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

Research on development of methods of graph theory and automat in steganography and searchable encryption Research on development of methods of graph theory and automat in steganography and searchable encryption luận văn tốt nghiệp thạc sĩ

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 MRc Algorithm 42 3.3 Analysis of The MRc 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 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 LIST OF PUBLICATIONS BIBLIOGRAPHY ii 58 62 67 68 69 69 71 75 77 79 81 82 83 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 36 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 41 45 47 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) 37 37 38 38 47 52 52 53 53 54 54 55 55 56 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 60 67 68 vi 30 30 31 or c39 9!28 !218t1 29tt2 = c39 9!28 !218t1 +9tt2 for palette images (5.10) Remark 5.3 For two algorithms eK and dK given as above, an arbitrary image block I in the input image F can be used many times in process of encrypting and decrypting the secret data So, for a give input image F , the secret data encrypted is not limited by the size of the input image F 5.3 Automata Technique Encrypted Data for Exact Pattern Matching on This section applies the automata approach proposed in Chapter to designing an algorithm for exact pattern matching on secret data encrypted by the cryptosystem proposed in Section 5.2 (Theorem 5.2) Suppose that Alice has a secret data and prefers to outsource this data to a cloud provider Bob As the provider is semi-trusted, Alice needs to encrypted her plaintext and wishes to only store ciphertext in the cloud Assume that Alice uses the cryptosystem (P, C, K , E, D) proposed in Section 5.2 to encrypt data with a pair of two secret parameters (S, k) in the cryptosystem, where S is a 2-Generators for GF (22 ) with elements and k = (f, K, I) ∈ K Because of limited storage space and computing ability, instead of downloading ciphertext, decrypting it and searching locally, Alice may ask Bob to perform pattern matching tasks on the ciphertext directly with a trapdoor of the pattern received from her Consider Σ to be an alphabet of size 256 Suppose that the secret data is a string over Σ x = x1 x2 xt3 for xi ∈ P, i = 1, t3 , t3 ≥ and t3 is often a large natural number, where P = Σ Before uploading the secret data x to Bob, Alice use the encrypting function ek ∈ E to encrypt each xi Then Alice computes yi = ek (xi ), i = 1, t3 , and the encrypted secret data is a string over Σ y = y1 y2 yt3 which is sent to Bob, where Σ is an alphabet Σ = {a |a = ek (a), a ∈ Σ} In general case, for x is any string over the alphabet Σ and a string y is obtained from x by the above way Then we can write y = ek (x) for short and y is a string over the alphabet Σ Remark 5.4 By using only one pair of two secret parameters (S, k), then the security of process of encrypting and decrypting the secret data x is similar to Formulas (5.3) (for gray images) or (5.4) (for palette images) Suppose that Bob needs to perform exact pattern matching task of an arbitrary pattern p on encrypted data y Based on previously introduced results in Chapter 3, here continues using automata technique to meet the requirement 75 Propostion 5.2 Let p be a pattern over the alphabet Σ Then P osp (a ) = P osp (a) for all a ∈ Σ , where a = dk (a ) and p = ek (p) Proof Set i = P osp (a), then a = pi , hence a = pi Without loss of generality, suppose P osp (a ) > i, then there exists i , i > i such that pi = a by Definition 3.3, then a = pi = dk (pi ) Then i < P osp (a), a contradiction So, we complete the proof Propostion 5.3 Let a pattern p and a text x be two strings over the same alphabet Σ and the function Sign be given by For all a ∈ Σ , Sign(a ) = If a ∈ p, Otherwise Then for all a ∈ Σ , a ∈ p if and only if Sign(a ) = Proof Suppose for all a ∈ Σ , a ∈ p if and only if there exists i, i = |p | such that a = pi if and only if a = pi if and only if Sign(a ) = Propostion 5.4 Let a pattern p and a text x be two strings over the same alphabet Σ Then p occurs at any position i in x if and only if p occurs at the position i in y, where y = ek (x) Proof Suppose that p occurs at any position i in x if and only if p = xi xi+1 xi+|p|−1 if and only if yi yi+1 yi+|p|−1 = p if and only if p occurs at the position i in y Propostion 5.5 Let p be a pattern over the alphabet Σ Then for all ≤ l ≤ |p|, Nextp (l) = Nextp (l), where p = ek (p) Proof Without loss of generality, suppose that lm = Nextp (l) < Nextp (l) for all ≤ l ≤ |p| Since pi = ek (pi ) for i = |p|, then p1 p2 plm +1 is both a proper prefix and suffix of p [1 l] by Definition 3.1 Hence, p1 p2 plm +1 is also both a proper prefix and suffix of p[1 l] by Definition 3.1 Then Nextp (l) > lm This is a contradiction to the supposition So, the proof is complete Propostion 5.6 Let p be a pattern over the alphabet Σ Then Appearancep (l, a ) = Appearancep (l, a) for all ≤ l ≤ |p|, a ∈ Σ , where a = dk (a ) and p = ek (p) Proof Clearly, |p| = |p | and for all ≤ i ≤ |p |, a ∈ Σ , a = pi if and only if a = pi By Lemma 3.1 and Proposition 5.5, Appearancep (l, a ) = Appearancep (l, a) Theorem 5.2 Let p be a pattern over the alphabet Σ Let two automata Mp = (Σ, Qp , q0 , δp , Fp ) and Mp = (Σ , Qp , q0 , δp , Fp ) be determined as in Theorem 3.2 Then Qp = Qp , Fp = Fp , δp (q, a ) = δp (q, a) for all q ∈ Qp , a ∈ Σ , where a = dk (a ) and p = ek (p) Proof It is easy to verify that |p| = |p | In addition, by Theorem 3.2 and Proposition 5.6, then Qp = Qp , Fp = Fp and δp (q, a ) = δp (q, a) Remark 5.5 The meaning of Theorem 5.2 in practice is to compute δp from δp 76 Let a pattern p and a text (secret data) x be two strings over the same alphabet Σ and assume |p| |x| For assuming that we have only the encrypted secret data y which is not decrypted to the secret data x, from Propositions 5.2, 5.3 and 5.4, Theorem 5.2, based on the MRc algorithm for c = and using the type a breaking point and the concept of Posp in Chapter 3, and by using the automaton Mp given as in Theorem 3.2, we have an exact pattern matching algorithm immediately that finds all occurrences of the pattern p in x as follows Note that the trapdoor according to the search pattern p is computed based on p, which includes the length of p, the functions Sign, Posp and the automaton Mp jump = |p|; While (jump ≤ |y|) { If (sign(yjump ) == 1) { q = 0; i = jump − P osp (yjump ) + 1; Do { q = δp (q, yi ); If (q == |p|) Mark an occurrence of p at i − |p| + in x; i + +; } While (q = and i ≤ |y|); jump = i − 1; } jump = jump + |p|; } Remark 5.6 Obviously, the above algorithm is the same as the MRc algorithm in Chapter for c = 1, using the type a breaking point and concepts of P osp , and where P osp and δp of the MRc algorithm are replaced with P osp and δp Furthermore, by Propositions 3.2 and 5.2, and Theorem 5.2, clearly in the worst case, this algorithm’s time complexity is O(n) 5.4 Automata Technique for Approximate Pattern Matching on Encrypted Data Suppose that Bob wants to approximate pattern matching of any pattern p on the ciphertext y From results proposed in Chapter 4, automata technique is still applied to meeting the requirement (Theorem 5.3) Propostion 5.7 Let p be a pattern over the alphabet Σ Then WConfig(p ) = WConfig(p), where p = ek (p) Proof Obviously, W0 belongs to WConfig(p ) and WConfig(p) Consider any W ∈ WConfig(p )\{W0 }, then we can set W = {w1 , w2 , , wl } for ≤ l ≤ |p | Then 77 there exists C = {u1 , u2 , , ul } in Config(p ) by Definition 4.2, where Wp (ui ) = wi for ≤ i ≤ l Then there exists a unique C, C = {u1 , u2 , , ul } ∈ Config(p), where ui = dk (ui ) for ≤ i ≤ l Set W = Wp (C), then W ∈ WConfig(p) by Definition 4.2 It easy to verify that Rmp (ui ) = Rmp (ui ) for ≤ i ≤ l by Definition 1.10, then Wp (ui ) = Wp (ui ) for ≤ i ≤ l by Definition 4.1 Hence, W = W , then WConfig(p ) ⊂ WConfig(p) Similarly, we have WConfig(p) ⊂ WConfig(p ) So, the proof is complete Propostion 5.8 Let p be a pattern over the alphabet Σ Then Refp (i, a ) = Refp (i, a) for for all ≤ i ≤ |p |, a ∈ Σ , where a = dk (a ) and p = ek (p) Proof Clearly, Wpi (a ) = Wpi (a) by Definition 4.3 So, Refp (i, a ) = Refp (i, a) by Definition 4.4 Hence, we complete the proof Theorem 5.3 Given a pattern p on Σ and a positive integer constant c with ≤ c ≤ |p| Let two automata APp c = (Σ, Qp , q0 , δp , Fp ) and APp c = (Σ , Qp , q0 , δp , Fp ) be determined as in Theorem 4.4 Then Qp = Qp , Fp = Fp , δp (q, a ) = δp (q, a) for all q ∈ Qp , a ∈ Σ , where a = dk (a ) and p = ek (p) Proof By Proposition 5.7, Qp = Qp Evidently, for all a ∈ Σ , a = dk (a ), a ∈ p if and only if a ∈ p Furthermore, by Definition 4.9 and Proposition 5.8, δp (W, a ) = δp (W, a) Then Fp = Fp So, the proof is complete Remark 5.7 The meaning of Theorem 5.3 in practice is to compute δp from δp Based on the approximate pattern matching problems considered in [66, 67, 73], the section introduces a new concept of the appearance of the pattern p in x with a given error This is a basis for giving requirements for the approximate pattern matching algorithm Definition 5.1 Given two strings p and x over Σ, and a string similarity measure d Let an error , > 0, ∈ Then p appears in x with the error if there exists a substring u of x such that d(p, u) ≤ To construct the approximate pattern matching algorithm, we need a function to measure the string similarity The most commonly used similarities are recalled in [71, 73, 77] Bakkelund [8] proposed a well known string similarity measure which is based on the longest commonly subsequence Similarly, here this section defines a new measure of similarity between two strings d(p, u) = − lcs(p, u) , min{|p|, |u|} (5.11) where p is a pattern and u is a substring of x Clearly, d given above is positive definite and symmetric Propostion 5.9 Given two strings p and x over the same alphabet Σ Let u be an arbitrary substring of y Then d(p , u ) = d(p, u), where p = ek (p), y = ek (x), u = dk (u ) Proof Clearly, |p | = |p|, |u | = |u| and lcs(p, u) = lcs(p , u ) d(p , u ) = d(p, u) So, we complete the proof 78 By Formula (5.11), By using the string similarity measure given in Formula (5.11), the automata technique proposed in Chapter for computing lcs(p , u ) will make an approximate pattern matching algorithm fast, and especially efficient for one pattern and a set of a large number of encrypted texts Given a pattern p and a text (secret data) x over the same alphabet Σ, and an arbitrary substring u of x Let , < < and d(p, u) be given as in Formula (5.11) such that d(p, u) ≤ Then by Proposition 5.9, d(p , u ) ≤ By Formula (5.11), we have lcs(p , u ) ≥ (1 − )min{|p |, |u |} (5.12) If there is u which is a substring of y such that lcs(p , u ) ≥ (1 − )|p|, then Formula (5.12) holds that means d(p , u ) ≤ Hence, there exists u such that u is a substring of x and d(p, u) ≤ So, the constant c in Theorem 4.4 is determined by c = (1 − )|p| Without decrypting y, based on Theorem 5.3, Definition 5.1 and Formula (5.11), use the automaton APp c given as in Theorem 4.4, we immediately have an approximate pattern matching algorithm which determines whether p appears in x with the error or not as follows, where the trapdoor responding to the pattern p is determined from p and , which consists of the constant c and the automaton APp c app = 0; q = W0 ; //The initial state of the automaton APp c is started from W0 For i = to |y| Do { q = δp (q, yi ); If (|q| = c) {app=1; Break;} } If (app = 1) Announce the appearance of the pattern p in x with the error ; Else Announce that p does not appear in x with the error Remark 5.8 Since we can compute δp from δp , the above proposed algorithm is similar to the Algorithm (the parallel algorithm) in Chapter In addition, according to Theorem 4.4, δp is computed in parallel way and the Algorithm costs the worst case time complexity O(n) with the supposition that the Algorithm uses k processors for k is an upper estimate of the lcs(p, x) As an immediately consequence, in the worst case, time complexity of the algorithm is O(n) when it uses (1 − )|p| processors 5.5 Conclusions From results of steganography, pattern matching and some suggestions in the next works in Chapters 2, and 4, this chapter has completed some parts of those works Based on the data hiding scheme (2, 9, 8) in Chapter 2, the chapter constructs a novel cryptosystem with high security This method allows both of encrypting and hiding to be done at once, ciphertexts not to depend on the input image size as existing hybrid techniques of cryptography and steganography In addition, this cryptosystem can be used to encrypt and decrypt secret data by users in SSE For the ciphertext made by the cryptosystem on users side, the chapter designs two pattern matching algorithms to search for any pattern 79 in it directly on cloud servers side The outstanding feature of the algorithms is that, they can be applied well to all cryptosystems that support encrypting letters of the secret data one by one The idea of the design is to apply the automata approach for the exact pattern matching and the longest common subsequence problems in Chapters and For the assumption that the approximate algorithm uses (1 − )m processors, the time complexities of these algorithms are both O(n) in the worst case, where , m and n are the error of a measure of similarity between two strings proposed in Section 5.4 and lengths of the pattern and secret data, respectively With the proposed automata approach to pattern matching algorithms, the automata constructed are only based on search patterns Then the algorithms will have lots of advantages in case of a given pattern and a very large set of ciphertexts stored in the cloud So, future work continues studying this technique to apply in SE 80 CONCLUSION Based on the supervision of Assoc Prof Dr Sc Phan Thi Ha Duong and Dr Vu Thanh Nam, and study on results using graph theory and automata technique proposed by P T Huy et al in steganography and searchable encryption, main contributions of the dissertation in these fields can be summarized as follows: A general approach based on the Galois field GF (pm ) using graph theory and automata to designing optimal and near optimal secret data hiding schemes for binary, gray and palette images; A flexible automata approach to constructing an efficient algorithm for the exact pattern matching problem in practice; Mathematical basis for the development of automata technique for the problem of computing the length of a longest common subsequence of two strings, and two efficient sequential and parallel algorithms based on this basis for the problem in practice; A cryptosystem and two algorithms for exact and approximate pattern matching on encrypted secret data based on the above results for searchable encryption Because the problem of development of methods of graph theory and automata in steganography and searchable encryption is topical, some following interest problems can be considered in the future: Whether there exists the optimal data hiding scheme (2, 8, 8) for 8-bit gray image with qcolour = 3; Improving the quality of stego image generated by proposed data hiding schemes for palette images; The problem of steganalysis attacks; Development of automata technique in SE 81 LIST OF PUBLICATIONS [T1] N H Truong (2019), “A New Digital Image Steganography Approach Based on The Galois Field GF (pm ) Using Graph and Automata”, KSII Transactions on Internet and Information Systems, 13(9), pp 4788-4813 (ISI) [T2] N H Truong (2019), “A New Approach to Exact Pattern Matching”, Journal of Computer Science and Cybernetics, 35(3), pp 197-216 [T3] N H Truong (2019), “Automata Technique for The LCS Problem”, Journal of Computer Science and Cybernetics, 35(1), pp 21-37 [T4] N H Truong (2020), “A Novel Cryptosystem Based on Steganography and Automata Technique for Searchable Encryption”, KSII Transactions on Internet and Information Systems (accepted for publication) (ISI) 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 ...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