Leakage Assessment Methodology - a clear roadmap for side-channel evaluations - Tobias Schneider and Amir Moradi Wednesday, September 16 th , 2015
Motivation Security Evaluation Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 2
Motivation Security Evaluation Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 3
Motivation Security Evaluation Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 4
Motivation Security Evaluation Does the chip leak information? Problem: Evaluation is not trivial. Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 5
Motivation Security Evaluation Does the chip leak information? Problem: Evaluation is not trivial. Non-Invasive Attack Testing Workshop, 2011 Goal: Establish testing methodology capable of robustly assessing the physical vulnerability of cryptographic devices. Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 6
Motivation Attack-based Testing Perform state-of-the-art attacks on the device under test (DUT) Attacks Intermediate Leakage Types: Values: Models: • DPA • Sbox In • HW × × • CPA • Sbox Out • HD • MIA • Sbox In/Out • Bit • … • … • … Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 7
Motivation Attack-based Testing Perform state-of-the-art attacks on the device under test (DUT) Attacks Intermediate Leakage Types: Values: Models: • DPA • Sbox In • HW × × • CPA • Sbox Out • HD • MIA • Sbox In/Out • Bit • … • … • … Problems: • High computational complexity • Requires lot of expertise • Does not cover all possible attack vectors Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 8
Motivation Testing based on t -Test 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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 9
Motivation Testing based on t -Test 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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 10
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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 11
Statistical Background • t -Test Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 12
Statistical Background t -Test Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 13
Statistical Background t -Test Sample 𝑅 0 Sample 𝑅 1 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 14
Statistical Background t -Test Sample 𝑅 0 Sample 𝑅 1 Null Hypothesis: Two population means are equal. Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 15
Statistical Background t -Test Sample 𝑅 0 Sample 𝑅 1 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 16
Statistical Background t -Test Sample 𝑅 0 Sample 𝑅 1 𝜈 1 𝜈 0 Sample mean: 2 2 𝑡 1 𝑡 0 Sample variance: 𝑜 1 𝑜 0 Sample size: Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 17
Statistical Background t -Test Sample 𝑅 0 Sample 𝑅 1 𝜈 1 𝜈 0 Sample mean: 2 2 𝑡 1 𝑡 0 Sample variance: 𝑜 1 𝑜 0 Sample size: 2 2 2 𝑜 0 + 𝑡 1 𝑡 0 𝑜 1 t = 𝜈 0 − 𝜈 1 v = 𝑢 -test statistic Degree of freedom 2 2 2 2 𝑡 0 𝑡 1 2 2 𝑜 0 + 𝑡 1 𝑡 0 𝑜 0 𝑜 1 𝑜 1 𝑜 0 − 1 + 𝑜 1 − 1 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 18
Statistical Background t -Test 𝑢 𝑤 Γ 𝑤 + 1 −𝑤+1 1 + 𝑢 2 2 Estimate the probability to accept null 2 𝑔 𝑢, 𝑤 = 𝜌𝑤 Γ 𝑤 hypothesis with Student’s 𝑢 distribution: 𝑤 2 ∞ 𝑞 = 2 𝑔 t, v 𝑒𝑢 Compute: |𝑢| Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 19
Statistical Background t -Test 𝑢 𝑤 Γ 𝑤 + 1 −𝑤+1 1 + 𝑢 2 2 Estimate the probability to accept null 2 𝑔 𝑢, 𝑤 = 𝜌𝑤 Γ 𝑤 hypothesis with Student’s 𝑢 distribution: 𝑤 2 ∞ 𝑞 = 2 𝑔 t, v 𝑒𝑢 Compute: |𝑢| Small 𝑞 values give evidence to reject the null hypothesis Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 20
Statistical Background t -Test 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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 21
Testing Methodology Specific 𝒖 -Test • • Non-Specific t -Test Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 22
Testing Methodology Specific t -Test Measurements 𝑈 𝑗 With Associated Data 𝐸 𝑗 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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 23
Testing Methodology Specific t -Test Measurements 𝑈 𝑗 𝑢𝑏𝑠𝑓𝑢 𝑐𝑗𝑢 𝐸 𝑗 = 0 With Associated Data 𝐸 𝑗 𝑅 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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 24
Testing Methodology Specific t -Test Measurements 𝑈 𝑗 𝑢𝑏𝑠𝑓𝑢 𝑐𝑗𝑢 𝐸 𝑗 = 0 𝑢𝑏𝑠𝑓𝑢 𝑐𝑗𝑢 𝐸 𝑗 = 1 With Associated Data 𝐸 𝑗 𝑅 0 𝑅 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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 25
Testing Methodology Non-Specific t -Test 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 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 26
Testing Methodology Non-Specific t -Test 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 Measurements 𝑈 𝑘 With Fixed Associated Data D 𝑅 0 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 27
Testing Methodology Non-Specific t -Test 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 Measurements 𝑈 Measurements 𝑈 𝑗 𝑘 With Random With Fixed Associated Data D 𝑗 Associated Data D 𝑅 0 𝑅 1 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 28
Higher-Order Testing • Multivariate • Univariate Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 29
Higher-Order Testing Multivariate Multivariate: Sensitive variable is shared: 𝑇 = 𝑇 1 ∘ 𝑇 2 Shares are processed at different time instances (SW) Leakages at different time instances need to be combined first Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 30
Higher-Order Testing Multivariate 𝑇 1 Multivariate: Sensitive variable is shared: 𝑇 = 𝑇 1 ∘ 𝑇 2 Shares are processed at different time instances (SW) Leakages at different time instances need to be combined first Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 31
Higher-Order Testing Multivariate 𝑇 1 𝑇 2 Multivariate: Sensitive variable is shared: 𝑇 = 𝑇 1 ∘ 𝑇 2 Shares are processed at different time instances (SW) Leakages at different time instances need to be combined first Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 32
Higher-Order Testing Multivariate 𝑇 1 𝑇 2 Multivariate: Sensitive variable is shared: 𝑇 = 𝑇 1 ∘ 𝑇 2 Shares are processed at different time instances (SW) Leakages at different time instances need to be combined first Centered Product: 𝑦′ = 𝑦 1 − 𝜈 1 ⋅ 𝑦 2 − 𝜈 2 Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 33
Higher-Order Testing Univariate 𝑇 1 𝑇 2 Univariate: Shares are processed in parallel (HW) Leakages at the same time instance need to be combined first Leakage Assessment Methodology | CHES 2015 | Tobias Schneider 34
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