Research on development of methods of graph theory and automat in steganography and searchable encryption

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, May 18, 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 38 CHAPTER AN AUTOMATA APPROACH TO EXACT PATTERN MATCHING 40 3.1 Introduction 40 3.2 The New Algorithm - The MR c Algorithm 42 3.3 Analysis of The MR c Algorithm 48 3.4 Experimental Results 51 3.5 Conclusions 56 CHAPTER AUTOMATA TECHNIQUE FOR THE LONGEST COMMON SUBSEQUENCE PROBLEM 57 4.1 Introduction 57 i 82 BIBLIOGRAPHY [1] A V Aho, D S Hirschberg, J D Ullman (1976), “Bounds on The Complexity of The Longest Common Subsequence Problem”, Journal of the Association for Computing Machinery, 23(1), pp 1-12 [2] O I I Al-Farraji (2016), “Combination between Steganography and Cryptography in Information Hiding by Using Same Key”, International Journal of Engineering Research and General Science, 4(6), pp 201-208 [3] C Allauzen, M Crochemore, M Raffinot (1999), “Factor Oracle: A New Structure for Pattern Matching”, In: J Pavelka, G Tel, M Bartoˇsek (Eds.) Theory and Practice of Informatics, 26th Conference on Current Trends in Theory and Practice of Informatics Milovy, Czech Republic, November 27 - December 4, 1999 Proceedings LNCS-1725, Springer, pp 295-310 [4] S AL-Mansoori, A Kunhu (2013), “Discrete Cosine Transform and Hash Functions toward Implementing a (Robust-Fragile) Watermarking Scheme”, Proc SPIE 8895, High-Performance Computing in Remote Sensing III, 889504 [5] V S Babu, K J Helen (2015), “A Study on Combined Cryptography and Steganography”, International Journal of Research Studies in Computer Science and Engineering, 2(5), pp 45-49 [6] A Baby, H Krishnan (2017), “Combined Strength of Steganography and Cryptography - A Literature Survey”, International Journal of Advanced Research in Computer Science, 8(3), pp 1007-1010 [7] R Baeza-Yates, G H Gonnet (1992), “A New Approach to Text Searching”, Communications of the ACM, 35(10), pp 74-82 [8] D Bakkelund (2009), “An LCS-based String Metric”, University of Oslo (Norway), September 23 [9] A Begum (2008), “A Greedy Approach for Computing Longest Common Subsequences”, Journal of Prime Research in Mathematics, Vol 4, pp 165-170 [10] T Berry, S Ravindran (2001), “Fast String Matching Algorithm and Experimental Results”, A Proceedings of the Prague Stringology Club Workshop 99, Collaborative Report DC-99-05, Czech Technical University, Prague, pp 16-26 [11] J Berstel, D Perrin (1985), “Theory of Codes”, Academic Press [12] P Bharti, R Soni (2012), “A New Approach of Data Hiding in Images using Cryptography and Steganography”, International Journal of Computer Applications, 58(18), pp 1-5 [13] G Birkhoff, S M Lane (1969), “A Survey of Modern Algebra” (Third edition), Macmillan Company 83 [14] A Blumer, J Blumer, D Haussler, A Ehrenfeucht, M T Chen, J Seiferas (1985), “The Smallest Automation Recognizing The Subwords of A Text”, Theoretical Computer Science, Vol 40, pp 31-55 [15] R S Boyer, J S Moore (1977), “A Fast String Searching Algorithm”, Communications of the ACM, 20(10), pp 762-772 [16] D Cantone, S Faro (2005), “Fast-Search Algorithms: New Efficient Variants of the Boyer-Moore Pattern-Matching Algorithm”, J Autom Lang Comb., 10(5/6), pp 589-608 [17] S Chakraborty, S K Bandyopadhyay (2013), “Steganography Method Based On Data Embedding By Sudoku Solution Matrix”, International Journal of Engineering Science Invention, 2(7), pp 2319-6726 [18] C C Chang, C S Tseng, C C Lin (2005), “Hiding Data in Binary Images”, In: Robert H Deng, Feng Bao, HweeHwa Pang, Jianying Zhou (Eds.) Information Security Practice and Experience, 1st International Conference, ISPEC 2005, Singapore, April 11-14, 2005 Proceedings LNCS-3439, Springer, 2005, pp 338-349 [19] A Chatterjee, A.K Das (2018), “Secret Communication Combining Cryptography and Steganography”, In: K Saeed, N Chaki, B Pati, S Bakshi, D Mohapatra (Eds.) Progress in Advanced Computing and Intelligent Engineering Advances in Intelligent Systems and Computing, Vol 563 Springer, Singapore, pp 281-291 [20] A Cheddad, J Condell, K Curran, P M Kevitt (2010), “Digital Image Steganography: Survey and Analysis of Current Methods”, Signal Processing, 90(3), pp 727-752 [21] J Chen, T S Chen, M W Cheng (2003), “A New Data Hiding Method in Binary Image”, Proceedings of the IEEE Fifth International Symposium on Multimedia Software Engineering, pp 88-93 [22] G Chugh (2013), “Information Hiding - Steganography & Watermarking: A Comparative Study”, International Journal of Advanced Research in Computer Science, 4(4), pp 165-171 [23] V Chvatal, D A Klarner, D E Knuth (1972), “Selected Combinatorial Research Problems”, Stan-CS-TR-72-292, pp 26 [24] T H Cormen, C E Leiserson, R L Rivest, C Stein (2001), “Introduction to Algorithms (Second edition)”, MIT Press, Chapter 32 [25] M Crochemore, W Rytter (1994), “Text Algorithms”, Oxford University Press [26] N Desmoulins, P A Fouque, C Onete, O Sanders (2018), “Pattern Matching on Encrypted Streams”, In: T Peyrin, S Galbraith (Eds.) Advances in Cryptology ASIACRYPT 2018 LNCS-11272, Springer, pp 121-148 [27] A Dhraief, R Issaoui, A Belghith (2011), “Parallel Computing The Longest Common Subsequence (LCS) on GPUs: Efficiency and Language Suitability”, Proceedings of the 1st International Conference on Advanced Communications and Computation, Spain, October 23-28, 2011, pp 143-148 [28] Q Dong, Z Guan, L Wu, Z Chen (2013), “Fuzzy Keyword Search over Encrypted Data in the Public Key Setting , In: J Wang, H Xiong, Y Ishikawa, J Xu, J Zhou (Eds.) Web-Age Information Management LNCS-7923, Springer, pp 729-740 84 [29] R Dowsley, A Michalas, M Nagel, N Paladi (2017), “A Survey on Design and Implementation of Protected Searchable Data in The Cloud”, Computer Science Review, Vol 26, pp 17-30 [30] B Durian, J Holub, H Peltola, J Tarhio (2009), “Tuning BNDM with q-Grams”, In: I Finocchi, J Hershberger (Eds.) Algorithm Engineering and Experiments, 10th Workshop, ALENEX 2009, New York, January 3, 2009 Proceedings., pp 29-37 [31] A Ehrenfeucht, R, M McConnell, N Osheim, S W Woo (2011), “Position Heaps: A Simple and Dynamic Text Indexing Data Structure”, Journal of Discrete Algorithms, Vol 9, pp 100-121 [32] S Faro, T Lecroq (2009), “Efficient Variants of The Backward-Oracle-Matching Algorithm”, International Journal of Foundations of Computer Science, 20(6), pp 967-984 [33] S Faro, T Lecroq (2013), “The Exact Online String Matching Problem: A Review of the Most Recent Results”, ACM Computing Surveys, 45(2), Article 13 [34] F Franek, C G Jennings, W F Smyth (2007), “A Simple Fast Hybrid PatternMatching Algorithm”, Journal of Discrete Algorithms, 5(4), pp 682-695 [35] K Fredriksson, S Grabowski (2005), “Practical and Optimal String Matching”, In: M P Consens, G Navarro (Eds.) String Processing and Information Retrieval, 12th International Conference, SPIRE 2005, Buenos Aires, Argentina, November 2-4, 2005 Proceedings, LNCS-3772, Springer, pp 376-387 [36] J Fridrich (1999), “A New Steganographic Method for Palette-Based Images”, Proceedings of The IS&T PICS Conference, pp 285-289 [37] J Fridrich, R Du (2000), “Secure Steganographic Methods for Palette Images”, Proceedings of The IS&T PICS Conference, pp 47-60 [38] Y K Gedam, J.N Varshapriya (2014), “Fuzzy Keyword Search Over Encrypted Data in Cloud Computing”, Journal of Engineering Research and Applications, 4(7), pp 197-202 [39] R C Gonzalez, R E Woods (2008), “Digital Image Processing”, Pearson Prentice Hall [40] F Han, J Qin, J Hu (2016), “Secure Searches in The Cloud: A Survey”, Future Generation Computer Systems, Vol 62, pp 66-75 [41] R Haynberg, J Rill, D Achenbach, J Mă uller-Quade (2013), Symmetric Searchable Encryption for Exact Pattern Matching using Directed Acyclic Word Graphs”, In: Samarati, Pierangela (Eds.) Security and Cryptography, the 10th International Conference on Security and Cryptography, SECRYPT 2013, Reykjavk, Iceland, July 29-31, 2013 Proceedings SciTePress, pp 403-410 [42] D S Hirschberg (1975), “A Linear Space Algorithm for Computing Maximal Common Subsequences”, Comm ACM, 18(6), pp 341-343 [43] J Holub, B Durian (2005), “Talk: Fast Variants of Bit Parallel Approach to Suffix Automata”, In: The Second Haifa Annual International Stringology Research Workshop of the Israeli Science Foundation 85 [44] J E Hopscoft, R Motwani, J D Ullman (2001), “Introduction to Automata Theory, Languages, and Computation” (Second Edition), Addison-Wesley [45] R N Horspool (1980), “Practical Fast Searching in Strings”, Software Practice and Experience, 10(6), pp 501-506 [46] C L Hou, C Lu, S C Tsai, W G Tzeng (2011), “An Optimal Data Hiding Scheme with Tree-Based Parity Check”, IEEE Transactions on Image Processing, 20 (3), pp 880-886 [47] P T Huy, N Q Khang (2002), “A New Algorithm for LCS Problem”, Proceedings of the 6th Vietnam Conference of Mathematics, Hue, September 7-10, 2002, pp 145-157 [48] P T Huy, C Kim, N H Thanh (2013), “Modules over Rings of Small Characteristics and Maximality of Data Hiding Ratio in CPTE Schemes”, American Journal of Applied Sciences, 10 (9), pp 1102-1108 [49] P T Huy, N H Thanh (2011), “On the Maximality of Secret Data Ratio in CPTE Schemes”, In: N T Nguyen, C G Kim, A Janiak (Eds.) Intelligent Information and Database Systems, Third International Conference, ACIIDS 2011, Korea, April 20-22, 2011, Proceedings, Part I LNCS-6591, Springer, pp 88-99 [50] P T Huy, N H Thanh, N T Dat, C Kim (2013), “Improving Optimal Parity Assignments in Palette Images”, Journal INFORMATION, 16 (4), pp 2661-2668 [51] P T Huy, N H Thanh, C Kim (2012), “Relationship between Correcting Code and Module Technique in Hiding Secret Data”, In: J J Park, A Zomaya, S S Yeo, S Sahni (Eds.) Network and Parallel Computing, Ninth International Conference, NPC 2012, Korea, September 6-8, 2012, Proceedings LNCS-7513, Springer, pp 297-307 [52] N T T Huyen, P T Huy (2002), “Fuzzy Approach in Some Pattern Matching Algorithms”, Vietnam J of Computer Science and Cybernetics, 18(3), pp 201-210 [53] S Ijeri, S Pujeri, B Shrikant, B A Usha (2012), “Image Steganography Using Sudoku Puzzle for Secured Data Transmission”, International Journal of Computer Applications, 48(17), pp 31-35 [54] C S Iliopoulos, M S Rahman (2009), “A New Efficient Algorithm for Computing The Longest Common Subsequence”, Theory Comput Syst, Vol 45, pp 355-371 [55] Indu, Prena (2016), “A Comparative Study of Different Longest Common Subsequence Algorithms”, International Journal of Recent Research Aspects, 3(2), pp 65-69 [56] J, Irvine, D Harle (2002), “Data Communications and Networks: An Engineering Approach”, John Wiley & Sons, Ltd [57] M Jain, S K Lenka (2016), “A Review of Digital Image Steganography using LSB and LSB Array”, International Journal of Applied Engineering Research, 11(3), pp 1820-1824 [58] N S Jho, D Hong (2013), “Symmetric Searchable Encryption with Efficient Conjunctive Keyword Search”, KSII Transactions on Internet and Information Systems, 7(5), pp 1328-1342 [59] T Jiang, M Li (1995), “On The Approximation of Shortest Common Supersequences and Longest Common Subsequences”, SIAM J Comput, 24(5), pp 1122-1139 86 [60] M S John, P SumaLatha, M Joshuva (2015), “A Comparative Study of Index-Based Searchable Encryption Techniques”, International Journal of Advanced Research in Computer Science, 6(3), pp 13-15 [61] N Khan, K S Gorde, M E Student (2015), “Data Security by Video Steganography and Cryptography Techniques”, International Journal of Emerging Trends in Electrical and Electronics, 11(5), pp 58-64 [62] I Khan, S Gupta, S Singh (2016), “A New Data Hiding Approach in Images for Secret Data Communication with Steganography”, International Journal of Computer Applications, 135(13), pp 9-14 [63] A Khan, A Siddiqa, S Munib, S A Malik (2014), “A Recent Survey of Reversible Watermarking Techniques”, Information Sciences, Vol 279, pp 251-272 [64] D E Knuth, J H Morris, Jr., V R Pratt (1977), “Fast Pattern Matching in Strings”, SIAM J Comput., 6(2), pp 323-350 [65] W C Kuo, S H Kuo, C C Wang, L C Wuu (2016), “High Capacity Data Hiding Scheme Based on Multi-bit Encoding Function”, Optik, Vol 127, pp 1762-1769 [66] G M Landau, U Vishkin (1986), “Efficient String Matching with k Mismatches”, Theoretical Computer Science, Vol 43, pp 239-249 [67] J V Leeuwen (1990), “Handbook Of Theoretical Computer Science”, Vol A, Elsevier MIT Press [68] T Lecroq (2007), “Fast Exact String Matching Algorithms”, Information Processing Letters, 102(6), pp 229-235 [69] X Li, S Cai, W Zhang, B Yang (2015), A “Further Study of Large Payloads Matrix Embedding”, Information Sciences, Vol 324, pp 257-269 [70] D Maier (1978), “The Complexity of Some Problems on Subsequences and Supersequences”, Journal of the ACM, 25(2), pp 322-336 [71] Z Mei, B Wu, S Tian, Y Ruan, Z Cui (2017), “Fuzzy Keyword Search Method over Ciphertexts Supporting Access Control”, KSII Transactions on Internet and Information Systems, 11(11), pp 5671-5693 [72] M H Mohamed, L M Mohamed (2016), “High Capacity Image Steganography Technique Based on LSB Substitution Method”, Applied Mathematics & Information Sciences, 10(1), pp 259-266 [73] G Navarro (2001), “A Guided Tour to Approximate String Matching”, ACM Computing Surveys, 33 (1), pp 3188 [74] G Navarro, M Raffinot (2000), “Fast and Flexible String Matching by Combining Bit-Parallelism and Suffix Automata”, ACM Journal of Experimental Algorithmics (JEA), 5(4), Article [75] H K Pan, Y Y Chen, Y C Tseng (2000), “A Secret of Data Hiding Scheme for TwoColor Images”, In: Proceedings ISCC 2000 Fifth IEEE Symposium on Computers and Communications, pp 750-755 [76] K J Panchal, F N Patel (2014), “Steganography: A Brief Survey”, International Journal of Modern Trends in Engineering and Research, 2(2), pp 747-750 87 [77] P H Paris, N Abadie, C Brando (2017), Linking Spatial Named Entities to The Web of Data for Geographical Analysis of Historical Texts”, Journal of Map & Geography Libraries, 13 (1), pp 82-110 [78] B Park, R Lu (2015), “Hyperspectral Imaging Technology in Food and Agriculture”, Springer [79] H Peltola, J Tarhio (2003), “Alternative Algorithms for Bit-Parallel String Matching”, In: M A Nascimento, E S de Moura, A L Oliveira (Eds.) String Processing and Information Retrieval, 10th International Symposium, SPIRE 2003, Manaus, Brazil, October 8-10, 2003 Proceedings LNCS-2857, Springer, pp 80-93 [80] M V Ramakrishnan, S Eswaran (2013), “A Comparative Study of Various Parallel Longest Common Subsequence (LCS) Algorithms”, International Journal of Computer Trends and Technology, 4(2), pp 183-186 [81] M I S Reddy, A P S Kumar (2016), “Secured Data Transmission Using Wavelet Based Steganography and Cryptography by Using AES Algorithm”, Procedia Computer Science, Vol 85, pp 62-69 [82] K H Rosen (2012), “Discrete Mathematics and Its Applications” (Seventh Edition), McGraw-Hill [83] K Ruohonen (2009), “Formal Languages”, Tampere University of Technology, pp 1-3 [84] S S Sheik, S K Aggarwal, A Poddar, N Balakrishnan, K Sekar (2004), “A Fast Pattern Matching Algorithm”, J Chem Inf Comput Sci., 44 (4), pp 1251-1256 [85] D X Song, D Wagner, A Perrig (2000), “Practical Techniques for Searches on Encrypted Data”, In: Proceeding 2000 IEEE Symposium on Security and Privacy, pp 44 [86] S Song, J Zhang, X Liao, J Du, Q Wen (2011), “A Novel Secure Communication Protocol Combining Steganography and Cryptography”, Procedia Engineering, Vol 15, pp 2767-2772 [87] C A Stanley (2005), “Pairs of Values and The Chi-squared Attack”, Department of Mathematics, Iowa State University, May 1, 2005 [88] D R Stinson (1995), “Cryptography: Theory and Practice (CRC Press Series on Discrete Mathematics and Its Application)”, CRC Press [89] M Strizhov, Z Osman, I Ray (2016), “Substring Position Search over Encrypted Cloud Data Supporting Efficient Multi-User Setup”, Future Internet, 8(3), 28 [90] D M Sunday (1990), “A Very Fast Substring Search Algorithm”, Communications of the ACM, 33(8), pp 132-142 [91] R Thathoo, A Virmani, S S Lakshmi, N Balakrishnan, K Sekar (2006), “TVSBS: A Fast Exact Pattern Matching Algorithm for Biological Sequences”, Current Sci., 91(1), pp 47-53 [92] Y C Tsengy, H K Pan (2001), “Secure and Invisible Data Hiding in 2-Color Images”, Proceedings IEEE INFOCOM, Vol 2, pp 887-896 [93] Varsha, R S Chhillar (2015), “Data Hiding Using Steganography and Cryptography”, International Journal of Computer Science and Mobile Computing, 4(4), pp 802-805 88 [94] R A Wagner, M J Fischer (1974), “The String-to-String Correction Problem”, J ACM, 21(1), pp 168-173 [95] L Wei, H Zhu, Z Cao, X Dong, W Jia, Y Chen, A Vasilakos (2014), “Security and Privacy for Storage and Computation in Cloud Computing”, Information Sciences, Vol 258, pp 371386 [96] R B Wolfgang, E J Delp (1999), “Fragile Watermarking Using The VW2D Watermark”, Proc SPIE 3657, Security and Watermarking of Multimedia Contents, pp 204-213 [97] M Y Wu, Y K Ho, J H Lee (2014), “An Iterative Method of Palette Based Image Steganography”, Pattern Recognition Letters, 25(3), pp 301-309 [98] S Wu, U Manber (1994), “A Fast Algorithm for Multi-Pattern Searching”, Technical Report TR-94-17, University of Arizona, Tucson [99] X Xu, L Chen, Y Pan, P He (2005), “Fast Parallel Algorithms for The Longest Common Subsequence Problem Using an Optical Bus”, Computational Science and Its Applications, ICCSA 2005, Proceedings, Part III, Singapore, May 9-12, 2005, pp 338-348 [100] R.M Yadav, D S Tomar, R K Baghel (2014), “A Study on Image Steganography Approaches in Digital Images”, Engineering Universe for Scientific Research and Management, 6(5) [101] J Yang, Y Xu, Y Shang (2010), “An Efficient Parallel Algorithm for Longest Common Subsequence Problem on GPUs”, Proceedings of the World Congress on Engineering, Vol 1, London, June 30 - July 2, 2010, pp 499-504 [102] W Yunling, W Jianfeng, C Xiaofeng (2016), “Secure Searchable Encryption: A Survey”, Journal of Communications and Information Networks, 1(4), pp 52-65 [103] B.B Zaidan, A A Zaidan, A K Al-Frajat, H A Jalab (2010), “On the Differences between Hiding Information and Cryptography Techniques: An Overview”, Journal of Applied Science, 10(15), pp 1650-1655 [104] Y Zhang, J Jiang, Y Zha, H Zhang, S Zhao (2013), “Research on Embedding Capacity and Efficiency of Information Hiding Based on Digital Images”, International Journal of Intelligence Science, 3(2), pp 77-85 89 ... 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. .. and automata in steganography and searchable encryption The purpose of the dissertation is to research on the development of new and quality solutions using graph theory and automata, suggesting... Prof Phan Trung Huy in steganography and searchable encryption, and under the direction of supervisors, the dissertation title assigned is research on development of methods of graph theory and