Leakage Detection with the χ²-Test

Amir Moradi, Bastian Richter, Tobias Schneider, François-Xavier Standaert

IACR Transactions on Cryptographic Hardware and Embedded Systems, Vol. 2018, No. 1, pp 209-237, 2018. (presentation at CHES 2018, Amsterdam, The Netherlands, September 9 – 12, 2018)


We describe how Pearson’s χ 2 -test can be used as a natural complement to Welch’s t -test for black box leakage detection. In particular, we show that by using these two tests in combination, we can mitigate some of the limitations due to the moment-based nature of existing detection techniques based on Welch’s t-test (e.g., for the evaluation of higher-order masked implementations with insufficient noise). We also show that Pearson’s χ²-test is naturally suited to analyze threshold implementations with information lying in multiple statistical moments, and can be easily extended to a distinguisher for key recovery attacks. As a result, we believe the proposed test and methodology are interesting complementary ingredients of the side-channel evaluation toolbox, for black box leakage detection and non-profiled attacks, and as a preliminary before more demanding advanced analyses.

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tags: leakage-detection, Side-Channel, t-test