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Protecting Circuits from Leakage Sebastian Faust @ Rome La Sapienza, January 18, 2009 Joint work with KU Leuven Tal Rabin Leo Reyzin Eran Tromer Vinod Vaikuntanathan IBM Research Boston University MIT IBM Research

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Beautiful Theory… 3. Prove that no adversary exists 1.Adversarial Model 2.Security Definition

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3 The Ugly Reality electromagneticacoustic probing cache optical power

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4 Motivation Many provably secure cryptosystems can be broken by side-channel attacks

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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.

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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

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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...

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8 M XY Any boolean circuit Circuit transformation Transformed circuit t-wire probing YX black-box indistinguishable [Ishai Sahai Wagner 03]

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9 Our goal Allow much stronger leakage.

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10 Our main construction A transformation that makes any circuit resilient against Global adaptive leakage May 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]

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11 antennas are dumb computationally weak can be powerful Computationally-weak leakage Assumption: the observed leakage is a computationally-weak function of the devices internal wires.

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12 Secure against global leakage We do not assume spatial locality, such as: t wires [ISW03] Only computation leaks information [MR04][DP08][Pie09][FKPR09]

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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

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14 1.Computation model 2.Security model 3.Circuit transformation 4.Proof approach 5.Extensions Rest of this talk

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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]C[M] X Y

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16 Allowed gates in C: + $ MC 1 Multiply in K: Add in K: Coin:Const: Copy:Memory: (Boolean circuits are easily implemented.) Original circuit

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17 Transformed circuit C [M ]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

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18 X M Model: single observation in leakage class L Y wires f (wires)

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19 X 0 f 0 L Y 0 f 0 (wires 0 ) M 1 M 2 M 3 Refreshed state refresh state allows total leakage to grow Model: adaptive observations X 1 f 1 L Y 1 f 1 (wires 1 ) X 2 f 2 L Y 2 f 2 (wires 2 )

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20 Simulation: Real: M i indistinguishable Model: L-secure transformation Adversary learns no more than by black-box access: X i f i L Y i f i (wires i ) Actual definition little bit more complicated Simulation: MiMi XiXi YiYi

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21 MM 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 K t (probabilistic) Dec: K t K (surjective linear function)

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22 b R {0,1} x0x0 Pr[b = b] - ½ negl for all x 0,x 1 K: (Enc,Dec) is L-leakage-indistinguishable if b Leakage: L-leakage-indistinguishability Consequence : Leakage functions in L cannot decode Enc (x b ) x1x1

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23 For any linear encoding scheme that is L-leakage indistinguishable we present an L -secure transformation for any circuit and state f f L Simple functions Thm: transformed circuit can tolerate these leakage functions Assumption: encoding can tolerate these leakage functions L Main construction

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24 f ? Enc(x) f AC 0 ? Dec Parity Some known circuit lower bounds imply L-leakage-indistinguishability of encodings hard for AC 0 depth: 2 size: O(t 2 ) Theorem const depth and poly size circuits Unconditional resilience against AC 0 leakage

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Is this practical? Not really… AC 0 not very realistic class of leakage functions sec parameter t has to be large (blow up t 2 ) But… AC 0 can approximate hamming weight Very powerful adversary (adaptive, statistical security) Make reasonable assumption on power of leakage functions (very important future work!)

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26 C[M]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

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27 + f(wires) Easy to attack Notation: Computing on encodings first attempt

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28 + + f(wires) ??? Works well for a single gate... but does not compose. Exponential security loss (for AC 0 ). Computing on encodings second attempt – use linearity

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29 M X 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 X wires

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30 Fool adversary: gate is non-verifiable by functions in L. Opaque gate: Enc(0) Samples from a fixed distribution. No inputs Opaque gate

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31 Wire simulators advantage: can change output of opaque without getting noticed (L-leakage-indistinguishable) Using the opaque gate Full transformation for gate: + ??? Enc(0) So can simulate this gate independent of all others gates.

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32 Other gates Similar transformation for other gates. The challenging case is the non-linear gate: multiplication. Hard to make leak-resilient; standard MPC doesnt work. Trick: give wire simulator enough degrees of freedom. Enc(0) + Dec Enc(0) + B S

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33 This property (suitably defined) composes ! If every gadget has a (shallow) wire simulator then the whole transformed circuit has a (shallow) wire simulator. Wire simulator composability Security for 1 round follows easily. For multiple rounds theres extra work due to adaptivity of the leakage and inputs.

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34 Summary of (positive) results Linear encoding + leakage class which cant decode + leak-free Enc(0) gates AC 0 / ACC 0 [q] leakage + leak-free 0-parity gates Any encoding + leakage class which cant decode + leak-free gates (relaxed) Noisy leakage + leak-free encoding gates Public-key encryption + Gen+Dec+Enc gadgets

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35 Achieved New model for side-channel leakage, which allows global leakage of unbounded total size Constructions for generic circuit transformation, for example, against all leakage in AC 0 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

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Leakage-Resilient Signatures Sebastian Faust KU Leuven Joint work with Eike Kiltz CWI Krzysztof Pietrzak CWI Guy Rothblum Princeton TCC 2010, Zurich, Switzerland.

Leakage-Resilient Signatures Sebastian Faust KU Leuven Joint work with Eike Kiltz CWI Krzysztof Pietrzak CWI Guy Rothblum Princeton TCC 2010, Zurich, Switzerland.

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