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Power, EM and all that: Is your crypto device really secure? Pankaj Rohatgi Dakshi Agrawal, Bruce Archambeault, Suresh Chari, Josyula R Rao IBM T.J. Watson Research Center

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Side-Channel Analysis: Some recent advances I: A new side channel: EM emanations –Extends power analysis style attacks to large classes of cryptographic hardware SSL Accelerators, Cryptographic tokens. – Additional leakages compared to power. II: Better Analysis: Template Attacks. –(Near) optimal use of side-channel data. –Single sample attacks for ephemeral keys.

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EM History Classified TEMPEST standards. –Partly declassified Jan '01, Other, openly published work on EM. –EM Leakages from Peripherals, E.g., Monitors: Van Eck, Anderson & Kuhn. –EM Leakage from smart-cards during computation. Quisquater & Samyde, E-smart 2001, Gemplus Team [GMO ’01], CHES ’01. –SEMA/DEMA attacks. Best results required decapsulation of chip packaging and/or precise micro-antenna positioning on chip surface

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Our EM Work Deeper understanding of EM leakages. –Similar to now declassified TEMPEST literature. Plenty of EM signals are available, provided you know what to look for and where. –Superior signals and attacks possible without micro- antennas or decapsulation. –Some attacks possible from a distance. EM side-channel(s) >> Power side-channel EM can break DPA-resistant implementations.

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EM Emanations Background Types of EM Emanations –Direct emanations from intended current flows. Maxwell ’ s equations, Ampere ’ s and Faraday ’ s laws. See [Quisquater,Samyde 01], Gemplus [GMO ’ 01] –Unintentional emanations from coupling effects. Depend on physical factors, e.g., circuit geometry. Most couplings ignored by circuit designers. Manifest as modulation of carriers (e.g. clock harmonics) present/generated/introduced in device. –AM or Angle (FM/Phase) Modulation. Compromising signals available via demodulation.

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AM: Example 1 ECCLib on 16Mhz Palm Pilot. –Posted on Internet by Feng Zhu, Northeastern Univ. Point multiplication (k * P) on a Koblitz curve over GF[2^163] using Solinas’s technique. –Doubling replaced by Frobenius Map ( t ) k = S s i t i ( t -adic NAF decomposition) s i 2 {0,1,-1} – Cost of kP ~ |k|/3 ~ 54 point additions/subtractions, Structure can be heard in demo Good signal via AM demodulation at 241Mhz.

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Map/(Add/Subtract) Sequence

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3 successive Frobenius Map computations

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Point Add/Sub

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Comparing two different point addition/subraction

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AM: Example 2 PCI-bus based RSA Accelerator S inside a Intel/Linux server. Multiple AM modulated carriers. –Several carriers at clock harmonics propogate upto 50 feet and through walls. Precise RSA timing available at 50 feet.

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Precise Timing (SSL Music) Music can be heard 50 feet away by AM- demodulating 299MHz clock harmonic carrier. Enables better timing attacks. S looping with ~3s each of –512-bit RSA –1024-bit RSA –2048-bit RSA –4096-bit RSA

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RSA Internals in S AM-demodulating an intermodulated carrier at Mhz, bandwidth 150Khz. Clear signal available upto 3-4 feet. –Further distance requires statistical techniques. Large class of attack techniques applicable. – Such techniques earlier restricted to power analysis attacks on RSA in smart-cards.

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S: Two identical 2048-bit exponentiations with 12-bit exponent. Data/Modulus Dependent Initialization Data & Key Dependent Exponentiation

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S: Initialization (Fixed modulus, 2 exponents X 2 data) E1, D1 E2, D1 E1, D2 E2, D2

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S: Data and Key Dependent Exponentiation (2 exponents X 2 data)

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Angle Modulation: Example 1 PCI based RSA/Crypto Accelerator R inside an Intel/Linux server. AM-demodulate a 99Mhz carrier (clock harmonic).

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R performing an RSA operation in a loop

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Internals of RSA Exponentiation in R with small exponent Data/Modulus Dependent Initialization Key & Data Dependent Exponentiation

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RSA Exponentiation Key/Data Dependent Internals Obscured by interfering signal G GENERATED asynchronously during operation

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Can we get RSA internals ? Not directly…. But, timing of asynchronously generated G affected by ongoing computation due to coupling effects. –Timing statistics of G (using ~1000 samples) gives information about internals!! –G strong enough to be captured at feet.

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G: Timing Statistics of G for fixed modulus, 3 exponents (2 same)

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EM vs. Power EM may be only side-channel available. Is EM useful in the presence of power channel? –Direct emanations: micro-sensor positioning, decorrelated noise [QS01, GMO 01] –Unintended emanations: Several EM carriers: DEMA/DPA correlation plots show extent of leakage from different EM carriers & comparison with power signal. –Different carriers carry different information. –Some EM leakages substantially different/better than Power leakages.

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4 Time Synchronized DPA/DEMA Correlation Plots

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Bad Instructions Instructions where some EM leakage >> Power leakage. Typically CPU intensive rather than bus intensive. All architectures have BAD Instructions. Caution: Bad Instructions can break power analysis resistant implementations. Bad Instruction Example: Bit-test on several 6805 based systems leaks tested bit.

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O TESTED BIT = 0 IN BOTH TRACES

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O TESTED BIT DIFFERENT

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Part II: Template Attacks Sometimes a single (few) side-channel sample available. –Stream ciphers, Ephemeral keys. –“System Level Countermeasures” to side channel attacks. Higher level protocols limit key usage. Non-linear key update countermeasure (Kocher et al [KJJ ’99]). Are these inherently immune to side-channel attacks? –Immune to traditional simple/differential attacks Easy to secure implementations against SPA/SEMA –Ensure signal differences < noise level. DPA/DEMA and higher order DPA/DEMA inapplicable. –Cannot remove noise by averaging over multiple samples. –Not against Template Attacks (with some assumptions).

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Example: RC4 on a smart-card At best, single trace during RC4 state initialization with ephemeral key available. i= j = 0; for (ctr=0;ctr < 256; ctr++) { j = key[i] + state[ctr] + j; SwapByte(state[ctr], state[j] ); i=i+1; } Can avoid SPA. No DPA style attack possible. One key byte used per iteration. Is a single sample enough to recover the whole key ? Can two fixed keys different in 1 st byte be distinguished during 1 st iteration ?

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Power Sample showing 6 iterations of loop

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Sample = Signal + Noise

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Signals (and signal difference) for two fixed keys with different first byte DIFFUSION Differences start in first iteration (Contamination)

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Signals difference for the two fixed keys with different first byte during first iteration of loop (CONTAMINATION) { j = key[i] + state[ctr] + j; SwapByte(state[ctr], state[j] ); i=i+1; }

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Sample noise vs. Signal differences (6 iterations)

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Sample noise vs. Signal difference in first iteration

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Template Attack Basics: How to distinguish between the two keys ? Don’t (cannot) eliminate sample noise, use it! How ? Use identical device (assumption) for building signal and noise templates T1 and T2 for keys K1 and K2 in 1 st iteration. T1 = {s1(t), D 1(t) }, T2= {s2(t), D 2(t) } Given sample S = s(t) use theoretically optimal maximum likelihood estimator: Which noise is more likely ? s(t)-s1(t) under D 1(t) OR s(t)-s2(t) under D 2(t)

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Theory vs. Practice Need T1 = {s1(t), D 1(t) }, T2= {s2(t), D 2(t) } s1(t), s2(t) easily estimated by averaging. What about D 1(t) and D 2(t) ? –Can be restricted to L sample points where s1(t) and s2(t) differ, e.g., L=42 in example. –Still infeasible to estimate a general probability dist. over R L. –Borrow from the large body of work in Signal Detection and Estimation Theory which deals with precisely this problem! Several realistic and computable noise models available. We used the popular Multivariate Gaussian Noise model

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Mutivariate Gaussian Noise Model Estimating D 1(t), D 2(t) reduces to estimating LxL noise covariance matrices S L:1 and S L:2 for keys K1 and K2 Maximum Likelihood test easy, matrix inverse/ multiplication/determinant and taking logs.

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Generalization and Results These 10 keys deliberately chosen to be very close. –Widely different keys easily separated with 100% success even with weaker noise models. Estimated that only a 5-6% error probability in identifying the correct 1 st byte out of 256 possibilities. Key byte 0xFE0xEE0xDE0xBE0x7E0xFD0xFB0xF70xED0xEB Technique generalizes to multiple choices for first key byte: E.g., among these 10 key bytes, correct classification probability:

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Attacking multi-byte keys 5-6% error in identifying single byte is too much. Maximum Likelihood: Retains hypothesis with max probability for observed noise (P max ) Approximate Approach: Retain ALL hypotheses with noise probability > (P max /c), c constant. Tradeoff between number of hypothesis retained and correctness.

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Approximate Approach Tradeoff c=1c=e 6 c=e 12 c=e 24 Success probability (retaining correct byte hypothesis out of 256) Avg. number of hypothesis retained

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Attacking Multi-byte Keys: Extend and Prune Base case: Narrow candidates for first byte to a small number (e.g., on average 1.3 possibilities with 98.67% correctness for c=e 6 ) Assume T i candidates for first i key bytes. –Extend: For each candidate, build larger templates for all 256 possible values of next byte. –Prune : Use approximate approach to reduce 256 T i candidates down to T i+1 < 1.3 * T i (diffusion). Tedious but feasible for reasonable sized keys. –N bytes: Failure probability 1.33N% (N=16, failure prob.= 21.5%) –Number of remaining candidates < 1.3^N (N=16, candidates < 67)

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For more information on topics such as –Multiple EM/Power channel attack techniques. –EM vulnerability assessment see & Upcoming CHES Questions?

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