Information leakage through covert channels and side channels is becoming a serious problem, especially when these are enhanced by modern processor architecture features. We show how processor architecture features such as simultaneous multithreading, control speculation and shared caches can inadvertently accelerate such covert channels or enable new covert channels and side channels. We first illustrate the reality and severity of this problem by describing concrete attacks. We identify two new covert channels. We show orders of magnitude increases in covert channel capacities. We then present two solutions, Selective Partitioning and the novel Random Permutation Cache (RPCache). The RPCache can thwart most cache-based software side channel attacks, with minimal hardware costs and negligible performance impact.