On the exact relationship between the Mutual Information Metric and the Success Rate Metric

In real scenarios, in order to evaluate the physical leakage amount of a crypto device and the key recovery efficiency of a side channel attack, two metrics were proposed. On one hand, the mutual information (MI) metric was proposed to quantify the physical leakage amount of a crypto device. On the other hand, the success rate (SR) metric was proposed to quantify the key recovery efficiency of a side channel attack. Although it is usually assumed that the physical leakage amount of a crypto device influences the key recovery efficiency of an attack a lot, the exact relationship between the MI metric and the SR metric is not clear, and one does not have a quantitative knowledge about the influence of the physical leakage amount of a crypto device on the key recovery efficiency of an attack. In light of this, we analyze and give the exact relationship between the MI metric and the SR metric. Additionally, we do empirical evaluations to verify the soundness of the theoretical analysis. The merit of this work is that one can use the MI metric to understand both the physical leakage amount of a crypto device and the key recovery efficiency of a side channel attack, which can accordingly decrease the evaluation complexity and shorten the evaluation period.