Formalising Event Reconstruction in Digital Investigations

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1 Formalising Event Reconstruction in Digital Investigations Pavel Gladyshev The thesis is submitted to University College Dublin for the degree of PhD in the Faculty of Science August 2004 Department of Computer Science Head of department: Prof. Barry Smyth Supervisor: Dr. Ahmed Patel

2 ii TO MY FAMILY

3 Contents List of Figures Abstract Declaration Acknowledgements vii ix x xi 1 Introduction Motivation Research objectives Research idea Dissertation structure Summary of achievements Legal view of digital evidence Legal concepts The nature of disputes resolved in courts The nature of legal proof Standards of proof Presumptions of fact Burden of proof Characteristics of evidence Classes of evidence Forensic science and evidence Requirements to scientific evidence Digital evidence Anonymity of digital information Context of digital information Automated interpretation of digital information Danger of damaged information Summary iii

4 CONTENTS 3 Concepts of digital forensics Investigative process Examination and analysis techniques Search techniques Reconstruction of events Time analysis Summary The need for a theory of event reconstruction Why digital forensics need a theory of event reconstruction State of the art Attack trees Visual investigative analysis Multilinear events sequencing Why-because analysis Summary and research problem statement Analysis of the state of the art Research problem statement Theoretical background Formal notation Mathematical notation ACL2 notation State machine model of computation Basic state machine model and its variations Creation of system models Analysis of finite computations Summary Formalisation of event reconstruction problem Informal example of state machine analysis Investigation at ACME Manufacturing Informal analysis illustrated with a state machine Evidential statements Assumption about reliability of evidence Formalisation of event reconstruction problem Finite state machine Run Partitioned run Formalisation of backtracing Formalisation of evidence Summary iv

5 CONTENTS 7 Event reconstruction algorithm Computing the meaning of a fixed-length observation sequence Computing the meaning of a generic observation sequence Computing the meaning of an evidential statement Running time of event reconstruction algorithm Prefix based representation of computation sets An upper bound on the running time of SolveFOS An upper bound on the running time of SolveOS An upper bound on the running time of SolveES Implementation of the event reconstruction algorithm Summary Evaluation Evaluation criteria Effectiveness of event reconstruction Efficiency of event reconstruction Legal admissibility of event reconstruction Comparison with other event reconstruction techniques Examples of formalised and automated event reconstruction Example 1. Networked printer analysis Example 2. Example of event time bounding Summary Conclusions and future work Problem Solution Lessons of the project Achievements Problems encountered Future work Extending formalisation of event reconstruction Developing more efficient event reconstruction algorithm Investigating new ways of constructing system models Developing practical applications Summary Bibliography 170 A Selected ACL2 functions and macros 179 A.1 Functions A.1.1 Logical functions A.1.2 Integer functions A.1.3 Functions for manipulating ordered pairs A.1.4 Functions for manipulating lists A.2 Macros v

6 CONTENTS B Prefix based representation of computation sets 182 B.1 Prefix based representation of computation sets B.2 Basic properties of prefix lists C Source code 187 C.1 fd.lisp C.2 util.lisp C.3 rec.lisp C.4 acme.lisp C.5 ft.lisp C.6 slack.lisp C.7 draw.lisp D Evidence of publication 212 vi

7 List of Figures 1.1 Event reconstruction by backtracing transitions Dissertation structure Stages of investigative process An example of time bounding Attack tree describing different ways to open a safe Example VIA chart Example MES-diagram WB-graph for the tarts rhyme Well founded order Counting state machine A 2-bit binary counter Interleaving model of concurrent system Turing machine A naive algorithm for finite computation analysis Data abstraction ACME Manufacturing LAN topology Transition graph of the print job directory model Evidence in ACME investigation Run of computation Functions ψ, ψ 1, and Ψ A run that gives two explanations to an observation sequence Evidential statement and related notions Finding explanations of a fixed-length observation sequence Computing the meaning of a fixed-length observation sequence Computing the meaning of a generic observation sequence Computing the meaning of an evidential statement Sample output of the program Comparison with other event reconstruction techniques ACME Manufacturing LAN topology Transition graph of the print job directory model vii

8 LIST OF FIGURES 8.4 Meaning of os Alice with infinitum = Meaning of restricted Alice s claim os Alice with infinitum = Meaning of evidential statement es ACME with infinitum = Formation of the slack space Times of transitions Finding observations that happened before given observation Calculating the earliest possible time of given observation Finding observations that happened after given observation Calculation of the latest possible time of given observation State machine model of the last cluster in a file One step of event reconstruction of observation sequence os final 152 B.1 Algorithm for computing IntersectPrefixes(x, y) B.2 Algorithm for computing X Y B.3 Algorithm for computing Ψ 1 (X) viii

9 Abstract The highly technical nature of computer crime facilitated the development of a new branch of forensic science called digital forensics. Instead of dead bodies, it collects and analyses data produced, transmitted, and stored by digital devices. The field of digital forensics is rapidly evolving. A major research challenge perceived by the digital forensic community is the need for theoretical basis validating correctness of methods and tools used by digital forensic investigators. An important part of digital forensic analysis is event reconstruction. It is the process of determining the events that happened during the incident. In digital forensic investigations, event reconstruction is fairly complex. A single push of a button triggers a chain of events inside one or more digital devices that produce the digital evidence. Informal, unaided reasoning is not always sufficient to comprehensively analyse this chain of events. One way to make event reconstruction more objective and rigorous is to employ mathematics. As a first step in this direction, this research aimed to give formal meaning to the problem of event reconstruction. More specifically, the objectives of this research were (1) to define a formal model of event reconstruction, and (2) to demonstrate that that model can be used as a basis for formalisation and automation of selected examples of digital forensic analysis. To achieve these objectives, the following approach was adopted. First, a study of digital forensic techniques and legal theory was undertaken to clarify the requirements to and place of event reconstruction in digital forensic analysis. Then, a review of existing event reconstruction techniques was carried out. The review has shown that none of these technique are fully adequate in digital forensic context. Next, a formal model of event reconstruction was defined. The defined model possesses the following features: The system under investigation is modeled as a finite state machine. A special-purpose formalism called evidential statement is used for describing the evidence. The outcome of event reconstruction is given precise mathematical meaning in terms of the finite state machine model of the system. The usefulness of the proposed model was then demonstrated by developing a generic event reconstruction algorithm, based on the defined model, and using that algorithm to formalise and automate selected examples of digital forensic analysis. Finally, several possible directions for future research have been suggested. ix

10 Declaration I declare that this thesis is my own work and has not been submitted in any form for another degree or diploma at this, or any other, University or institute of tertiary education. Pavel Gladyshev August, x

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