### 2.15. Statistical Methods

Many attacks on cryptosystems involve statistical analysis of ciphertexts and also of data collected from the victim’s machine during one or more private-key operations. For a proper understanding of these analysis techniques, one requires some knowledge of statistics and random variables. In this section, we provide a quick overview of some statistical gadgets. We make the assumption that the reader is already familiar with the elementary notion of probability. We denote the probability of an event E by Pr(E).

#### 2.15.1. Random Variables and Their Probability Distributions

An experiment whose outcome is random is referred to as a random experiment. The set of all possible outcomes of a random experiment is called the ...