Protecting Circuits from Leakage

Sebastian Faust

@ Rome La Sapienza, January 18, 2009

Joint work with

KU Leuven

Tal RabinLeo ReyzinEran TromerVinod Vaikuntanathan

IBM Research

Boston University

MIT

IBM Research

Beautiful Theory…

3. Prove that no adversary exists

1. Adversarial Model

2. Security Definition

3

The Ugly Reality

electromagnetic acoustic

probing

cache

optical

power

4

Motivation

Many provably secure

cryptosystems can be broken by

side-channel attacks

5

Engineering approach

Ad-hoc countermeasures typically tailored to defeat specific attacks

But security only if protection against all known side channel attacks all new attacks during the

device's lifetime.

6

Cryptographic approach

Face the music: computational devices are not black-box.

Cryptosystem should protect already at algorithmic-level against side-channel attacks

Prove security against well-defined class of resource-bounded adversaries

Related Work

[CDHKS00]: Canetti, Dodis, Halevi, Kushilevitz, Sahai: Exposure-Resilient Functions and All-Or-Nothing Transforms

[ISW03]: Ishai, Sahai, Wagner: Private Circuits: Securing Hardware against Probing Attacks

[MR04]: Micali, Reyzin: Physically Observable Cryptography

[GTR08]: Goldwasser, Tauman-Kalai, Rothblum: One-Time Programs

[DP08]: Dziembowski, Pietrzak: Leakage-Resilient Cryptography in the Standard Model

[Pie09]: Pietrzak: A leakage-resilient mode of operation

[AGV09]: Akavia, Goldwasser, Vaikuntanathan: Simultaneous Hardcore Bits and Cryptography against Memory Attacks

[ADW09]: Alwen, Dodis, Wichs: Leakage-Resilient Public-Key Cryptography in the Bounded Retrieval Model

[FKPR09]: Faust, Kiltz, Pietrzak, Rothblum: Leakage-Resilient Signatures

[DHT09]: Dodis, Lovett, Tauman-Kalai: On Cryptography with Auxiliary Input

[SMY09]: Standaert, Malkin, Yung: A Unified Framework for the Analysis of Side-Channel Key-Recovery Attacks

...

8

M

X Y

Any boolean circuitCircuit transformation

Transformed circuitt-wire

prob

ing

Y

'M

X

blac

k-bo

x

indistinguishable

[Ishai Sahai Wagner ’03]

9

Our goal

Allow much stronger leakage.

10

Our main construction

A transformation that makes any circuit resilient against

• Global adaptive leakageMay depend on whole state and intermediate results, and chosen adaptively by a powerful on-line adversary.

• Arbitrary total leakage Bounded just per observation.

[DP08]

But we must assume something:• Leakage function is computationally weak

[MR04]

• A simple leak-free component

[MR04]

11

“antennas are dumb”

computationally weak

can be powerful

Computationally-weak leakage

Assumption: the observed leakage is a computationally-weak functionof the device’s internal wires.

12

Secure against global leakage

We do not assume spatial locality, such as:

• t wires

[ISW03]• “Only computation leaks information”

[MR04][DP08][Pie09][FKPR09]

13

Leak-free components

• Secure memory[GKR08]

• Secure processor [G89][GO95]

• Here: simple component that samples from a fixed distribution, e.g:securely draw strings with parity 0.

• No stored secrets or state• No input, so can be precomputed

• Can be relaxed

14

1. Computation model

2. Security model

3. Circuit transformation

4. Proof approach

5. Extensions

Rest of this talk

15

Original circuit

Original circuit C of arbitrary functionality(e.g., crypto algorithms), with state M,over a finite field K.Example: AES encryption with secret key M.

C[M]

X Y

16

Allowed gates in C:

● +

$

M C

1

Multiply in K: Add in K:

Coin: Const:

Copy:Memory:

(Boolean circuits are easily implemented.)

Original circuit

17

Transformed circuit

C ’[M ’]

X Y

Same underlying gates as in C, plus opaque gate (later).

Soundness: for any X,M: C[M](X) = C ‘[M ‘](X)

Transformed state

18

XM

Model: single observation in leakage class L

Y

Lf wires

f(wires)

19

X0

f0 ∈L

Y0

f0(wires0)

M’1 M’2 M’3Refreshed state Refreshed state

refresh state allows total leakage to grow

Model: adaptive observations

X1

f1 ∈L

Y1

f1(wires1)

X2

f2 ∈L

Y2

f2(wires2)

20

Simulation: Real:M’i

indistinguishable

Model: L-secure transformation

Adversary learns no more than by black-box access:

Xi

fi ∈L

Yi

fi (wiresi)

Actual definition little bit more complicated

Simulation:Mi

Xi Yi

21

M M

Problem: Adversary learns one bit of the state

Solution: Share each value over many wires [ISW03, generalized]

Every value encoded by a linear secret sharing scheme (Enc,Dec)with security parameter t:

Motivating example

1-wire probing

Enc: K Kt (probabilistic)

Dec: Kt K (surjective linear function)

22

b R {0,1}

x0

Pr[b‘ = b] - ½ ≤ negl

for all x0,x1 K:

(Enc,Dec) is L-leakage-indistinguishable if

b‘

Leakage: L-leakage-indistinguishability

))(Enc( bxfLf

Consequence:

Leakage functions in L cannot decode

Enc(xb)

x1

23

For any linear encoding scheme that isL-leakage indistinguishable

we present an L -secure transformationfor any circuit and state

f’fL

Simple functions

Thm: transformed circuit can tolerate these leakage functions

Assumption: encoding can tolerate these leakage functions

L’

Main construction

‘

24

f ’

?

Enc(x)

f ’ AC0

?

f AC0

DecParity

Some known circuit lower bounds imply L-leakage-indistinguishability of encodings

hard for AC0

depth: 2 size: O(t2)

Theorem

const depth and poly size circuits

Unconditional resilience against AC0 leakage

Is this practical?

Not really…

• AC0 not very realistic class of leakage functions

• sec parameter t has to be large (blow up ≈t2)

But…

• AC0 can approximate hamming weight

• Very powerful adversary (adaptive, statistical security)

• Make reasonable assumption on power of leakage functions (very important future work!)

26

C[M] C ’[M’]

Transformation: high level

• The state is encoded: M ’ = Enc(M)

• Circuit topology is preserved

• Every wire is encoded

• Inputs are encoded; outputs are decoded

• Every gate is converted into a gadget operating on encodings

27

+

)(Enc aa

)(Enc bb

)(Dec aa

)(Dec bb

c )(Enc cc

c

f(wires)

Easy to attack

Notation: )(Enc xx

Computing on encodingsfirst attempt

28

+1a

+

1b

tbta

1c

tc

f(wires)???

Works well for a single gate... but does not compose.Exponential security loss (for AC0).

Computing on encodingssecond attempt – use linearity

)(Enc aa

)(Enc bb c

29

MX

Y

Since f can verify arbitrary gates in circuit, wires must be consistent with X and Y.Problem: simulator does not know the state M, so hard to simulate internal wires!

Solution: to fool the adversary, introduce a non-verifiable atomic gate.

X, f

Y, f (wires)

Intuition: wire simulation

M Y

f

Xwires

30

Fool adversary:gate is non-verifiable by functions in L.

Opaque gate: Enc(0)

• Samples from a fixed distribution.

• No inputs

Opaque gate

31

Wire simulator’s advantage:can change output of opaque without getting noticed(L-leakage-indistinguishable)

Using the opaque gate

Full transformationfor gate:+

a

b oba

)(

???

c

c

Lf

a

bEnc(0)

cba

,,So can simulate

this gate independentof all others gates.

32

Other gates

• Similar transformation for other gates.• The challenging case is the non-linear gate: multiplication.

Hard to make leak-resilient; standard MPC doesn’t work.Trick: give wire simulator enough degrees of freedom.

a

b

Enc(0)a

b

jiba

Enc(0)Enc(0)

+

Dec

Dec

Dec

Enc(0)

+qo

B S

c

33

This property (suitably defined)

composes!

If every gadgethas a (shallow) wire simulator

then the whole transformed circuithas a (shallow) wire simulator.

Wire simulator composability

Security for 1 round follows easily.

For multiple rounds there’s extra work due to adaptivity of the leakage and inputs.

34

Summary of (positive) results

Linear encoding +leakage class

which can’t decode +leak-free Enc(0) gates

AC0 / ACC0[q] leakage +leak-free 0-parity gates

Any encoding +leakage class

which can’t decode +leak-free gates (relaxed)

Noisy leakage +leak-free encoding gates

Public-key encryption + Gen+Dec+Enc

gadgets

35

Achieved

• New model for side-channel leakage, which allows global leakage ofunbounded total size

• Constructions for generic circuit transformation,for example, against all leakage in AC0 or noisy leakages.

• General proof technique + several additional applications.

Open problems

• More leakage classes: find a reasonable assumption on the power of leakage functions!

• Smaller leak-free components

• Proof/falsify black-box necessity conjecture

• Circumvent necessity result (e.g., non-blackbox constructions)

Conclusions

http://eprint.iacr.org/2009/379