Bucketing and information flow analysis for provable timing attack mitigation

This paper investigates the effect of bucketing in security against timing-channel attacks. Bucketing is a technique proposed to mitigate timing-channel attacks by restricting a system's outputs to only occur at designated time intervals, and has the effect of reducing the possible timing-channel observations to a small number of possibilities. However, there is little formal analysis on when and to what degree bucketing is effective against timing-channel attacks. In this paper, we show that bucketing is in general insufficient to ensure security. Then, we present two conditions that can be used to ensure security of systems against adaptive timing-channel attacks. The first is a general condition that ensures that the security of a system decreases only by a limited degree by allowing timing-channel observations, whereas the second condition ensures that the system would satisfy the first condition when bucketing is applied and hence becomes secure against timing-channel attacks. A main benefit of the conditions is that they allow separation of concerns whereby the security of the regular channel can be proven independently of concerns of side-channel information leakage, and certain conditions are placed on the side channel to guarantee the security of the whole system. Further, we show that the bucketing technique can be applied compositionally in conjunction with the constant-time-implementation technique to increase their applicability. While we instantiate our contributions to timing channel and bucketing, many of the results are actually quite general and are applicable to any side channels and techniques that reduce the number of possible observations on the channel. It is interesting to note that our results make non-trivial (and somewhat unconventional) uses of ideas from information flow research such as channel capacity and refinement order relation.