In an algorithmic complexity attack, a malicious party takes advantage of the worst-case behavior of an algorithm to cause denial-of-service. A prominent algorithmic complexity attack is regular expression denial-of-service (ReDoS), in which the attacker exploits a vulnerable regular expression by providing a carefully-crafted input string that triggers worst-case behavior of the matching algorithm. This paper proposes a technique for automatically finding ReDoS vulnerabilities in programs. Specifically, our approach automatically identifies vulnerable regular expressions in the program and determines whether an "evil" input string can be matched against a vulnerable regular expression. We have implemented our proposed approach in a tool called REXPLOITER and found 41 exploitable security vulnerabilities in Java web applications.