In this paper, we take the fundamental perspective of fuzzing as a learning process. Suppose before fuzzing, we know nothing about the behaviors of a program $\mathcal{P}$: What does it do? Executing the first test input, we learn how $\mathcal{P}$ behaves for this input. Executing the next input, we either observe the same or discover a new behavior. As such, each execution reveals "some amount" of information about $\mathcal{P}$'s behaviors. A classic measure of information is Shannon's entropy. Measuring entropy allows us to quantify how much is learned from each generated test input about the behaviors of the program. Within a probabilistic model of fuzzing, we show how entropy also measures fuzzer efficiency. Specifically, it measures the general \emph{rate} at which the fuzzer discovers new behaviors. Intuitively, \emph{efficient fuzzers maximize information}.

From this information theoretic perspective, we develop Entropic, an entropy-based power schedule for greybox fuzzing which assigns more energy to seeds that maximize information. We implemented Entropic into the popular greybox fuzzer LibFuzzer. Our experiments with more than 250 open-source programs (60 \emph{million} LoC) demonstrate a substantially improved efficiency and \emph{confirm} our hypothesis that an efficient fuzzer maximizes information. Entropic has been independently evaluated and invited for integration into main-line LibFuzzer. Entropic now runs on more than 25,000 machines fuzzing hundreds of security-critical software systems simultaneously and continuously.