Information theoretical evaluation of the bucketing technique to mitigate timing attacks

Timing attack are regarded as serious threats to many practical security mechanisms. However, it is difficult to estimate the risk of attack because we cannot predict the ability and the behavior of attackers. To tackle this issue, Köpf et al. focus on the mutual information between a secret key and timing observations that an attacker acquires. Any attacker cannot learn more information than the mutual information, and the discussion of this approach gives a certain upperbound on the risk of timing attacks. Köpf et al. adopted this approach to evaluate the contribution of a bucketing technique that was proposed by themselves. However, the mathematical discussion therein needs more improvement. The purpose of this study is to refine the discussion of Köpf, and give more precise understanding of the contribution of the bucketing technique.