Information leakage through passive timing attacks on RSA decryption system

The threat of timing attacks is especially serious when an attacker actively controls the input to a target program. Countermeasures are studied to deter such active attacks, but the attacker still has the chance to learn something about the concealed information by passively watching the running time of the target program. The risk of passive timing attacks can be measured by the mutual information between the concealed information and the running time. However, the computation of the mutual information is hardly possible except for toy examples. This study focuses on three algorithms for RSA decryption, derives formulas of the mutual information under several assumptions and approximations, and calculates the mutual information numerically for practical security parameters.