Vijay Ganesh

A decision procedure for bit-vectors and arrays

STP is a decision procedure for the satisfiability of quantifier-free formulas in the theory of bit-vectors and arrays that has been optimized for large problems encountered in software analysis applications. The basic architecture of the procedure consists of word-level pre-processing algorithms followed by translation to SAT. The primary bottlenecks in software verification and bug finding applications are large arrays and linear bit-vector arithmetic. New algorithms based on the abstraction-refinement paradigm are presented for reasoning about large arrays. A solver for bit-vector linear arithmetic is presented that eliminates variables and parts of variables to enable other transformations, and reduce the size of the problem that is eventually received by the SAT solver. These and other algorithms have been implemented in STP, which has been heavily tested over thousands of examples obtained from several real-world applications. Experimental results indicate that the above mix of algorithms along with the overall architecture is far more effective, for a variety of applications, than a direct translation of the original formula to SAT or other comparable decision procedures.

EXPRESSION: a language for architecture exploration through compiler/simulator retargetability

We describe EXPRESSION, a language supporting architectural design space exploration for embedded systems-on-chip (SOC) and automatic generation of a retargetable compiler/simulator toolkit. Key features of our language-driven design methodology include: a mixed behavioral/structural representation supporting a natural specification of the architecture, explicit specification of the memory, subsystem allowing novel memory organizations and hierarchies; clean syntax and ease of modification supporting architectural exploration; a single specification supporting consistency and completeness checking of the architecture; and efficient specification of architectural resource constraints allowing extraction of detailed reservation tables for compiler scheduling. We illustrate key features of EXPRESSION through simple examples and demonstrate its efficacy in supporting exploration and automatic software toolkit generation for an embedded SOC codesign flow.

HAMPI: a solver for string constraints

Many automatic testing, analysis, and verification techniques for programs can be effectively reduced to a constraint generation phase followed by a constraint-solving phase. This separation of concerns often leads to more effective and maintainable tools. The increasing efficiency of off-the-shelf constraint solvers makes this approach even more compelling. However, there are few effective and sufficiently expressive off-the-shelf solvers for string constraints generated by analysis techniques for string-manipulating programs. We designed and implemented Hampi, a solver for string constraints over fixed-size string variables. Hampi constraints express membership in regular languages and fixed-size context-free languages. Hampi constraints may contain context-free-language definitions, regular language definitions and operations, and the membership predicate. Given a set of constraints, Hampi outputs a string that satisfies all the constraints, or reports that the constraints are unsatisfiable. Hampi is expressive and efficient, and can be successfully applied to testing and analysis of real programs. Our experiments use Hampi in: static and dynamic analyses for finding SQL injection vulnerabilities in Web applications; automated bug finding in C programs using systematic testing; and compare Hampi with another string solver. Hampis source code, documentation, and the experimental data are available at http://people.csail.mit.edu/akiezun/hampi.

EXE: Automatically Generating Inputs of Death

This article presents EXE, an effective bug-finding tool that automatically generates inputs that crash real code. Instead of running code on manually or randomly constructed input, EXE runs it on symbolic input initially allowed to be anything. As checked code runs, EXE tracks the constraints on each symbolic (i.e., input-derived) memory location. If a statement uses a symbolic value, EXE does not run it, but instead adds it as an input-constraint; all other statements run as usual. If code conditionally checks a symbolic expression, EXE forks execution, constraining the expression to be true on the true branch and false on the other. Because EXE reasons about all possible values on a path, it has much more power than a traditional runtime tool: (1) it can force execution down any feasible program path and (2) at dangerous operations (e.g., a pointer dereference), it detects if the current path constraints allow any value that causes a bug. When a path terminates or hits a bug, EXE automatically generates a test case by solving the current path constraints to find concrete values using its own co-designed constraint solver, STP. Because EXE’s constraints have no approximations, feeding this concrete input to an uninstrumented version of the checked code will cause it to follow the same path and hit the same bug (assuming deterministic code). EXE works well on real code, finding bugs along with inputs that trigger them in: the BSD and Linux packet filter implementations, the dhcpd DHCP server, the pcre regular expression library, and three Linux file systems.

Taint-based directed whitebox fuzzing

We present a new automated white box fuzzing technique and a tool, BuzzFuzz, that implements this technique. Unlike standard fuzzing techniques, which randomly change parts of the input file with little or no information about the underlying syntactic structure of the file, BuzzFuzz uses dynamic taint tracing to automatically locate regions of original seed input files that influence values used at key program attack points (points where the program may contain an error). BuzzFuzz then automatically generates new fuzzed test input files by fuzzing these identified regions of the original seed input files. Because these new test files typically preserve the underlying syntactic structure of the original seed input files, they tend to make it past the initial input parsing components to exercise code deep within the semantic core of the computation. We have used BuzzFuzz to automatically find errors in two open-source applications: Swfdec (an Adobe Flash player) and MuPDF (a PDF viewer). Our results indicate that our new directed fuzzing technique can effectively expose errors located deep within large programs. Because the directed fuzzing technique uses taint to automatically discover and exploit information about the input file format, it is especially appropriate for testing programs that have complex, highly structured input file formats.

Z3-str: a z3-based string solver for web application analysis

Analyzing web applications requires reasoning about strings and non-strings cohesively. Existing string solvers either ignore non-string program behavior or support limited set of string operations. In this paper, we develop a general purpose string solver, called Z3-str, as an extension of the Z3 SMT solver through its plug-in interface. Z3-str treats strings as a primitive type, thus avoiding the inherent limitations observed in many existing solvers that encode strings in terms of other primitives. The logic of the plug-in has three sorts, namely, bool, int and string. The string-sorted terms include string constants and variables of arbitrary length, with functions such as concatenation, sub-string, and replace. The int-sorted terms are standard, with the exception of the length function over string terms. The atomic formulas are equations over string terms, and (in)-equalities over integer terms. Not only does our solver have features that enable whole program symbolic, static and dynamic analysis, but also it performs better than other solvers in our experiments. The application of Z3-str in remote code execution detection shows that its support of a wide spectrum of string operations is key to reducing false positives.

Automatic error finding in access-control policies

Verifying that access-control systems maintain desired security properties is recognized as an important problem in security. Enterprise access-control systems have grown to protect tens of thousands of resources, and there is a need for verification to scale commensurately. We present a new abstraction-refinement technique for automatically finding errors in Administrative Role-Based Access Control (ARBAC) security policies. ARBAC is the first and most comprehensive administrative scheme for Role-Based Access Control (RBAC) systems. Underlying our approach is a change in mindset: we propose that error finding complements verification, can be more scalable, and allows for the use of a wider variety of techniques. In our approach, we use an abstraction-refinement technique to first identify and discard roles that are unlikely to be relevant to the verification question (the abstraction step), and then restore such abstracted roles incrementally (the refinement steps). Errors are one-sided: if there is an error in the abstracted policy, then there is an error in the original policy. If there is an error in a policy whose role-dependency graph diameter is smaller than a certain bound, then we find the error. Our abstraction-refinement technique complements conventional state-space exploration techniques such as model checking. We have implemented our technique in an access-control policy analysis tool. We show empirically that our tool scales well to realistic policies, and is orders of magnitude faster than prior tools.

Word equations with length constraints: what's decidable?

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality over string terms (word equations), linear inequality over the length function (length constraints), and membership in regular sets. These questions are important in logic, program analysis, and formal verification. Variants of these questions have been studied for many decades by mathematicians. More recently, practical satisfiability procedures (aka SMT solvers) for these formulas have become increasingly important in the context of security analysis for string-manipulating programs such as web applications. We prove three main theorems. First, we give a new proof of undecidability for the validity problem for the set of sentences written as a ∀∃ quantifier alternation applied to positive word equations. A corollary of this undecidability result is that this set is undecidable even with sentences with at most two occurrences of a string variable. Second, we consider Boolean combinations of quantifier-free formulas constructed out of word equations and length constraints. We show that if word equations can be converted to a solved form, a form relevant in practice, then the satisfiability problem for Boolean combinations of word equations and length constraints is decidable. Third, we show that the satisfiability problem for quantifier-free formulas over word equations in regular solved form, length constraints, and the membership predicate over regular expressions is also decidable.

HAMPI: a string solver for testing, analysis and vulnerability detection

Many automatic testing, analysis, and verification techniques for programs can effectively be reduced to a constraint-generation phase followed by a constraint-solving phase. This separation of concerns often leads to more effective and maintainable software reliability tools. The increasing efficiency of offthe-shelf constraint solvers makes this approach even more compelling. However, there are few effective and sufficiently expressive off-the-shelf solvers for string constraints generated by analysis of string-manipulating programs, and hence researchers end up implementing their own ad-hoc solvers. Thus, there is a clear need for an effective and expressive string-constraint solver that can be easily integrated into a variety of applications. To fulfill this need, we designed and implemented Hampi, an efficient and easy-to-use string solver. Users of the Hampi string solver specify constraints using membership predicate over regular expressions, context-free grammars, and equality/dis-equality between string terms. These terms are constructed out of string constants, bounded string variables, and typical string operations such as concatenation and substring extraction. Hampi takes such a constraint as input and decides whether it is satisfiable or not. If an input constraint is satisfiable, Hampi generates a satsfying assignment for the string variables that occur in it. We demonstrate Hampis expressiveness and efficiency by applying it to program analysis and automated testing: We used Hampi in static and dynamic analyses for finding SQL injection vulnerabilities in Web applications with hundreds of thousands of lines of code.We also used Hampi in the context of automated bug finding in C programs using dynamic systematic testing (also known as concolic testing). Hampis source code, documentation, and experimental data are available at http://people.csail.mit.edu/akiezun/hampi

An online proof-producing decision procedure for mixed-integer linear arithmetic

Efficient decision procedures for arithmetic play a very important role in formal verification. In practical examples, however, arithmetic constraints are often mixed with constraints from other theories like the theory of arrays, Boolean satisfiability (SAT), bit-vectors, etc. Therefore, decision procedures for arithmetic are especially useful in combination with other decision procedures. The framework for such a combination is implemented at Stanford in the tool called Cooperating Validity Checker (CVC) [SBD02]. This work augments CVC with a decision procedure for the theory of mixed integer linear arithmetic based on the Omega-test [Pug91] extended to be online and proof producing. These extensions are the most important and challenging part of the work, and are necessary to make the combination efficient in practice.