Correlation Power Analysis. Chujiao Ma
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1 Correlation Power Analysis Chujiao Ma
2 Power Analysis Simple Power Analysis (SPA) different operations consume different power Differential Power Analysis (DPA) different data consume different power Correlation Power Analysis (CPA) more advanced than DPA there is correlation between data and power 2
3 Power Trace Power dissipation of operation is proportional to the hamming weight of the data. Brier et al. 2004
4 Correlation Strength of relationship between two variables. Correlation refers to the noisiness/variance and the direction Not concerned with the slope Only for linear relationships Perfect linear relationship (strong correlation): +/-1 No relationship (no correlation): 0
5 CPA Hamming weight model: Power dissipation of an operation at a specific time is proportional to the hamming weight of the processing data Correlation coefficient: The correlation coefficient indicates how two random variables (Power and Data) matches each other. 5
6 Correlation Analysis Pearson s coefficient obtained by dividing the covariance of the two variables by the product of their standard deviations. N = number of traces W = power traces H = Hamming distance Values between 1 and -1 (perfect linear correlation). No linear dependency produce value of 0.
7 Correlation Analysis Rank correlation coefficient extent to which, as one variable increases, the other variable increases/decreases, without being represented by a linear relationship. For data (x, y), if an increase in x is always accompanied by an increase in y, then it is a perfect rank correlation. If (x, y) are not in a straight line, Pearson coefficient may be much lower.
8 CPA Process Identify the target operation Select power model, target, selection function, a set of inputs Measurement/Data collection Setup for instrumentation Feed the selected inputs to the device Data analysis Signal processing For each value of the key related to the targeted state Generate the value of the targeted state from the guess Use the value and power traces to compute the correlation coefficient Find the max coefficient Evaluation
9 Attacking the S-Box (or Table Lookup) Plaintext Key xor Table Key xor If a plaintext byte is known, as well as a first-round table lookup, a key byte is learned Table Table Key xor Ciphertext The same is true for cipher text bytes and final round table lookups
10 Hamming Weight: DPA Ciphertext HW Power trace e6a636e30c85f35e980f3546a04daff e9f7a9d7d2387d7ee8c7c5235c354dd
11 Hamming Weight: CPA Ciphertext HW Power trace e6a636e30c85f35e980f3546a04daff7 3 e9f7a9d7d2387d7ee8c7c5235c354dd 5
12 Hamming Weight SubBytes S in (?) SBox 16 Sin(?) C(?) 0 no transition 1 yes transition ShiftRow S out DPA output: Key guess C(i:i+1) ShiftRow C(?) CPA output: sum( )
13 Correlation Analysis Given H (Hamming weight) and W (power traces), compute the correlation coefficient: N = number of traces Compute correlation coefficient for each key guess The key with max coefficient is the correct key
14 Correlation Curve The highest absolute value of ρ suggests the correct key guess 14 Brier et al. 2004
15 Key Guess Correlation 1 st round: sub-keys are 24, 19, 8, 8, 5, 50, 43, 2 Brier et al. 2004
16 CPA vs. DPA CPA Attack using relationship between data and power Looks at correlation between all key guesses DPA Attack using relationship between data and power Looks at difference of category averages for all key guess Faster, more accurate than DPA Slower and less efficient than CPA
17 CPA vs. DPA results CPA generally have less noise and require less traces to guess the correct key. Le et al. 2006
18 Countermeasures Desynchronize via operations, delay or other circuitry. Increase noise Random masking Counters to countermeasure: Signal processing Curve selection/statistical analysis Higher order DPA Mathematical security vs. computational security
19 Citation Eric Brier and Christophe Clavier and Francis Olivier. Correlation Power Analysis with a Leakage Model. Cryptographic Hardware and Embedded Systems - CHES 2004: 6th International Workshop Thanh-Ha Le and Jessy Clédière and Cécile Canovas and Bruno Robisson and Christine Servière and Jean-Louis Lacoume. A Proposition for Correlation Power Analysis Enhancement. Cryptographic Hardware and Embedded Systems - CHES Fan Zhang, Zhijie Jerry Shi. "Differential and Correlation Power Analysis Attacks on HMAC-Whirlpool. Eighth International Conference on Information Technology: New Generations,
20 Proj 4: CPA Loop through key guess and ciphertext/trace Find Hamming Weight Find Pearson s correlation coefficient Find max of the array of coefficient
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