Abu?erover?owoccurswheninputiswrittenintoamemorybu?erthatisnot large enough to hold the input. Bu?er over?ows may allow a malicious person to gain control over a computer system in that a crafted input can trick the defectiveprogramintoexecutingcodethatisencodedintheinputitself.They are recognised as one of the most widespread forms of security vulnerability, and many workarounds, including new processor features, have been proposed to contain the threat. This book describes a static analysis that aims to prove the absence of bu?er over?ows in C programs. The analysis is conservative in the sense that it locates every possible over?ow. Furthermore, it is fully automatic in that it requires no user annotations in the input program. Thekeyideaoftheanalysisistoinferasymbolicstateforeachp- gram point that describes the possible variable valuations that can arise at that point. The program is correct if the inferred values for array indices and pointer o?sets lie within the bounds of the accessed bu?er. The symbolic state consists of a ?nite set of linear inequalities whose feasible points induce a convex polyhedron that represents an approximation to possible variable valuations. The book formally describes how program operations are mapped to operations on polyhedra and details how to limit the analysis to those p- tionsofstructuresandarraysthatarerelevantforveri?cation.Withrespectto operations on string bu?ers, we demonstrate how to analyse C strings whose length is determined by anul character within the string.

InhaltsangabeIntroduction.- Technical Background.- Value Range Analysis.- Analysing C.- Soundness.- An abstraction of C.- Combining Value and Content Abstraction.- Combining Pointer and Value-Range Analysis.- Efficiency.- Completeness.- Analysing String Buffers.- Widening with Landmarks.- Further Refinements.- Related Tools.- The Astrée Anlyser.- SLAM and ESPX.- CCured.- Other Approaches.- Contributions.- A Semantics for C.- Core C.- Preliminaries.- The Environments.- Concrete Semantics.- Collecting Semantics.- Related Work.- Abstracting Soundly.- Abstract State Space.- An Introductory Example.- Points-To Analysis.- The Points-To Abstract Domain.- Related Work.- Numeric Domains.- The Domain of Convex Polyhedra.- Operations on Polyhedra.- Multiplicity Domain.- Combining the Polyhedral and Multiplicity Domain.- Related Work.- Taming Casting and Wrapping.- Modelling the Wrapping of Integers.- A Language Featuring Finite Integer Arithmetic.- The Syntax of SubC.- The Semantics of SubC.- Polyhedral Analysis of Finite Integers.- Revisiting the Domain of Convex Polyhedra.- Implicit Wrapping of Polyhedral Variables.- Explicit Wrapping of Polyhedral Variables.- Wrapping Variables with a Finite Range.- Wrapping Variables with Infinite Ranges.- Wrapping Several Variables.- An Algorithm for Explicit Wrapping.- An Abstract Semantics for SubC.- Discussion.- Related Work.- Overlapping Memory Accesses and Pointers.- Memory as a Set of Fields.- Memory Layout for Core C.- Access Trees.- Related Work.- Mixing Values and Pointers.- Abstraction Relation.- Abstract Semantics.- Expressions and Simple Assignments.- Assigning Structures.- Casting, &-Operations and Dynamic Memory.- Discussion and Related Work.- Ensuring Efficiency.- Planar Polyhedra.- Operations on Inequalities.- Entailment on Single Inequalities.- Operations on Sets of Inequalities.- Entailment Checking.- Removing Redundancies.- Convex Hull.- Linear Programming and Planar Polyhedra.- Widening Planar Polyhedra.- The TVPI Abstract Domain.- Principles of the TVPI Domain.- Entailment Check.- Convex Hull.- Projection.- Reduced Product Between Bounds and Inequalities.- Incremental Closure.- Approximating General Inequalities.- Linear Programming in the TVPI Domain.- Widening of TVPI Polyhedra.- Related Work.-The Integral TVPI Domain.- The Merit of Z-Polyhedra.- Improving Precision.- Limiting the Growth of Coefficients.- Harvey's Integral Hull Algorithm.- Calculating Cuts Between Two Inequalities.- Integer Hull in the Reduced Product Domain.- Planar Z-Polyhedra and Closure.-Possible Implementations of a Z-TVPI Domain.- Tightening Bpunds Across Projections.- Discussion and Implementation.- Related Work.- Interfacing Analysis and Numeric Domain.- Separating Interval from Relational Information.- Inferring Relevant Fields and Addresses.- Typed Abstract Variables.- Populating the Field Map.- Applying Widening in Fixpoint Calculations.- Improving Precision.- Tracking String Lengths.- Manipulating Implicitly Terminated Strings.- Analysing the String Loop.- Calculating a Fixpoint of the Loop.- Prerequisites for String Buffer Analysis.- Incorporating String Buffer Analysis.- Extending the Abstraction Relation.- Related Work.- Widening with Landmarks.- An Introduction to Widening/Narrowing.- The Limitations of Narrowing.- Improving Widening and Removing Narrowing.- Revisiting the Analysis of String Buffers.- Applying the Widening/Narrowing Approach.- The Rationale Behind Landmarks.- Creating Landmarks for Widening.- Using Landmarks in Widening.- Acquiring Landmarks.- Using Landmarks at a Widening Point.- Extrapolation Operator for Polyhedra.- Related Work.- Combining Points-To and Numeric Analysis.- Boolean Flags in the Numeric Domain.- In

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