The Levene test based-leakage assessment

The secret information is split into several parts(multivariate) in the high-order mask. The test vector leakage assessment (TVLA) relied on Welch's -test(T-test), the analysis of variance (ANOVA) and normalized inter-class variance (NICV) relied on Fisher-test(F-test) are preliminary assessment for univariate. It is necessary to combine several univariates when we perform the leakage detection on the high-order mask. We find that the combined traces are mostly the non-normal distribution. While T-test and F-test are applied to the normal distribution in statistics. In order to evaluate the effect of T-test, NICV, ANOVA on the non-normal distribution, we introduce a metric observed power () in statistics. And we find the are below the threshold 0.8, which indicates an unreliable result. To solve the problem, we propose the Levene-test based-leakage assessment (LTBLA) in this work. The LTBLA follows the same procedure as TVLA with Levene-test and add the identification of distribution in TVLA. There is the leakage if the P-value is below the threshold The experiments show that in order to obtain the P-value that is below the threshold, the number of traces are acquired by Levene-test, which is of ANOVA and of T-test. For the skewed distribution, the number of traces are needed, while the sample size of ANOVA is around. More surprisingly, the P-values of T-test is around , if the number of traces is . Because Hotelling's -test is the testing without combing for the multivariate. We also compare Levene-test with Hotelling's -test. For the normal traces, the number of traces are needed by Levene-test, while the sample size of Hotelling's -test is about . For the skewed distribution, the sample size of Levene-test is about less than Hotelling's -test. For the normal distribution, the small difference among the three tests in the sample size. For the skewed distribution the difference of sample size between Levene-test and T-test or ANOVA is more than two orders of magnitude. T-test and ANOVA have the risk of missed detection under the same sample complexity. LTBLA follows the same procedure as TVLA with Levene-test for the skewed distribution to avoid the unreliable results.