Theoretical Estimation on the Success Rate of the Asymptotic Higher Order Optimal Distinguisher

Since its first publication at ASIACRYPT 2014, higher order optimal distinguisher (HOOD) has been the most efficient style of higher order side channel attacks that can be used to evaluate the physical security of a masking device. In practice, the efficiency of HOOD can be empirically evaluated with the success rate (SR) metric. In the empirical evaluation, a large number of power traces are needed, and HOOD should be repeated thousands of times under the values of different parameters, which can make the evaluation process cumbersome and the evaluation price high. In light of this, the exact relationship between the SR of the asymptotic HOOD and the values of different parameters is theoretically built, and the soundness of the theoretical analysis is empirically verified in both the simulated scenario and the real scenario. Then, by setting the values of different parameters, the SR of the asymptotic HOOD can be theoretically estimated. Here, as the signal-to-noise ratio of a masking device approaches to zero, the SR of the asymptotic HOOD approaches to the SR of HOOD. Overall, this contribution may help evaluators to efficiently evaluate the physical security of a masking device with HOOD.