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Revealing the secrets of success Theoretical efficiency of - - PowerPoint PPT Presentation

Dec 14, 2023 1.04k likes •1.32k views

Revealing the secrets of success Theoretical efficiency of side-channel distinguishers Annelie Heuser, Sylvain Guilley, Olivier Rioul INSTITUT MINES-TLCOM Outline Motivation State of the art New metric: success metric (SM)

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INSTITUT MINES-TÉLÉCOM

Revealing the secrets of success

Theoretical efficiency of side-channel distinguishers

Annelie Heuser, Sylvain Guilley, Olivier Rioul

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INSTITUT MINES-TÉLÉCOM

REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

Outline

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  • Motivation
  • State of the art
  • New metric: success metric (SM)
  • Empirical evaluation
  • Closed-form expression of SM
  • Outlook
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REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

Problem Statement

3 Interclass Information Analysis Kolmogorov-Smirnov Analysis Linear Regression Linear Correlation Analysis Difference of Means Mutual Information Analysis Empirically

  • Real measurements (portable?)
  • Simulations (model suitable?)

How to compare side-channel distinguishers? Theoretically

  • Is this realistic?
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REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

State of the Art [Standaert+09] Unified framework for the analysis

  • f side-channel key recovery attacks
  • Estimated success rate (o-th order)
  • Estimated guessing entropy

4 E m p i r i c a l C r i t e r i a

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REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

[WhitnallOswald11] A fair evaluation framework for comparing side-channel distinguisher

  • Theoretical evaluation criteria

(e.g., nearest distinguishing margin)

  • Distinguisher is provided with full information about the

leakage

  • New insights in the theoretical behavior

5 T h e

  • r

e t i c a l C r i t e r i a

State of the Art

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[Fei+12] Algorithmic confusion analysis for DPA

  • Closed-form expression of one-bit DPA for the

success rate using a multivariate normal CDF

Algorithmic confusion coefficient Signal-to-noise ratio Number of traces

State of the Art

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REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

7 Theoretical Criteria Empirical Criteria

displays the practical

  • utcome

ad-hoc computation displays the theoretical distinguishability equivalent to the practical outcome?

State of the Art

coincides with the empirical success rate

New metric

more insights on parameters Closed-form expression

reflects relevant parameters

  • nly DPA;

multivariate CDF estimation

“simple“ closed-form expression for any additive distinguisher

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REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

8 measured leakage with RV modeling the key secret key on the device sensitive variable depending on the key sensitive variable - correct key guess

Notation

Side-channel Model

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REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

9 distinguisher difference estimated difference

Distinguisher

Notation

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REVEALING THE SECRETS OF SUCCESS, A. HEUSER, S. GUILLEY, O. RIOUL

10 Estimation Bias Estimation Variance such that the mean-squared error of the estimation is given by

Statistical parameter from Estimation Theory

Notation

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11 Failure rate To derive our new metric we start with the theoretical success rate:

Success Metric

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  • 1. Union bound

Normal approximation Chebyshev/ Chernov bound Approximate the failure rate: Failure rate

Success Metric

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  • 2. Normal Approximation

exponentially for large m

Success Metric

Assumption

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  • 3. First order approximation

Since we achieved exponentially convergence

FR = 1 - SR

Success Metric

Relation to failure rate Normal approximation

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15 Derived from the theoretical success rate through approximations, we define the success metric as

Success Metric

Roughly speaking

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16 is the first DES Sbox in each setting we conducted 300 experiments

Empirical Evaluation

  • Correlation Power Analysis (CPA)
  • Mutual Information Analysis (MIA)
  • Histograms
  • Parzen window
  • Kolmogorov-Smirnov Analysis (KSA)

S e t u p D i s t i n g u i s h e r

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17 Noise level = 4

Empirical Evaluation

S R a n d S M c

  • i

n c i d e

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18 Relative Distinguishing Margin

Empirical Evaluation

[WhitnallOswald11]

T h e

  • r

e t i c a l C r i t e r i a does not depends on

  • number of traces
  • estimation method
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19 Using 50 traces

Empirical Evaluation

Using 500 traces

SM depends on the number of traces

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20 Using 500 traces

Empirical Evaluation

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Closed-form expressions for additive distinguisher

Success Metric

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= =

One-bit models

[Fei+12]

  • nly valid for one-bit

models

Generalized Confusion Coefficient

We assume that that the sensitive variable is normalized

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CPA

  • ne-bit DPA

Closed-form Expression

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  • Introduced the success metric that is

derived from the theoretical success rate

  • Success metric coincide with the

empirical success rate

  • We are able to make predictions about

crossings that are not visible in the SR

  • Extended the idea of confusion
  • Derived a closed-form expression for the

success metric that is easier to compute

  • Explain the ranking of various

distinguishers

  • Determine the influence of the

leakage model

  • Sbox
  • Mask
  • nonlinear relationship

between X and Y*

  • Determine the influence of the

estimation

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Conclusion & Future Work

Future Work Conclusion

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Questions?

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