adversarial ModelsAttacks - standard model: Chosen-plaintext attacks Chosen-ciphertext attacks Composition Self-referential encryption Circular encryption ....

Attacks outside standard model: Timing attacks [Kocher 96] Fault detection [BDL 97, BS 97] Power analysis [KJJ 99] Cache attacks [OST 05] Memory attacks [HSHCPCFAF 08] ...

Side channel:

Any information not captured by the abstract “standard” model

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“Outside of a few classified military programs, side-channel attacks have been largely ignored by computer security researchers, who have instead focused on creating ever more robust encryption schemes and network protocols.”

W. Wayt Gibbs, Scientific American, May 2009

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Thesis of this talk

Many tools developed in the foundations of cryptography are helpful for protecting against

side-channel attacks

Proof by a 2nd example...

and not only at implementation time

Incorporate side-channel attacks in the design of systems

And yesterdays talk

and workshop?

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Outline of the Talk Cache Attacks

Address Obliviousness

Remotely-keyed Encryption Schemes (RKES)

Adapting RKES for obtaining Address

Oblivious Encryption

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Cache Attacks

Cryptanalysis through Cache Address Leakage Dag Arne Osvik, Adi Shamir and Eran Tromer

Slides based on Eran Tromer

Slides shamelessly stolen from Eran Tromer

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Cache attacksPure software

No special privileges No interaction with the cryptographic code

Very efficient Full AES key extraction from Linux encrypted partition

in 65 milliseconds)Compromise otherwise well-secured systems

“Commoditize” side-channel attacks:

Easily deployed software breaks many common systems

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CPU core60% (until recently)

Main memory7-9%

Why cache?

cacheAnnual speedincrease:

Typicallatency:

50-150ns0.3ns → timing gap

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Address leakageThe cache is a shared resource:cache state affects, and is affected by, all processes

leading to crosstalk between processes.Cached data is subject to memory protection

Not attackedThe “metadata” leaks information about memory

access patterns: Which addresses are being accessed.

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Associative memory cacheDR

AM

cach

ememory block

(64 bytes)

cache line(64 bytes)

cache set

(4 cache lines)

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S-box tables in memoryDR

AM

cach

e

S-boxtab

le

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Detecting access to AES tablesDR

AM

cach

e

Atta

cker

mem

ory

S-boxtab

le

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What to Measure

Two approaches to exploit Inter-process crosstalk:

Measuring the effect of the cache on the encryption Need precise timing

Measuring the effect of the encryption on the cache

Bernstein; Percival; Bonneau and Mironov

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DRA

Mca

che

T0A

ttack

erm

emor

y 1. Make sure the tables are cached

2. Evict one cache set

3. Time an encryption. See if it’s slow

Measuring effect of cache on encryption

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What to Measure

Two approaches to exploit Inter-process crosstalk:

Measuring the effect of the cache on the encryption Need precise timing

Measuring the effect of the encryption on the cache

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Measuring effect of encryption on cacheDR

AM

cach

e

Attacker

memory

1. Completely evict tables from cache

S-boxtab

le

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Measuring effect of encryption on cacheDR

AM

cach

e

Attacker

memory

1. Completely evict tables from cache

2. Trigger a single encryptionS-box

table

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Measuring effect of encryption on cacheDR

AM

cach

e

Attacker

memory 1. Completely

evict tables from cache

2. Trigger a single encryption

3. Access attacker’s memory. See which cache sets are slow

S-boxtab

le

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Advantages of Measuring effect of encryption on cache

Yields more information (64) from a single encryption

Insensitive to timing variance in encryption code path

No real need to trigger the encryption – can wait until it happens by itself

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Protection

Address Obliviousness Want the computation to access addresses in a manner

that is oblivious to input Plaintext Keys?

There exist slooow implementations of address oblivious encryption

True for AES

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Protection: The Oblivious RAM Model

Oblivious Turing Machine: At any point in time know where the heads are

The access pattern is independent of the input Important: to convert to circuits

Oblivious RAM The access pattern is independent of the data

Probability distribution!

Suggested by Goldreich 1987

Pippenger and Fischer 1979

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Model

CPU

Main memory

Small private memory

qi

M[qi]

Secure zone CPU needs to simulate locations i1, i2, …Accesses addresses q1, q2…

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Oblivious RAM RequirementsAny sequence of locations i1, i2, …induces a distribution on sequences of requests q1, q2…

Functionality: should be able to figure out the original content Security: for any two sequence of locations

i1, i2, … i’1, i’2, … induced distributions of requests should be indistinguishable

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Oblivious RAM Constructions

Trivial: O(n) slowdown O(log n) bits private memory

Known: polylog slowdown [Goldreich-Ostrovsky 96] O(log n) bits private memory Some improvements –Williams, Sion and Carbunar 2008

Can we do better? Want constant or less overhead Also need to be able to run a few primitives obliviously

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Want: Address Oblivious Encryption At least wrt the key

Work on large chunks Partition the encryption process into:

A slow but short part: implemented securely Fast and insecure part: should not have consequences

beyond values encryptedWant to be able to express that partition is secure

Recycle a scheme/definition for remotely keyed encryption

Matt Blaze, Joan Feigenbaum and Moni Naor, Eurocrypt 1998

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Who will guard the guards?No cryptographic protocol is stronger than the mechanism

protecting its secret keys. Almost any computer connected to the world will be corrupted

(at least partly) at some point in time. However: in most systems no safe place for storing the keys.

Idea: add a special purpose device for encryption Smart Card

Where should I put it....?

Quis custodiet ipsos custodes

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Special purpose deviceAdvantages: Limited functionality, fewer places to err, easier

to design Can design once and for all. Should work with all systems.

Can be cheap smart card

Host Crypto device

High Bandwidth Channel

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Special purpose deviceProblems: Bandwidth from device to host. Should be as high

as any link. Does not grow with the host: Keys/device may live

many years.

Host Crypto device

High Bandwidth Channel

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Remotely keyed encryption How to do high bandwidth encryption/decryption Taking advantage of: The power (bandwidth, computing) of the host. Superior security of the crypto device

Security risk: host is completely controlled by attacker for certain periods of time.

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Model: Communicating parties Two parties: Host and Device. To encrypt/decrypt (Host, Device) interact.

Desirable: lower communication than plaintext.

Host Crypto device

Plaintext

Ciphertext

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Model: Adversary

Adversary A attacks the system: Host Phase Adversary A controls the Host and

all its communication links. A cannot see internal computation of the device

Challenge Phase Adversary A ceases control of the internal communication. Can still attack the pair (Host, Device) externally.

No moderate physical pressure!

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What do we know to do Definition of Security for Remotely Keyed Encryption Schemes

(RKES). Length Preserving Encryption and Length Increasing Encryption

Constructions where encrypting n blocks requires Fixed communication and computation at the device.

Proportional to a single block

…

n

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Length Preserving Encryption Saves on memory and communication bandwidth Easy to embed in existing systems doesn't

destroy formats (sectors, packets) Problem: what to do with repeated blocks? Solutions:

Chaining (CFB,CBC) reveals prefix information. Permutation on very large blocks our approach.

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Definition Length Preserving RKESInput X = (X1, …, Xn) Output Y = (Y1 …,Yn)

Each xi, yi 2 {0,1}b : Non RKES security:

Encryption function should be a pseudo random permutation Even if adversary A can access and -1 A cannot distinguish it from a random permutation.

Too strong for RKES: is not random for A:

A has a short description of on the values it saw at the attack phase

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Definition Length Preserving RKESInput X = (x1, …, xn) Output Y = (y1 …,yn)

Each xi, yi 2 {0,1}b :

Idea: call it secure if A cannot distinguish a switch to a random permutation after host phase.

What about X1, …, Xm from Host Phase? Well, except them...

Problem: they are not well defined! Due to low communication

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Definition: The Arbiter

Add a new (fictitious) party: the arbiter B Filters the message of the Challenge Phase.

The arbiter B acts as a simple function of the communication of the Host Phase.

The number of messages filtered by B in the Challenge Phase should be bounded by m The number of interactions in the Host Phase.

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Tools Pseudo random function Fk : {0, 1}b {0,1}b

Pseudo random permutation Ek:{0, 1}b {0,1}b

Ek should be a strong pseudo random permutation E and F may be implemented by ``common'' block ciphers.

Length preserving encryption scheme GS:{0, 1}nb {0,1}nb

If S is random, then GS(x1, …, xn) is pseudo random for all (x1, …, xn) . Possible realizations: a pseudo random generator, permutation on large or small

blocks. A collision intractable hash function

S is used only once!

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Tools Pseudo random function Fk : {0, 1}b {0,1}b

Pseudo random permutation Ek:{0, 1}b {0,1}b

Length preserving encryption scheme GS:{0, 1}nb {0,1}nb

A collision intractable hash function HH : {0, 1}nb {0,1}b :

Should be infeasible to come up with X Y such that H(X) = H(Y).

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The NR Framework

Compose Q= 1 ° ° 2 where: 1, and 2 are permutations. 1 and 2 are lightweight

mostly Device. is heavy

mostly Host.

Plaintext

Ciphertext

1

2

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The Construction 1 and 2 change only the first block 1 (x1, …, xn) = (w, x2, …, xn)

w is a function of x1 and hx =H(x2, …, xn)

2(y1, …, yn) = (z, y2, …, yn) z is a function of y1 and hy =H(y2, …, yn)

is defined by two keys (k3 , k4)

(w, x2, …, xn) = (z, y2, …, yn) where z = Ek3

(w)

(y2, …, yn) = GFk4(w)(x2, …, xn)

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Properties of 1 and 2

Non Colliding Encryption A Good sequences different X's have different

z's.

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Evaluation Evaluation of 1 by (Host, Device)

Host: compute hx = H(x2, …, xn) Send (x1; hx).

Device: compute w based on its secret keys. Evaluation of by (Host, Device):

Device computes S = Fk4(w) and z = Ek3

(w) Sends (S, z).

Host computes (y2, …, yn) = GS(x2, …, xn)

Evaluation of 2 by (Host, Device) Host: compute hy=H(y2, …, yn) and send it. Device: compute y1 based on its secret keys.

Same way for Inversion

Host

device

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The Arbiter

Arbiter B: On encryption query x1, x2, …, xn

Compute h = H(x2, …, xn) Check whether (h, x1) occurred in the

transcript of the host phase.

Decryption: similar

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Connecting to Address Obliviousness

Device implemented by an address hiding implementation of Block Cipher

Host implemented without address obliviousness

Security: No information about the key is leaked Only information on actual plaintext may be leaked: If hash function implementation is not address

oblivious

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Efficiency

To encrypt a large number of blocks: Need a fixed number of address oblivious computations Number of encryptions proportional to chunk Compute a cryptographic hash function

Do we need a cryptographic hash function H? Adversary need not see the results Open question: come up with an address oblivious universal

hash function

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תודה רבהThank You