String constraint solving refers to solving combinatorial problems involving constraints over string variables. String solving approaches have become popular over the last years given the massive use of strings in different application domains like formal analysis, automated testing, database query processing, and cybersecurity. This paper reports a comprehensive survey on string constraint solving by exploring the large number of approaches that have been proposed over the last decades to solve string constraints.

A Survey on String Constraint Solving.

SMT solvers are at the basis of many applications, such as program verification, program synthesis, and test case generation. For all these applications to provide reliable results, SMT solvers must answer queries correctly. However, since they are complex, highly-optimized software systems, ensuring their correctness is challenging. In particular, state-of-the-art testing techniques do not reliably detect when an SMT solver is unsound. In this paper, we present an automatic approach for generating test cases that reveal soundness errors in the implementations of string solvers, as well as potential completeness and performance issues. We synthesize input formulas that are satisfiable or unsatisfiable by construction and use this ground truth as test oracle. We automatically apply satisfiability-preserving transformations to generate increasingly-complex formulas, which allows us to detect many errors with simple inputs and, thus, facilitates debugging. The experimental evaluation shows that our technique effectively reveals bugs in the implementation of widely-used SMT solvers and applies also to other types of solvers, such as automata-based solvers. We focus on strings here, but our approach carries over to other theories and their combinations.

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Automatically testing string solvers

String-number conversion is an important class of constraints needed for the symbolic execution of string-manipulating programs. In particular solving string constraints with string-number conversion is necessary for the analysis of scripting languages such as JavaScript and Python, where string-number conversion is a part of the definition of the core semantics of these languages. However, solving this type of constraint is very challenging for the state-of-the-art solvers. We propose in this paper an approach that can efficiently support both string-number conversion and other common types of string constraints. Experimental results show that it significantly outperforms other state-of-the-art tools on benchmarks that involves string-number conversion.

Efficient handling of string-number conversion

Timing side channels arise in software when a program's execution time can be correlated with security-sensitive program input. Recent results on software side-channel detection focus on analysis of program's source code. However, runtime behavior, in particular optimizations introduced during just-in-time (JIT) compilation, can impact or even introduce timing side channels in programs. In this paper, we present a technique for automatically detecting such JIT-induced timing side channels in Java programs. We first introduce patterns to detect partitions of secret input potentially separable by side channels. Then we present an automated approach for exploring behaviors of the Java Virtual Machine (JVM) to identify states where timing channels separating these partitions arise. We evaluate our technique on three datasets used in recent work on side-channel detection. We find that many code variants labeled "safe" with respect to side-channel vulnerabilities are in fact vulnerable to JIT-induced timing side channels. Our results directly contradict the conclusions of four separate state-of-the-art program analysis tools for side-channel detection and demonstrate that JIT-induced side channels are prevalent and can be detected automatically.

https://dl.acm.org/doi/pdf/10.1145/3377811.3380432

JVM fuzzing for JIT-induced side-channel detection

Cryptosystems like AES and triple-DES are designed to encrypt a sequence of input bytes (the plaintext) into a sequence of output bytes (the ciphertext) in such a way that the output carries no information about that plaintext except its length. In recent years, concerns have been raised about ”side-channel” attacks on various cryptosystems—attacks that make use of some kind of leaked information about the cryptographic operations (e.g., power consumption or timing) to defeat them. In this paper, we describe a somewhat different kind of side-channel provided by data compression algorithms, yielding information about their inputs by the size of their outputs. The existence of some information about a compressor’s input in the size of its output is obvious; here, we discuss ways to use this apparently very small leak of information in surprisingly powerful ways.

Compression and information leakage of plaintext

Recently, symbolic program analysis techniques have been extended to quantitative analyses using model counting constraint solvers. Given a constraint and a bound, a model counting constraint solver computes the number of solutions for the constraint within the bound. We present a parameterized model counting constraint solver for string and numeric constraints. We first construct a multi-track deterministic finite state automaton that accepts all solutions to the given constraint. We limit the numeric constraints to linear integer arithmetic, and for non-regular string constraints we over-approximate the solution set. Counting the number of accepting paths in the generated automaton solves the model counting problem. Our approach is parameterized in the sense that, we do not assume a finite domain size during automata construction, resulting in a potentially infinite set of solutions, and our model counting approach works for arbitrarily large bounds. We experimentally demonstrate the effectiveness of our approach on a large set of string and numeric constraints extracted from software applications. We experimentally compare our tool to five existing model counting constraint solvers for string and numeric constraints and demonstrate that our tool is as efficient and as or more precise than other solvers. Moreover, our tool can handle mixed constraints with string and integer variables that no other tool can.

https://dl.acm.org/doi/pdf/10.1145/3236024.3236064

Parameterized model counting for string and numeric constraints

Quantitative program analysis is an emerging area with applications to software reliability, quantitative information flow, side-channel detection and attack synthesis. Most quantitative program analysis techniques rely on model counting constraint solvers, which are typically the bottleneck for scalability. Although the effectiveness of formula caching in expediting expensive model-counting queries has been demonstrated in prior work, our key insight is that many subformulas are shared across non-identical constraints generated during program analyses. This has not been utilized by prior formula caching approaches. In this paper we present a subformula caching framework and integrate it into a model counting constraint solver. We experimentally evaluate its effectiveness under three quantitative program analysis scenarios: 1) model counting constraints generated by symbolic execution, 2) reliability analysis using probabilistic symbolic execution, 3) adaptive attack synthesis for side-channels. Our experimental results demonstrate that our subformula caching approach significantly improves the performance of quantitative program analysis.

Subformula caching for model counting and quantitative program analysis

Information leakage is a signi cant problem in modern software systems. Information leaks due to side channels are especially hard to detect and analyze. In recent years, techniques have been developed for automated synthesis of adaptive side-channel attacks that recover secret values by iteratively generating inputs to reveal partial information about the secret based on the sidechannel observations. Prominent approaches of attack synthesis use symbolic execution, model counting, and meta-heuristics to maximize information gain. These approaches could bene t by reusing results from prior steps in each step. In this paper, we present an incremental approach to attack synthesis that reuses model counting results from prior iterations in each attack step to improve efficiency. Experimental evaluation demonstrates that our approach drastically improves performance, reducing the attack synthesis time by an order of magnitude.

Incremental Attack Synthesis

Information leaks are a significant problem in modern computer systems and string manipulation is prevalent in modern software. We present techniques for automated synthesis of side-channel attacks that recover secret string values based on timing observations on string manipulating code. Our attack synthesis techniques iteratively generate inputs which, when fed to code that accesses the secret, reveal partial information about the secret based on the timing observations, leading to recovery of the secret at the end of the attack sequence. We use symbolic execution to extract path constraints, automata-based model counting to estimate the probability of execution paths, and meta-heuristic methods to maximize information gain based on entropy for synthesizing adaptive attack steps.

William Eiers

Papers

Parameterized model counting for string and numeric constraints

Subformula caching for model counting and quantitative program analysis

Incremental Attack Synthesis

Attack Synthesis for Strings using Meta-Heuristics

Attack Synthesis for Strings using Meta-Heuristics