No abstract

A side channel attack is a means of security attacks that tries to restore secret information by analyzing side-information such as electromagnetic wave, heat, electric energy and running time that are unintentionally emitted from a computer system. The side channel attack that focuses on the running time of a cryptosystem is specifically named a "timing attack". Timing attacks are relatively easy to carry out, and particularly threatening for tiny systems that are used in smart cards and IoT devices because the system is so simple that the processing time would be clearly observed from the outside of the card/device. 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.