On Simple Linear String Equations

This paper presents a novel backward constraint solving technique for analyzing text processing programs. String constraints are represented using a variation of word equation called Simple Linear String Equation (SLSE). SLSE supports precise modeling of various regular string substitution semantics in Java regex, which allows it to capture user input validation operations widely used in web applications. On the other hand, SLSE is more restrictive than a word equation in that the location where a variable can occur is restricted. We present the theory of SLSE, and a recursive algorithm that can compute the solution pool of an SLSE. Given the solution pool, any concrete variable solution can be generated. The algorithm is implemented in a Java library called SUSHI. SUSHI can be applied to vulnerability analysis and compatibility checking. In practice, it generates command injection attack strings with very few false positives.