Nghiên cứu phát triển các phương pháp của lý thuyết đồ thị và otomat trong giấu tin mật và mã hóa tìm kiếm (Research on development of methods of graph theory and automata in steganography and searchable

MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY —————————— Nguyen Huy Truong RESEARCH ON DEVELOPMENT OF METHODS OF GRAPH THEORY AND AUTOMATA IN STEGANOGRAPHY AND SEARCHABLE ENCRYPTION DOCTORAL DISSERTATION IN MATHEMATICS AND INFORMATICS Hanoi - 2020 MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY —————————— Nguyen Huy Truong RESEARCH ON DEVELOPMENT OF METHODS OF GRAPH THEORY AND AUTOMATA IN STEGANOGRAPHY AND SEARCHABLE ENCRYPTION Major: Mathematics and Informatics Major code: 9460117 DOCTORAL DISSERTATION IN MATHEMATICS AND INFORMATICS SUPERVISORS: Assoc Prof Dr Sc Phan Thi Ha Duong Dr Vu Thanh Nam Hanoi - 2020 DECLARATION OF AUTHORSHIP I hereby certify that I am the author of this dissertation, and that I have completed it under the supervision of Assoc Prof Dr Sc Phan Thi Ha Duong and Dr Vu Thanh Nam I also certify that the dissertation’s results have not been published by other authors Hanoi, February 03, 2020 PhD Student Nguyen Huy Truong Supervisors Assoc Prof Dr Sc Phan Thi Ha Duong Dr Vu Thanh Nam ACKNOWLEDGMENTS I am extremely grateful to Assoc Prof Dr Sc Phan Thi Ha Duong I want to thank Dr Vu Thanh Nam I would also like to extend my deepest gratitude to Late Assoc Prof Dr Phan Trung Huy I would like to thank my co-workers from School of Applied Mathematics and Informatics, Hanoi University of Science and Technology for all their help I also wish to thank members of Seminar on Mathematical Foundations for Computer Science at Institute of Mathematics, Vietnam Academy of Science and Technology for their valuable comments and helpful advice I give thanks to PhD students of Late Assoc Prof Dr Phan Trung Huy for sharing and exchanging information in steganography and searchable encryption Finally, I must also thank my family for supporting all my work CONTENTS Page LIST OF SYMBOLS iii LIST OF ABBREVIATIONS iv LIST OF FIGURES v LIST OF TABLES vi INTRODUCTION CHAPTER PRELIMINARIES 1.1 Basic Structures 1.1.1 Strings 1.1.2 Graph 1.1.3 Deterministic Finite Automata m 1.1.4 The Galois Field GF (p ) 1.2 Digital Image Steganography 1.3 Exact Pattern Matching 11 1.4 Longest Common Subsequence 12 1.5 Searchable Encryption 15 CHAPTER DIGITAL IMAGE STEGANOGRAPHY BASED ON THE GALOIS FIELD USING GRAPH THEORY AND AUTOMATA 16 2.1 Introduction 16 2.2 The Digital Image Steganography Problem 18 2.3 A New Digital Image Steganography Approach 19 2.3.1 Mathematical Basis based on The Galois Field 19 2.3.2 Digital Image Steganography Based on The Galois Field GF (pm ) Using Graph Theory and Automata 21 2.4 The Near Optimal and Optimal Data Hiding Schemes for Gray and Palette Images 29 2.5 Experimental Results 34 2.6 Conclusions 37 CHAPTER AN AUTOMATA APPROACH TO EXACT PATTERN MATCHING 39 3.1 Introduction 39 3.2 The New Algorithm - The MRc Algorithm 41 3.3 Analysis of The MRc Algorithm 47 3.4 Experimental Results 50 3.5 Conclusions 55 CHAPTER AUTOMATA TECHNIQUE FOR THE LONGEST COMMON SUBSEQUENCE PROBLEM 56 4.1 Introduction 56 i 4.2 4.3 4.4 4.5 Mathematical Basis Automata Models for Solving The LCS Problem Experimental Results Conclusions CHAPTER CRYPTOGRAPHY BASED ON STEGANOGRAPHY AND AUTOMATA METHODS FOR SEARCHABLE ENCRYPTION 5.1 Introduction 5.2 A Novel Cryptosystem Based on The Data Hiding Scheme (2, 9, 8) 5.3 Automata Technique for Exact Pattern Matching on Encrypted Data 5.4 Automata Technique for Approximate Pattern Matching on Encrypted Data 5.5 Conclusions CONCLUSION BIBLIOGRAPHY LIST OF PUBLICATIONS ii 57 61 66 67 68 68 70 74 76 78 80 81 88 LIST OF SYMBOLS Σ Σ∗ An alphabet The set of all strings on Σ ∅ The empty set The empty string |S| The number of elements of a set S |u| The length of a string u m GF (p ) The Galois field is constructed from the polynomial ring Zp [x], where p is prime and m is a positive integer n m (GF (p ), +, ·) A vector space over the field GF (pm ) LCS(p, x) A longest common subsequence of p and x lcs(p, x) The length of a LCS(p, x) LeftID(u) The least element the leftmost location of u Rmp (u) The last component of LeftID(u) in p (I, M, K, Em, Ex) A data hiding scheme I A set of all image blocks with the same size and image format M A finite set of secret elements K A finite set of secret keys Em An embedding function embeds a secret element in an image block Ex An extracting function extracts an embedded secret element from an image block qcolour The number of different ways to change the colour of each pixel in an arbitrary image block I An image block M A secret element K A secret key Adjacent(cp , a) An adjacent vertex of cp A string of length c c block Pos p (z) The last position of appearance of z in p Mp An automaton accepting the pattern p Config(p) The set of all the configurations of p Wp (u) The weight of u in p Wp (C) The weight of C WConfig(p) The set of the weights of all the configurations of p i Wp (a) The weight of a at the location i in p Wmp (a) The heaviest weight of a in p W (a) The weight of a in p iii LIST OF ABBREVIATIONS AOSO BF BFS BMH BNDM CTL EBOM ER FJS FOPA FSBNDM HASH HCIH LBNDM LCS LSB MSDR MSE NP OPA PA PCT PSNR RGB SA SAE SBNDM SE SSE TVSBS WF WL Average Optimal Shift Or Brute Force Breadth First Search Boyer Moore Horspool Backward Nondeterministic Dawg Matching Chang Tseng Lin Extended Backward Oracle Matching Embedding Rate Franek Jennings Smyth Fastest Optimal Parity Assignment Forward SBNDM Hashing High Capacity of Information Hiding Long BNDM Longest Common Subsequence Least Significant Bit Maximal Secret Data Ratio Mean Square Error Nondeterministic Polynomial Optimal Parity Assignment Parity Assignment Pan Chen Tseng Peak Signal to Noise Ratio Red Green Blue Shift Add Searchable Asymmetric Encryption Simplified BNDM Searchable Encryption Searchable Symmetric Encryption Thathoo Virmani Sai Balakrishnan Sekar Wagner Fischer Wu Lee iv LIST OF FIGURES Figure Figure Figure Figure Figure 1.1 1.2 1.3 1.4 1.5 A simple graph A spanning tree of the graph given in Figure 1.1 The transition diagram of A in Example 1.3 The basic diagram of digital image steganography The degree of appearance of the pattern p 12 Figure 2.1 The nine commonly used 8-bit gray cover images sized 512 × 512 pixels 35 Figure 2.2 The nine commonly used 8-bit palette cover images sized 512 × 512 pixels 35 Figure 2.3 The binary cover image sized 2592 × 1456 pixels 36 Figure 3.1 Sliding window mechanism Figure 3.2 The basic idea of the proposed approach Figure 3.3 The transition diagram of the automaton Mp , p = abcba v 40 44 46 LIST OF TABLES Table 1.1 An adjacency list representation of the simple graph given in Figure 1.1 Table 1.2 The performing steps of the BF algorithm 11 Table 1.3 The dynamic programming matrix L 13 Table 2.1 Elements of the Galois field GF (22 ) represented by binary strings and decimal numbers Table 2.2 Operations + and · on the Galois field GF (22 ) Table 2.3 The representation of E and the arc weights of G for the gray image Table 2.4 The payload, ER and PSNR for the optimal data hiding scheme (1, 2n − 1, n) for palette images with qcolour = Table 2.5 The payload, ER and PSNR for the near optimal data hiding scheme (2, 9, 8) for gray images with qcolour = Table 2.6 The payload, ER and PSNR for the near optimal data hiding scheme (2, 9, 8) for palette images with qcolour = Table 2.7 The comparisons of embedding and extracting time between the chapter’s and Chang et al.’s approach for the same optimal data hiding scheme (1, N, log2 (N + 1) ), where N = 2n − 1, for the binary image with qcolour = Time is given in second unit Table Table Table Table Table Table Table Table Table Table 3.1 The performing steps of the MR1 algorithm 3.2 Experimental results on rand4 problem 3.3 Experimental results on rand8 problem 3.4 Experimental results on rand16 problem 3.5 Experimental results on rand32 problem 3.6 Experimental results on rand64 problem 3.7 Experimental results on rand128 problem 3.8 Experimental results on rand256 problem 3.9 Experimental results on a genome sequence (with |Σ| = 4) 3.10 Experimental results on a protein sequence (with |Σ| = 20) 36 37 37 37 46 51 51 52 52 53 53 54 54 55 Table 4.1 The Refp of p = bacdabcad Table 4.2 The comparisons of the lcs(p, x) computation time for n = 50666 Table 4.3 The comparisons of the lcs(p, x) computation time for n = 102398 59 66 67 vi 30 30 31 ...MINISTRY OF EDUCATION AND TRAINING HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY —————————— Nguyen Huy Truong RESEARCH ON DEVELOPMENT OF METHODS OF GRAPH THEORY AND AUTOMATA IN STEGANOGRAPHY AND. .. purpose of the dissertation is to research on the development of new and quality solutions using graph theory and automata, suggesting their applications in, and applying them to steganography and searchable. .. upload information to the servers and then access it on the Internet online Meanwhile, enterprises can not spend big money on maintaining and owning a system consisting of hardware and software