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Master's Thesis MASTER'S THESIS Steganography in Reed-Solomon Codes Peter Hanzlik Master program Master of Science in Information Security Luleå University of Technology Department of Business Administration, Technology and Social Sciences Abstract In the thesis is described a steganographic system that embeds hidden data into communication channel that utilizes Reed-Solomon error-correction codes. A formal model of Reed-Solomon covert channel is proposed by stating requirements that are laid on such technique. The model was validated by experimental research methods. Findings indicate that the proposed model satisfies the primary attributes of steganography: capacity, imperceptibility and robustness. The research provides a stand base for further researches in the wide range of applications of Reed-Solomon codes. Table of Contents 1 Introduction ........................................................................................................................................... 1 1.1 Problem Description ...................................................................................................................... 1 1.1.1 Digital Watermarking ............................................................................................................ 1 1.1.2 Message Hiding ..................................................................................................................... 2 1.1.3 Video Stream Resynchronization .......................................................................................... 3 1.1.4 Steganographic File System ................................................................................................... 3 1.2 Research Problem.......................................................................................................................... 4 1.3 Research Design ............................................................................................................................ 6 1.4 Data Collection and Visualization .................................................................................................. 8 1.5 Scope ............................................................................................................................................. 8 2 Coding Theory ..................................................................................................................................... 10 2.1 Hamming Distance ...................................................................................................................... 10 2.2 Types of Codes ............................................................................................................................. 10 2.3 Errors ........................................................................................................................................... 12 2.4 Galois Fields ................................................................................................................................. 12 2.4.1 Arithmetic in Finite Field ..................................................................................................... 14 2.4.2 Construction of Finite Field GF(23) ...................................................................................... 16 3 Reed-Solomon Codes .......................................................................................................................... 17 3.1 Characteristics of Reed-Solomon codes ...................................................................................... 17 3.2 Encoding Reed-Solomon Codes ................................................................................................... 19 3.3 Decoding Reed-Solomon Codes .................................................................................................. 22 3.3.1 Syndrome Computation ...................................................................................................... 24 3.3.2 Determination of the Error-locator Polynomial .................................................................. 25 3.3.3 Finding roots of error-locator polynomial ........................................................................... 29 3.3.4 Calculation of Error Values .................................................................................................. 30 4 Steganography in Reed-Solomon Codes ............................................................................................. 33 4.1 General Steganography System .................................................................................................. 34 4.2 Model of Reed-Solomon Covert Channel .................................................................................... 35 4.2.1 Requirements for a Steganographic Technique over RS Codes .......................................... 38 4.2.2 Specific Steganographic Technique over RS Codes ............................................................. 41 5 Validation ............................................................................................................................................ 44 5.1 Methodology of the Validation ................................................................................................... 44 5.2 Findings........................................................................................................................................ 48 5.2.1 Simulation of Individual Errors ............................................................................................ 48 5.2.2 Simulation of Burst Errors ................................................................................................... 50 5.3 Result ........................................................................................................................................... 53 5.4 Possible Areas of Application ...................................................................................................... 53 5.4.1 Digital Watermarking .......................................................................................................... 53 5.4.2 Message Hiding ................................................................................................................... 54 5.4.3 Video Stream Resynchronization ........................................................................................ 55 5.4.4 Steganographic File System ................................................................................................. 55 Conclusion and Discussion .......................................................................................................................... 56 References ................................................................................................................................................... 58 Table of Figures Figure 1: Error-correction Process ................................................................................................................. 5 Figure 2: Rise of Errors ................................................................................................................................ 12 Figure 3: Reed-Solomon Coder/Decoder .................................................................................................... 17 Figure 4: Reed-Solomon Codeword ............................................................................................................ 18 Figure 5: Decoding Process ......................................................................................................................... 23 Figure 6: A Generic Steganography System ................................................................................................ 34 Figure 7: Inserting Steganographic Data into Error-correction ................................................................... 36 Figure 8: Model of Reed-Solomon Covert Channel ..................................................................................... 36 Figure 9: Steganographic Algorithm over Reed-Solomon Codes ................................................................ 41 Figure 10: Flow Chart of the Steganographic Technique ............................................................................ 42 Figure 11: Class Diagram ............................................................................................................................. 44 Figure 12: Pilot Study - Test Repetitions ..................................................................................................... 46 Figure 13: Individual Error Distribution ....................................................................................................... 49 Figure 14: Steganographic Locations Distribution ...................................................................................... 49 Figure 15: Burst Error Distribution .............................................................................................................. 51 Figure 16: Steganographic Locations Distribution ...................................................................................... 51 List of Tables Table 1: Basic Operations in GF(2) .............................................................................................................. 14 Table 2: Elements of GF(23) ......................................................................................................................... 16 Table 3: Pilot Study - Standard Deviation of Error Location Frequency ...................................................... 47 Table 4:
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