[PPT] - Leakage Assessment Methodology - a clear roadmap for side-channel PowerPoint Presentation

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Leakage Assessment Methodology

a clear roadmap for side-channel evaluations -

Tobias Schneider and Amir Moradi Wednesday, September 16th, 2015

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Motivation Security Evaluation

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Motivation Security Evaluation

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Motivation Security Evaluation

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Motivation Security Evaluation

Problem: Evaluation is not trivial. Does the chip leak information?

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Motivation Security Evaluation

Problem: Evaluation is not trivial. Does the chip leak information? Non-Invasive Attack Testing Workshop, 2011 Establish testing methodology capable of robustly assessing the physical vulnerability of cryptographic devices. Goal:

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Perform state-of-the-art attacks on the device under test (DUT)

Attacks Types:

DPA
CPA
MIA
…

Intermediate Values:

Sbox In
Sbox Out
Sbox In/Out
…

Leakage Models:

HW
HD
Bit
…

× ×

Motivation Attack-based Testing

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Perform state-of-the-art attacks on the device under test (DUT)

Attacks Types:

DPA
CPA
MIA
…

Intermediate Values:

Sbox In
Sbox Out
Sbox In/Out
…

Leakage Models:

HW
HD
Bit
…

× ×

Problems:

High computational complexity
Requires lot of expertise
Does not cover all possible attack vectors

Motivation Attack-based Testing

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Tries to detect any type of leakage at a certain order

Proposed by CRI at NIST workshop

Advantages:

Independent of architecture
Independent of attack model
Fast & simple
Versatile

Motivation Testing based on t-Test

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Tries to detect any type of leakage at a certain order

Proposed by CRI at NIST workshop

Advantages:

Independent of architecture
Independent of attack model
Fast & simple
Versatile

Problems:

No information about hardness of attack
Possible false positives if no care about

evaluation setup

Motivation Testing based on t-Test

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Contribution

1. Explain statistical background in a (hopefully) more

understandable way

2. More detailed discussion of higher-order testing
3. Hints how to design fast & correct measurement setup
4. Optimization of analysis phase

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Statistical Background

t-Test

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Statistical Background t-Test

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Statistical Background t-Test

Sample 𝑅0 Sample 𝑅1

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Statistical Background t-Test

Sample 𝑅0 Sample 𝑅1

Null Hypothesis: Two population means are equal.

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Sample 𝑅0 Sample 𝑅1

Statistical Background t-Test

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Sample 𝑅0 Sample 𝑅1

Statistical Background t-Test

Sample mean: Sample variance: Sample size: 𝜈0 𝑡0

2

𝑜0 𝜈1 𝑡1

2

𝑜1

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Sample 𝑅0 Sample 𝑅1

Statistical Background t-Test

Sample mean: Sample variance: Sample size: 𝜈0 𝑡0

2

𝑜0 𝜈1 𝑡1

2

𝑜1

t = 𝜈0 − 𝜈1 𝑡0

2

𝑜0 + 𝑡1

2

𝑜1 v = 𝑡0

2

𝑜0 + 𝑡1

2

𝑜1

2

𝑡0

2

𝑜0

2

𝑜0 − 1 + 𝑡1

2

𝑜1

2

𝑜1 − 1

Degree of freedom 𝑢-test statistic

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Estimate the probability to accept null hypothesis with Student’s 𝑢 distribution:

𝑔 𝑢, 𝑤 = Γ 𝑤 + 1 2 𝜌𝑤 Γ 𝑤 2 1 + 𝑢2 𝑤

−𝑤+1 2

𝑞 = 2

|𝑢| ∞

𝑔 t, v 𝑒𝑢

Statistical Background t-Test

Compute:

𝑤 𝑢

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Estimate the probability to accept null hypothesis with Student’s 𝑢 distribution:

𝑔 𝑢, 𝑤 = Γ 𝑤 + 1 2 𝜌𝑤 Γ 𝑤 2 1 + 𝑢2 𝑤

−𝑤+1 2

𝑞 = 2

|𝑢| ∞

𝑔 t, v 𝑒𝑢

Statistical Background t-Test

Compute: Small 𝑞 values give evidence to reject the null hypothesis

𝑤 𝑢

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For testing usually only the 𝑢-value is estimated
Compared to a threshold of t > 4.5
𝑞 = 2𝐺 −4.5, 𝑤 > 1000 < 0.00001
Confidence of > 0.99999 to reject the null hypothesis

Statistical Background t-Test

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Testing Methodology

Specific 𝒖-Test
Non-Specific t-Test

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Measurements 𝑈𝑗 With Associated Data 𝐸𝑗

Testing Methodology Specific t-Test

Specific t-Test:

Key is known to enable correct partitioning
Test is conducted at each sample point separately (univariate)
If corresponding 𝑢-test exceeds threshold ⇒ DPA probable

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Measurements 𝑈𝑗 With Associated Data 𝐸𝑗

Testing Methodology Specific t-Test

𝑅0

𝑢𝑏𝑠𝑕𝑓𝑢 𝑐𝑗𝑢 𝐸𝑗 = 0

Specific t-Test:

Key is known to enable correct partitioning
Test is conducted at each sample point separately (univariate)
If corresponding 𝑢-test exceeds threshold ⇒ DPA probable

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Measurements 𝑈𝑗 With Associated Data 𝐸𝑗

Testing Methodology Specific t-Test

𝑅0

𝑢𝑏𝑠𝑕𝑓𝑢 𝑐𝑗𝑢 𝐸𝑗 = 0

𝑅1

𝑢𝑏𝑠𝑕𝑓𝑢 𝑐𝑗𝑢 𝐸𝑗 = 1

Specific t-Test:

Key is known to enable correct partitioning
Test is conducted at each sample point separately (univariate)
If corresponding 𝑢-test exceeds threshold ⇒ DPA probable

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Non-Specific t-Test:

fixed vs. random t-test
Avoids being dependent on any intermediate value/model
Detected leakage of single test is not always exploitable
Semi-fixed vs. random t-test useful in certain cases

Testing Methodology Non-Specific t-Test

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Non-Specific t-Test:

fixed vs. random t-test
Avoids being dependent on any intermediate value/model
Detected leakage of single test is not always exploitable
Semi-fixed vs. random t-test useful in certain cases

Testing Methodology Non-Specific t-Test

Measurements 𝑈

𝑘

With Fixed Associated Data D

𝑅0

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Non-Specific t-Test:

fixed vs. random t-test
Avoids being dependent on any intermediate value/model
Detected leakage of single test is not always exploitable
Semi-fixed vs. random t-test useful in certain cases

Testing Methodology Non-Specific t-Test

Measurements 𝑈

𝑘

With Fixed Associated Data D

𝑅0

Measurements 𝑈𝑗 With Random Associated Data D𝑗

𝑅1

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Higher-Order Testing

Multivariate
Univariate

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Higher-Order Testing Multivariate

Multivariate:

Sensitive variable is shared: 𝑇 = 𝑇1 ∘ 𝑇2
Shares are processed at different time instances (SW)
Leakages at different time instances need to be combined first

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Higher-Order Testing Multivariate

Multivariate:

Sensitive variable is shared: 𝑇 = 𝑇1 ∘ 𝑇2
Shares are processed at different time instances (SW)
Leakages at different time instances need to be combined first

𝑇1

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Higher-Order Testing Multivariate

Multivariate:

Sensitive variable is shared: 𝑇 = 𝑇1 ∘ 𝑇2
Shares are processed at different time instances (SW)
Leakages at different time instances need to be combined first

𝑇1 𝑇2

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Higher-Order Testing Multivariate

Multivariate:

Sensitive variable is shared: 𝑇 = 𝑇1 ∘ 𝑇2
Shares are processed at different time instances (SW)
Leakages at different time instances need to be combined first

𝑇1 𝑇2

Centered Product: 𝑦′ = 𝑦1 − 𝜈1 ⋅ 𝑦2 − 𝜈2

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Higher-Order Testing Univariate

Univariate:

Shares are processed in parallel (HW)
Leakages at the same time instance need to be combined first

𝑇1 𝑇2

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Higher-Order Testing Univariate

Univariate:

Shares are processed in parallel (HW)
Leakages at the same time instance need to be combined first

𝑇1 𝑇2

Variance: 𝑦′ = 𝑦 − 𝜈 2 In general: 𝑦′ = 𝑦 − 𝜈 𝑒 In some cases: 𝑦′ =

𝑦−𝜈 𝑡 𝑒

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Correct Measurement

Setup
Case Study: Microcontroller
Case Study: FPGA

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Correct Measurement Setup

PC Oscilloscope Control Target

…

Plaintext Ciphertext Measure Trigger

Pitfalls:

Order of fixed and random inputs should

be random as well

Communication between Control and

Target should be masked (if possible)

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Correct Measurement Setup

PC Oscilloscope Control Target

…

Plaintext Ciphertext Measure Trigger

Pitfalls:

Order of fixed and random inputs should

be random as well

Communication between Control and

Target should be masked (if possible)

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Correct Measurement CS: Microcontroller

AES with masking & shuffling (DPA contest v4.2)
No shared communication
First-order test

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Correct Measurement CS: Microcontroller

AES with masking & shuffling (DPA contest v4.2)
No shared communication
First-order test
Leakage associated to unmasked plaintext

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Correct Measurement CS: Microcontroller

Detectable first order leakage

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Correct Measurement CS: FPGA

A note on the security of Higher-Order Threshold Implementations Oscar Reparaz, ePrint Report 2015/001

First Order Second Order

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Correct Measurement CS: FPGA

A note on the security of Higher-Order Threshold Implementations Oscar Reparaz, ePrint Report 2015/001

First Order Second Order

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Correct Measurement CS: FPGA

A note on the security of Higher-Order Threshold Implementations Oscar Reparaz, ePrint Report 2015/001

First Order Second Order Fifth Order Second Order (bivariate)

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Efficient Computation

Classical Approach
Incremental
Multivariate
Parallelization

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Efficient Computation Classical Approach

Measurement Phase 𝑈 Time

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Leakage Assessment Methodology | CHES 2015 | Tobias Schneider

Efficient Computation Classical Approach

Measurement Phase 𝑈

1

𝑈 Time

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Efficient Computation Classical Approach

Measurement Phase 𝑈

𝑜−1

… 𝑈

2

𝑈

1

𝑈 Time

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Efficient Computation Classical Approach

Measurement Phase Analysis Phase 𝑈

𝑜−1

… 𝑈

2

𝑈

1

𝑈 Time t-Test

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Efficient Computation Classical Approach

Measurement Phase Analysis Phase 𝑈

𝑜−1

… 𝑈

2

𝑈

1

𝑈 Time t-Test Result

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Efficient Computation Classical Approach

t = 𝜈0 − 𝜈1 𝑡0

2

𝑜0 + 𝑡1

2

𝑜1 𝜈1, 𝑡1

2

𝜈0, 𝑡0

2

Requires estimation of: Reminder:

𝜈 = 𝐹 𝑈
𝑡2 = 𝐹

𝑈 − 𝜈 2

t-Test

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Efficient Computation Classical Approach

t = 𝜈0 − 𝜈1 𝑡0

2

𝑜0 + 𝑡1

2

𝑜1 𝜈1, 𝑡1

2

𝜈0, 𝑡0

2

Requires estimation of: Reminder:

𝜈 = 𝐹 𝑈
𝑡2 = 𝐹

𝑈 − 𝜈 2

𝑈

𝑜−1

… 𝑈

1

𝑈 t-Test

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Efficient Computation Classical Approach

t = 𝜈0 − 𝜈1 𝑡0

2

𝑜0 + 𝑡1

2

𝑜1 𝜈1, 𝑡1

2

𝜈0, 𝑡0

2

Requires estimation of: Reminder:

𝜈 = 𝐹 𝑈
𝑡2 = 𝐹

𝑈 − 𝜈 2

𝑈

𝑜−1

… 𝑈

1

𝑈 t-Test Pass 1

𝜈 = 𝐹 𝑈

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Efficient Computation Classical Approach

t = 𝜈0 − 𝜈1 𝑡0

2

𝑜0 + 𝑡1

2

𝑜1 𝜈1, 𝑡1

2

𝜈0, 𝑡0

2

Requires estimation of: Reminder:

𝜈 = 𝐹 𝑈
𝑡2 = 𝐹

𝑈 − 𝜈 2

𝑈

𝑜−1

… 𝑈

1

𝑈 t-Test Pass 1

𝜈 = 𝐹 𝑈

Pass 2

𝑡2 = 𝐹 𝑈 − 𝜈 2

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Efficient Computation Classical Approach

t = 𝜈0 − 𝜈1 𝑡0

2

𝑜0 + 𝑡1

2

𝑜1 𝜈1, 𝑡1

2

𝜈0, 𝑡0

2

Requires estimation of: Reminder:

𝜈 = 𝐹 𝑈
𝑡2 = 𝐹

𝑈 − 𝜈 2

𝑈

𝑜−1

… 𝑈

1

𝑈 t-Test Pass 1

𝜈 = 𝐹 𝑈

Pass 2

𝑡2 = 𝐹 𝑈 − 𝜈 2

Pass 3

Required for certain higher-order tests

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Efficient Computation Classical Approach

Problems:

1) Measurement phase need to be completed 2) All measurements need to be stored 3) Traces need to be loaded multiple times

Solution: Incremental Computation

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Efficient Computation Incremental

Idea: Update intermediate values for each new trace

𝑈

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Efficient Computation Incremental

Idea: Update intermediate values for each new trace

𝑈 𝜈, 𝑡2

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Efficient Computation Incremental

Idea: Update intermediate values for each new trace

𝑈 𝜈, 𝑡2 𝑈

1

𝜈, 𝑡2

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Efficient Computation Incremental

Idea: Update intermediate values for each new trace

𝑈 𝜈, 𝑡2 𝑈

1

𝜈, 𝑡2 … 𝜈, 𝑡2 𝑈

𝑜−1

𝜈, 𝑡2

Higher-order tests require the computation of additional values

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Efficient Computation Incremental

Idea: Update intermediate values for each new trace

𝑈 𝜈, 𝑡2 𝑈

1

𝜈, 𝑡2 … 𝜈, 𝑡2 𝑈

𝑜−1

𝜈, 𝑡2

Advantages:

1) Can be run in parallel to measurement phase 2) Does not require that all measurements are stored 3) Loads each trace only once

Higher-order tests require the computation of additional values

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Efficient Computation Incremental

Problem: Computation of intermediate values

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Efficient Computation Incremental

Problem: Computation of intermediate values Approach 1: Use raw moments dth-order raw moment: 𝑁𝑒 = 𝐹 𝑈𝑒 Given: 𝑁1 𝑁2 𝜈 = 𝑁1 𝑡2 = 𝑁2 − 𝑁1 2 Compute:

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Efficient Computation Incremental

Problem: Computation of intermediate values Approach 1: Use raw moments dth-order raw moment: 𝑁𝑒 = 𝐹 𝑈𝑒 Given: 𝑁1 𝑁2 𝜈 = 𝑁1 𝑡2 = 𝑁2 − 𝑁1 2 Compute: Higher-order test require additional moments Example: Univariate 1st-5th order tests require 𝑁1 − 𝑁10

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Efficient Computation Incremental

𝑈 𝑁1 − 𝑁10 𝑈

1

… 𝑈

𝑜−1

𝑁1 − 𝑁10 𝑁1 − 𝑁10 𝑁1 − 𝑁10

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Efficient Computation Incremental

𝑈 𝑁1 − 𝑁10 𝑈

1

… 𝑈

𝑜−1

𝑁1 − 𝑁10 𝑁1 − 𝑁10 𝑁1 − 𝑁10 t-Test Result

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Efficient Computation Incremental

𝑈 𝑁1 − 𝑁10 𝑈

1

… 𝑈

𝑜−1

𝑁1 − 𝑁10 𝑁1 − 𝑁10 𝑁1 − 𝑁10 t-Test Result t-Test Result

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Efficient Computation Incremental

𝑈 𝑁1 − 𝑁10 𝑈

1

… 𝑈

𝑜−1

𝑁1 − 𝑁10 𝑁1 − 𝑁10 𝑁1 − 𝑁10 t-Test Result

Easy to find update formulas for: 𝑁𝑒 =

𝑗=0 𝑜−1 𝑈𝑗 𝑒

𝑜 Problem: Numerical unstable for large number of traces

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Efficient Computation Incremental

𝑈 𝑁1 − 𝑁10 𝑈

1

… 𝑈

𝑜−1

𝑁1 − 𝑁10 𝑁1 − 𝑁10 𝑁1 − 𝑁10 t-Test Result

Easy to find update formulas for: 𝑁𝑒 =

𝑗=0 𝑜−1 𝑈𝑗 𝑒

𝑜 Problem: Numerical unstable for large number of traces

Method Order 1 Order 2 Order 3 Order 4 Order 5 3-Pass 25.08399 1258.18874 15.00039 96.08342 947.25523 Raw 25.08399 1258.14132 14.49282

1160.83799
1939218.83401

Example: Computation of variance based on simulations (100M traces ) with 𝒪 100,25

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Efficient Computation Incremental

Approach 2: Use central moments (and 𝑁1) dth-order central moment: 𝐷𝑁𝑒 = 𝐹 (𝑈 − 𝜈)𝑒 Given: 𝑁1 C𝑁2 𝜈 = 𝑁1 𝑡2 = 𝐷𝑁2 Compute:

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Efficient Computation Incremental

Approach 2: Use central moments (and 𝑁1) dth-order central moment: 𝐷𝑁𝑒 = 𝐹 (𝑈 − 𝜈)𝑒 Given: 𝑁1 C𝑁2 𝜈 = 𝑁1 𝑡2 = 𝐷𝑁2 Compute: Not that easy to find update formulas for: 𝐷𝑁𝑒 =

𝑗=0 𝑜−1 𝑈𝑗 − 𝜈 𝑒

𝑜 Multivariate tests require adjusted formulas

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Comparison to the raw moments approach:

Slightly higher computational effort
Less numerical problems, higher accuracy

Efficient Computation Incremental

Method Order 1 Order 2 Order 3 Order 4 Order 5 3-Pass 25.08399 1258.18874 15.00039 96.08342 947.25523 Raw 25.08399 1258.14132 14.49282

1160.83799
1939218.83401

Ours 25.08399 1258.18874 15.00039 96.08342 947.25523

Incremental formulas for tests at arbitrary orders can be found in the paper.

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𝑢𝑜,0 𝑢𝑜,1 𝑢𝑜,2 𝑢𝑜,3 𝑢𝑜,4

Trace n

Efficient Computation Parallelization

𝑢𝑜+1,0 𝑢𝑜+1,1 𝑢𝑜+1,2 𝑢𝑜+1,3 𝑢𝑜+1,4

Trace n+1

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𝑢𝑜,0 𝑢𝑜,1 𝑢𝑜,2 𝑢𝑜,3 𝑢𝑜,4

Trace n

Thread Thread 1 Thread 2 Thread 3 Thread 4

Efficient Computation Parallelization

𝑢𝑜+1,0 𝑢𝑜+1,1 𝑢𝑜+1,2 𝑢𝑜+1,3 𝑢𝑜+1,4

Trace n+1

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𝑢𝑜,0 𝑢𝑜,1 𝑢𝑜,2 𝑢𝑜,3 𝑢𝑜,4

Trace n

Thread Thread 1 Thread 2 Thread 3 Thread 4

Efficient Computation Parallelization

𝑢𝑜+1,0 𝑢𝑜+1,1 𝑢𝑜+1,2 𝑢𝑜+1,3 𝑢𝑜+1,4

Trace n+1

𝑢𝑜,0 𝑢𝑜,1 𝑢𝑜,2 𝑢𝑜,3 𝑢𝑜,4

Trace n

Thread

𝑢𝑜+1,0 𝑢𝑜+1,1 𝑢𝑜+1,2 𝑢𝑜+1,3 𝑢𝑜+1,4

Trace n+1

Thread 1

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Efficient Computation Parallelization

𝑢𝑜,0 𝑢𝑜,1 𝑢𝑜,2 𝑢𝑜,3 𝑢𝑜,4

Trace n

Thread

𝑢𝑜+1,0 𝑢𝑜+1,1 𝑢𝑜+1,2 𝑢𝑜+1,3 𝑢𝑜+1,4

Trace n+1

Thread 1 Thread 2 Thread 3

Example:

1st-5th order t-test
100,000,000 traces (each with 3,000 sample points)
9h on 2 x Intel Xeon X5670 CPUs @ 2.93 GHz (24 hyper-threading cores)

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Conclusion

Recommendations
Summary
Future Work

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Conclusion Recommendations

Fixed vs. random:

DUT with masking countermeasure
With masked communication

Semi-fixed vs. random:

DUT with hiding countermeasure
Without masked communication

Specific t-test:

DUT with no countermeasures
Failed in former non-specific tests
Identify suitable intermediate values for key recovery

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Testing based on the t-test is simple and fast
Has become popular in recent years

Things to consider:

Correct measurement phase is critical
Analysis phase can be strongly optimized
Higher-order testing easily possible

Additional important aspects:

Alignment and signal processing is necessary
Finding of points of interest

Conclusion Summary

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Incremental computing for other attacks/evaluation techniques

Conclusion Future Work

Robust and One-Pass Parallel Computation of Correlation-Based Attacks at Arbitrary Order Tobias Schneider, Amir Moradi, Tim Güneysu, ePrint Report 2015/571

MCP-DPA MCC-DPA CPA

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