Estimating Residual Risk in Greybox Fuzzing

For any errorless fuzzing campaign, no matter how long, there is always some residual risk that a software error would be discovered if only the campaign was run for just a bit longer. Recently, greybox fuzzing tools have found widespread adoption. Yet, practitioners can only guess when the residual risk of a greybox fuzzing campaign falls below a specific, maximum allowable threshold. In this paper, we explain why residual risk cannot be directly estimated for greybox campaigns, argue that the discovery probability (i.e., the probability that the next generated input increases code coverage) provides an excellent upper bound, and explore sound statistical methods to estimate the discovery probability in an ongoing greybox campaign. We find that estimators for blackbox fuzzing systematically and substantially under-estimate the true risk. An engineer-who stops the campaign when the estimators purport a risk below the maximum allowable risk-is vastly misled. She might need execute a campaign that is orders of magnitude longer to achieve the allowable risk. Hence, the key challenge we address in this paper is adaptive bias: The probability to discover a specific error actually increases over time. We provide the first probabilistic analysis of adaptive bias, and introduce two novel classes of estimators that tackle adaptive bias. With our estimators, the engineer can decide with confidence when to abort the campaign.