# Coverage-based Greybox Fuzzing as Markov chain

Marcel Böhme, Van Thuan Pham, Abhik Roychoudhury

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)

### Abstract

Coverage-based Greybox Fuzzing (CGF) is a random testing approach that requires no program analysis. A new test is generated by slightly mutating a seed input. If the test exercises a new and interesting path, it is added to the set of seeds; otherwise, it is discarded. We observe that most tests exercise the same few "high-frequency" paths and develop strategies to explore significantly more paths with the same number of tests by gravitating towards low-frequency paths. We explain the challenges and opportunities of CGF using a Markov chain model which specifies the probability that fuzzing the seed that exercises path <formula><tex>$i$</tex></formula> generates an input that exercises path <formula><tex>$j$</tex></formula>. Each state (i.e., seed) has an energy that specifies the number of inputs to be generated from that seed. We show that CGF is considerably more efficient if energy is inversely proportional to the density of the stationary distribution and increases monotonically every time that seed is chosen. Energy is controlled with a power schedule. We implemented several schedules by extending AFL. In 24 hours, AFLFast exposes 3 previously unreported CVEs that are not exposed by AFL and exposes 6 previously unreported CVEs <formula><tex>$7 \times$</tex></formula> faster than AFL. AFLFast produces at least an order of magnitude more unique crashes than AFL. We compared AFLFast to the symbolic executor Klee. In terms of vulnerability detection, AFLFast is significantly more effective than Klee on the same subject programs that were discussed in the original Klee paper. In terms of code coverage, AFLFast only slightly outperforms Klee while a combination of both tools achieves best results by mitigating the individual weaknesses.

Original language English 489-506 18 IEEE Transactions on Software Engineering 45 5 https://doi.org/10.1109/TSE.2017.2785841 Published - May 2019 Yes

### Keywords

• automated testing
• fuzzing
• path exploration
• symbolic execution
• vulnerability detection