In this contribution, criteria for the sequences employed in spread spectrum (SS) watermarking and steganography are discussed. These criteria are: Sharp autocorrelation function (ACF), large linear complexity (LC), large length (L), normal distribution assumption and bi-polar.
Nghiên cứu khoa học công nghệ ON THE GENERATION AND SELECTION OF SEQUENCES FOR SPREAD SPECTRUM WATERMARK AND STEGANOGRAPHY Nguyen Le Cuong* Abstract: In this contribution, criteria for the sequences employed in spread spectrum (SS) watermarking and steganography are discussed These criteria are: sharp autocorrelation function (ACF), large linear complexity (LC), large length (L), normal distribution assumption and bi-polar The reasons for choosing those criteria and the methods for generating and evaluating sequences satisfying them are explained and analyzed via the so-called D-transform, as a result, these sequences can be represented in a hardware-oriented form Some simulation results are also referenced to demonstrate outstanding features of generated sequences such as very good auto-correlation function (ACF) and large linear complexity (LC) for watermarking and steganography Keywords: Nonlinear sequences, Spread spectrum watermark, Steganography INTRODUCTION Along with the digitalization of media assets, the rapid growth of the Internet, and the speed of file transfers, the danger of intellectual right violation become obvious Therefore, it is necessary to have mechanisms to protect these digital assets and associated rights In this regard, digital watermarking is considered as an effective measure against the illegal copies of images, music titles, and video films In the digital watermarking process the information such as hidden copyright notices or verification messages are added to the cover media like digital images, audio/video or documents signals, to protect the ownership rights These hidden messages consist of a group of bits giving information about the author of the signal or the signal itself In the last decade, the spread spectrum communications (CDMA, HSPA) has developed rapidly, this concept has been borrowed not only successfully for watermarking [1-11] But also widely applied beyond cryptography like: RFID, EPC, BARCODE [12,13] and anti-jamming, protective jamming [14,15] In the above-mentioned applications the following merits of the sequences are most desired: Sharp ACF Large linear complexity (LC) Large length (L) Normal distribution assumption Bi-polar This fact is obviously an encouraging motive for carrying out an in-depth study on nonlinear sequences satisfying those demands As we already know, in spread spectrum communication a narrow-band signal is spread and then transmitted over a much larger bandwidth such that the signal energy presented in any signal frequency is undetectable That effect is caused by the following process: The transmitter first modulates the data signal with a carrier signal, and then spreads the modulated signal, by applying modulo-2 addition to it with a spreading signal The spreading signal is generated from a PN sequence running periodically at a much higher rate than the original data signal On the receiving end, the receiver first performs a correlation process on the incoming signal, that is, it applies the modulo-2 addition to the incoming signal with a synchronized copy of the spreading signal so that the original data signal is recovered in original bandwidth At the same time, the identical modulo-2 addition in the receiving end will Tạp chí Nghiên cứu KH&CN quân sự, Số 53, 02 - 2018 49 Kỹ thuật điều khiển & Điện tử spread out the power of the interference, which is supposed to be narrowband and therefore provides interference rejection for the SS signal hence will increase the receiving signal-to-noise (SNR) of the signal of interest Similarly, a watermark is spread over many frequency bins so that the energy in one bin is very small and certainly undetectable if the spreading sequence is not known Since the location, the spreading sequence and the content of the watermark are known to the watermark verification process, it is possible to concentrate these weak signals into a single output with high SNR thank to the so-called processing gain It is worth to make the remark that the correlation process is not only applied in spread spectrum watermark (ss watermark) but widely used in other watermark schemes [16-19] Without going into the details of the watermarking process we concentrate on the issue of appropriate sequences selection The paper is organized as follows: at the end of this section, we will review the related work in spread spectrum watermarking process The preliminaries are represented in next section In the next section, attention will be paid to the: design and analysis issues However, due to the constraint scope of the paper, only the correlation and linearity analysis, which is the most important property in watermarking, is discussed The remaining requirements (robustness against attacks, balance…) will be discussed later in other contributions In the last section, some comparisons and conclusions are given It is clear that spread spectrum watermark is closely related to spreading sequences The sequences with above-mentioned properties have been widely used to improve the attributes of the watermarking process (image as well as audio watermarking) In the DCT domain, the popular direct-sequence spread-spectrum watermarking approach is employed because such spreading gives a robust but invisible watermark and it allows various types of detectors for blind watermark extraction [1] The PN sequence is generated by a pseudorandom noise generator which has been initialized with a seed that depends on the secret key, which significantly improves the robustness of the system This key is known only to the legal owner of the watermarked document and without it the generation of the watermark at the receiver is impossible Furthermore, the spreading sequence must have noise-like properties in order to spread the spectrum of the input signal In other words, the mean of the sequence should be precisely zero and its autocorrelation should approach the delta function Consequently, a bi-polar pseudorandom sequence which takes the values, with relative frequencies 1/2 each will be the suitable candidate for this choice [2, 3] In order to survive the attack better, the nonlinear sequences are also introduced [4, 5] There have been also a proposal for employing PN key or PN sequences for copyright protection steganography [6, 7] However, the correlation properties are somehow relaxed or not sufficiently discussed PRELIMINARY The watermark detection, in general, is based on the correlation analysis (not only for spread spectrum watermark) because the correlation is crucial for noise removing which plays a decisive role in signal quality [8-11,17-19] Therefore, in this paper we insist on the finding PN sequences with spiky ACF and high LC value We measured the similarity between the original watermark and the watermark extracted from the attacked image using the correlation factor given below: N wi wˆ i ˆ (w,w) i 1 N wi i 1 50 N wˆ i i 1 Nguyen Le Cuong, “On the generation and selection of … watermark and steganography.” Nghiên cứu khoa học công nghệ Where N is the number of pixels in the watermark, w and w are the original and the extracted watermarks respectively The correlation factor may take values {0,1} In general, a correlation coefficient of about 0.75 or above is considered acceptable.This correlation factor can also be taken as a measure of robustness [17] In many papers The Structural similarity.index measure SSIM based on Normal correlation factor is widely used and defined as: h w ˆ ij w ij w SSIM i 1 j 1 h w ˆ ij w ij w i 1 j 1 The Structural Similarity Index Measure (SSIM) is closely related to PSNR (peak signal to noise ratio): 2552 SSIM PSNR 10log10 10log10 1 SSIM 2 Where σ is covariance between Wij and W*ij For more details please see [16-19] It is clear that correlation property is no doubt the first preference for the sequence selection in watermark and steganography DESIGN AND ANALYSIS ISSUES 3.1 The combinatorial approach Since there is a one-to-one correspondence between cyclic difference sets and almost balanced binary sequences with the autocorrelation property [20-23], the constructing all cyclic difference sets is equivalent to finding all almost-balanced binary sequences with the desired autocorrelation property This problem has been thoroughly discussed and reported in the literature so that we just give a short reference here Definition - cyclic difference set (CDS) [20, 21]: A set of distinct integers D = {d1, d2, …, dk} modulo an integer υ is called integer difference set or difference set denoted by (υ, k, λ) if every integer b ≠ (mod υ) can be expressed in the exactly λ way in the form di dj ≡ b (mod υ), where di, dj belong to the integer set D Example 1: i j 9 10 5 10 D = {1,3,4,5,9} is a (11, 5, 2) – difference set λ=2 It is well known that CDS characteristic sequence of period υ defined by: 0 for t D s(t)= 1 for t D (1) Has the two-level autocorrelation function for 0(mod ) Rs ( ) otherwise 4(k ) Tạp chí Nghiên cứu KH&CN quân sự, Số 53, 02 - 2018 (2) 51 Kỹ thuật điều khiển & Điện tử Example 3.2: Consider a CDS(15,7,3), and D = {0 5-7 10,11-13,14} The corresponding sequence S(t) determined by (1) is: 011110101100100 and has a twolevelled ACF Definition 2- CDS with Singer parameters [22-23]: Cyclic difference sets in GF(2n) with Singer parameters are those with parameters (2n – 1, 2n – – 1, 2n − − 1) for some integer n or their complements Sets of sequences with Singer parameters are: q-ary msequences, q-ary GMW sequences, and q-ary cascaded GMW sequences and they are having interleaved structure and ideal two-level ACF [24] Example 3.3: The GMW or m-like sequence [20,25]: {bi}={0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0,1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0,1,1,0,1,0, 0,0,0,1,0,0,0,1,0,1,1,0,1,1,1,1,1,1,0,1} has ideal two level ACF 3.2 D-transform for interleaved sequences Since most of the sequences with ideal ACF are having interleaved structure, time multiplexing technique is very useful tool for analyze them In technical term, interleaving is nothing but time multiplexing, which is very well known to telecommunication engineers and is traditionally represented via delay operation (D-transform) [25] [26] Definition 4: The D-transform of a sequence {bi} over GF(p) is denoted by D[bi] or F and designed by: ∞ bi Di D[bi ] = F = (3) i=1 For example, let {bi} = 010111, D-transform of bn is D(bi) = D + D3 + D4 + D5 The inverse transform of D is D-1 = {bi} The D-transform of the generator sequence {bi} of a linear feedback shift register (LFSR) is then given by: S(D) b(D)= (4) G(D) Where G(D) of degree n is the generating polynomial of an LFSR and S(D) of degree ≤ n-1 specifies the initial condition corresponding to a particular shifted version of {bi} 3.3 Shift sequences (interleaving orders) by D-transform Since interleaving process and D-transform are both sort of time multiplexing [25,26] one can easily derive the multiplexing (interleaving) order ITp straightforwardly Example 3.5: Let m = 3, n = and let α be a primitive element of GF(26) with primitive polynomial b(D) = D6 + D5 + over GF(2) Let {bi} denote the m-sequence generated by b(D): {bi} = {0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0} Decimation of {bi} by T = 9, we obtain {ai} = {bi} and rearrange in time multiplexing manner as: 011111101 010110011 011101101 001001110 001011110 010100011 000010000 52 Nguyen Le Cuong, “On the generation and selection of … watermark and steganography.” Nghiên cứu khoa học công nghệ We can see that the columns are time multiplexing order (shift sequences) ITp = {∞,5,3,5,6,3,3,2,5}, where ∞ represents Null sequence 3.4 Correlation analysis of PN sequences designed for watermark and steganography As it has been shown in [24, 25, 27] ACF of PN sequences is closely related to ITp and can be intuitively demonstrated like this: (a) (b) Fig Correlation matrix of (a) GF(2 ) = + d2 + d3 + d4 + d8 with = {Inf, 2, 4, 2, 8, 12, 4, 0, 1, 9, 9, 14, 8, 5, 0, 3, 2}, (b) GF(28) = + d + d3 + d5 + d8 with IpT = {Inf, 5, 10, 8, 5, 6, 1, 3, 10, 3, 12, 11, 2, 2, 6, 9, 5} It is clear that in order to ensure the best ACF of the sequence there must be only one coincidence position, denoted by Yellow ‘0’ in each diagonal of the ACF (ITp ) matrix In other words, the interleaved sequence and its shift version presented by ITp have only one position where subsequences are exactly in the same phase 3.5 Linear complexity analysis of PN sequences designed for watermark and steganography LC can be defined in many ways: The linear complexity of a sequence S is equal to the degree of the minimal polynomial generates the sequences; In trace representation method the linear complexity is determined by the minimum number of terms in its trace function expression; In D-transformation the linear complexity can be calculated by Euclid algorithm Let S(t)=S(0),S(1),…S(L-1) be a binary sequence of period L and define the sequence polynomial(similar to D-transform) S(x) = S(0)+S(1)x+S(2)x2+…+S(L-1)xL-1 Then, its minimal polynomial is determined as follows: Tạp chí Nghiên cứu KH&CN quân sự, Số 53, 02 - 2018 53 Kỹ thuật điều khiển & Điện tử ms (x) x L 1 gcd(x L 1,S(x)) (5) And its linear complexity is LCs = L-deg(gcd(xL-1,S(x))) Where gcd(xL-1,S(x)) denotes the greatest common divisor of xL-1 and S(x) According to [22-27], Linear Complexity can be calculated by: Trace function representation [22-24]; D-transformation (Euclid algorithm and DFT (discrete Fourier Transform)) [25-27] Below tables show simulation results of LC for different sequences: Table LC for sequences in GF(210) with subsequences in GF(25) GF(25) STT GF(210) 101001 100101 111101 101111 111011 110111 10010000001 20 40 10 80 40 20 10000001001 40 20 80 10 20 40 11011000001 40 20 80 10 20 40 10000011011 20 40 10 80 40 20 11100100001 20 40 10 80 40 20 10000100111 40 20 80 10 20 40 10110100001 20 40 10 80 40 20 10000101101 40 20 80 10 20 40 10100110001 20 40 10 80 40 20 10 10001100101 40 20 80 10 20 40 11 11110110001 80 10 20 40 40 20 12 10001101111 10 80 40 20 20 40 13 11010001001 40 20 20 40 10 80 14 10010001011 20 40 40 20 80 10 15 10100011001 40 20 20 40 10 80 16 10011000101 20 40 40 20 80 10 17 11101011001 40 20 80 10 20 40 18 10011010111 20 40 10 80 40 20 19 11100111001 20 40 40 20 80 10 20 10011100111 40 20 20 40 10 80 21 11001111001 20 40 40 20 80 10 22 10011110011 40 20 20 40 10 80 23 11111111001 20 40 40 20 80 10 24 10011111111 40 20 20 40 10 80 25 10110000101 10 80 40 20 20 40 26 10100001101 80 10 20 40 40 20 27 11000100101 40 20 20 40 10 80 28 10100100011 20 40 40 20 80 10 29 10111100101 80 10 20 40 40 20 30 10100111101 10 80 40 20 20 40 31 11000010101 20 40 40 20 80 10 32 10101000011 40 20 20 40 10 80 33 11101010101 80 10 20 40 40 20 34 10101010111 10 80 40 20 20 40 54 Nguyen Le Cuong, “On the generation and selection of … watermark and steganography.” Nghiên cứu khoa học công nghệ STT 35 36 37 38 39 40 41 42 43 44 45 46 47 STT 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 GF(25) 101001 100101 111101 101111 111011 110111 11010110101 20 40 10 80 40 20 10101101011 40 20 80 10 20 40 11110001101 80 10 20 40 40 20 10110001111 10 80 40 20 20 40 11101001101 40 20 20 40 10 80 10110010111 20 40 40 20 80 10 11100011101 40 20 80 10 20 40 10111000111 20 40 10 80 40 20 11101111101 80 10 20 40 40 20 10111110111 10 80 40 20 20 40 11011111101 40 20 20 40 10 80 10111111011 20 40 40 20 80 10 11001000011 20 40 10 80 40 20 12 Table LC for sequences in GF(2 ) with subsequences in GF(2 ) and GF(23) GF(24) GF(23) GF(212) 11001 10011 1101 101 1100101000001 108 12 48 12 1000001010011 12 108 12 48 1001011000001 108 12 12 48 1000001101001 12 108 48 12 1101111000001 12 108 48 12 1000001111011 108 12 12 48 1011111000001 12 108 48 12 1000001111101 108 12 12 48 1001100100001 12 108 12 48 1000010011001 108 12 48 12 1000101100001 108 12 12 48 1000011010001 12 108 48 12 1101011100001 108 12 48 12 1000011101011 12 108 12 48 1110000010001 108 12 12 48 1000100000111 12 108 48 12 1111100010001 108 12 12 48 1000100011111 12 108 48 12 1100010010001 108 12 48 12 1000100100011 12 108 12 48 1101110010001 12 108 48 12 1000100111011 108 12 12 48 1111001010001 108 12 48 12 1000101001111 12 108 12 48 1110101010001 12 108 12 48 1000101010111 108 12 48 12 1101011010001 12 108 12 48 1000101101011 108 12 48 12 1010000110001 108 12 12 48 GF(210) Tạp chí Nghiên cứu KH&CN quân sự, Số 53, 02 - 2018 55 Kỹ thuật điều khiển & Điện tử STT GF(212) 30 31 1000110000101 1100110110001 GF(24) 11001 12 12 GF(23) 10011 108 108 1101 48 48 101 12 12 The following conclusion can be drawn: whilst the ACF remain the same in all kind of interleaving, the LC spectrum shows a significant difference That means we can expect that the SSIM and PSNR are almost the same for all chosen sequences and pay more attentions to the robustness against Massey-Berlekamp attack 3.6 Rise the security to GPS and military level For this purpose, PN sequences are two folded useful PN sequences are exploited to assign a certain amount of chips in a PN sequence to represent secret data [28] This approach will be discussed in another contribution In the context of secure wireless communications, Pseudo-noise (PN) masking technique has been proven to be an effective technique against unauthorized data collection (eavesdropping) Typical examples of PN masking technique are military-grade communications and global-positioning systems (GPS) [28,29] In fact, in a PN-masked secure SS embedding approach, the embedded SS signal is scrambled by random-like PN masks such that no subspace of embedded signal can be found and tracked in the dataembedded host Thank to scrambling process (randomization) in SS embedding scheme, the performance in terms of recovery bit-error-rate (BER) at the intended receiver is maintained at almost the same level (since the ACF of scrambled data is as good as that of the conventional SS embedding (i.e almost no performance loss), while the unauthorized users will have BER close to 0.5 (i.e almost perfect security) due to a high spike in crosscorrelation (see fig Since the proposed PN masked SS embedding schemes can efficiently minimize the likelihood that embedded data are "stolen" by the unauthorized users, they are suitable for the applications with high-security requirements, such as steganography and covert communications With random-like PN-masked carriers, the SS signal of interest behaves like white noise and no subspace of embedded signal (e.g statistic distribution) can be tracked from the observation data Therefore, PN masked SS embedding in can efficiently prevent illegitimate data extraction by unauthorized users who have no knowledge of PN masks Mathematically, the whitening effect can be explained like this 3.7 {1} and {0} distribution Let {O} be the output signal of the scrambler, {I} be the input sequences (embedded SS signal generating forced response) and {u} represents LFSR sequences (free response) The probabilities of '0' and '1' bits in {O} are Po(0) and Po(1) respectively The probabilities of '0' and '1' bits in {I} are PI(0) and PI(1) respectively Similarly, the probabilities of '0' and '1' bits in {u} are PU(0) and PU(1), respectively Since scrambler is a linear system in GF(2n), we can apply the superposition rule and have: O I u So, the probability of '1' in {O} equals the probability of '1’ in XOR – operation: P0 (1) PI (1).Pu (0) PI (0).Pu (1) Since {u} satisfies the balance condition ,we get: Pu (1) Pu (0) Under the assumption that {I} and {U} are statistically independent, we have: 56 Nguyen Le Cuong, “On the generation and selection of … watermark and steganography.” Nghiên cứu khoa học công nghệ or 1 1 P0 (1) PI (1) PI (0) PI (1) PI (0) 2 2 P0 (1) P0 (0) So, any input sequence with unbalanced distribution will become balanced (noise-like) 3.8 ACF ACF of {O} in binary form is calculated as: R(k ) A D A D Where, A and D are the agreement and disagreement positions between {O} and its shift version respectively So, ACF is: R(k ) A D A D 2D D 1 P0 (1) A D A D A D In other words, {O} looks like noise with: P0 (1) P0 (0) R(k ) And following simulation results in [30] showed the randomization effect of scramblers: Fig ACF of nonlinear PN sequence generated by polynomial of degree 12 Fig CCF between two sequences Tạp chí Nghiên cứu KH&CN quân sự, Số 53, 02 - 2018 57 Kỹ thuật điều khiển & Điện tử CONCLUSIONS AND FUTURE WORKS The spiky ACF of nonlinear sequences ensure the good quality of embedding and extracting processes both in watermark and steganography Since the LC spectrum is widespread, it is important to select the right sequences The differences in LC may be as high as n.100 or even n.1000 This fact will surely affect the robustness of watermark and steganography In order to increase the security of watermark and steganography to the higher level (military or GPS), nonlinear PN sequences can be used as masking sequences.The large values of LC ensure the resistance against Berlekamp–Massey algorithm attack PN masked SS embedding in can efficiently prevent illegitimate data extraction by unauthorized users who have no knowledge of PN masks Mathematical tools for finding out the desired sequences are also represented via Dtransform, a hardware-oriented method and any input sequence with unbalanced distribution will become balanced (noise-like) by the randomization effect of scramblers We hope, in the future contributions, the process for choosing the right interleaving will be addressed in details In our opinion, the application of nonlinear interleaved sequences in steganography and cryptography fully deserves the attention of academic circle REFERENCE [1] [2] [3] [4] [5] [6] [7] [8] [9] 58 Ashok Patel, Bart Kosko, “Noise Benefits in Quantizer-Array Correlation Detection and Watermark Decoding,” IEEE Transactions on signal processing, Vol 59, No 2, February 2011, pp 448-505 Alexia Briassouli and Michael G Strintzis, “Locally Optimum Nonlinearities for DCT Watermark Detection,” IEEE Transactions on image processing, Vol 13, No 12, December 2004, pp 1604-1617 X Kang, J Huang, and W.Zeng, “Improving Robustness of Quantization-Based Image Watermarking via Adaptive Receiver,” IEEE Transactions on Multimedia, Vol 10, No 6, October 2008, pp 953-959 Al-Rawi1.S.S, Sadiq.A.T, Farhan B.G, “Digital Video Quality Metric Based on Watermarking Technique with Gaffe Generator,” Computer Science and Engineering 2012, 2, pp 138-146 T Rachwalik, J Szmidt, R Wicik, and J Zabłocki, “Generation of Nonlinear Feedback Shift Registers with special-purpose hardware,” Military Communication Institute Poland 2012 P Senatore, “A Blind Video Watermarking Algorithm for Copyright Protection based on Dual Tree Complex Wavelet Transform", Journal of Information Hiding and Multimedia Signal Processing, November 2006, pp 1147-116 Rizky M Nugraha, “Implementation of Direct Sequence Spread Spectrum Steganography on Audio Data,” 2011 International Conference on Electrical Engineering and Informatics, 17-19 July 2011, Bandung, Indonesia Sudip Ghosh, Somsubhra Talapatra, Debasish Mondal, Navonil Chatterjee, Hafizur Rahaman and Santi P Maity, “VLSI Architecture for Spread Spectrum Image Watermarking using Binary Watermark,” IEEE International Conference on Advances in Computing and Communications(ICACC), from 9-11 August 2012 at Rajagiri School of Engineering & Technology, Cochin, Kerala, India, Pp.166-169, 2012 Sudip Ghosh, Somsubhra Talapatra, Debasish Mondal, Navonil Chatterjee, Hafizur Rahaman and Santi P Maity, “VLSI Architecture for Spread Spectrum Image Watermarking using BinaryWatermark,” IEEE International Conference on Nguyen Le Cuong, “On the generation and selection of … watermark and steganography.” Nghiên cứu khoa học công nghệ [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] Advances in Computing and Communications(ICACC), Kerala, India, pp.166169, 2012 Sudip Ghosh, Somsubhra Talapatra, Navonil Chatterjee, Santi P Maity and Hafizur Rahama, “FPGA based Implementation of Embedding and Decoding Architecture for Binary Watermark by Spread Spectrum Scheme in Spatial Domain,” Bonfring International Journal of Advances in Image Processing, Vol 2, No 4, December 2012 1-8 Dubreuil & T P Berger Universite de Limoges Spread Spectrum, “Cryptography and Information Hiding”, Departement de Mathematiques, FRANCE 2011 Joan Melia-Segu, “Multiple-Polynomial LFSR based Pseudorandom Number Generator for EPC Gen2 RFID Tags,” Universitat Oberta de Catalunya Spain 2010 A.Mitrokotsa, M.R.T.Beye, P.PerisLope, “Classification of RFID Threats based on Security Princip”, TU Delft 2011 Christina Popper, “Jamming-resistant Broadcast Communication without Shared Keys”, Usenix Security Symp 2009 Christina Popper, “Anti-jamming Broadcast Communication using Uncoordinated Spread Spectrum Techniques", IEEE Journal on Selected Areas in Communications, Vol 28, No 5, June 2010, pp 1-13 Alan C Brooks, Xiaonan Zhao Thrasyvoulos N Pappas, “Structural similarity quality metrics in a coding context: exploring the space of realistic distortions,” IEEE Transactions on image processing, Vol 17, No 8, August 2008, pp 1-13 Alain Horé MOIVRE, Djemel Ziou, “Image quality metrics: PSNR vs SSIM", International Conference on Pattern Recognition, 2010 Baisa L Gunjal, Suresh N Mali, “ROI Based Embedded Watermarking of Medical Images for Secured Communication in Telemedicine World Academy of Science,” Engineering and Technology, Vol 6, No 8, 2012, pp 997 -1002 Ali Al-Haj, “Combined DWT-DCT,” Digital Image Watermarking Journal of Computer Science (9): 740-746, 2007 B Gordon, W H Mills and L R Welch, “Some new difference sets,” Canad J Math., Vol.14, 1962, pp 614–625 L D Baumert, “Cyclic Difference Sets,” Lecture Notes in Mathematics, Springer Verlag 1971 J Kim and H.Y.Song, “Existence of Cyclic Hadamard Difference Sets and its Relation to Binary Sequences with Ideal Autocorrelation,” Journal of Communications and Networks, Vol.1, No.1, MARCH 1999, pp 14-18 S W Golomb and G Gong, "Signal Design for Good Correlation - for Wireless Communication, Cryptography and Radar", Cambridge University Press, 2005 C.-Y Lai and C.-K Lo, "Nonlinear orthogonal spreading sequence design for third generation DS-CDMA systems", IEE Proceeding Communication, Vol 149, No 2, 2002, pp 405-410 Hieu L M., Quynh L C., “Design and Analysis of Sequences with Interleaved Structure by d-Transform,” IETE Journal of Research, Vol 51, No l, pp 61-67, Jan Feb 2005 Massey, J L., Serconek, S., “Linear complexity of periodic sequences: a general theory,” In Proc Advances in Cryptology – CRYPTO ’96, Lecture Notes in Computer Science 358–371 Cuong N L., “A comparative study on some mathematical tools used in design and analysis of interleaved sequences”, Journal of Science and Technology, Nov 2016 Tạp chí Nghiên cứu KH&CN quân sự, Số 53, 02 - 2018 59 Kỹ thuật điều khiển & Điện tử [28] Taeho Kang, Xiang Liu, “Survey of Security Mechanisms with Direct Sequence Spread Spectrum Signals”, Journal of Computing Science and Engineering, Vol 7, No 3, September (2013) 187-197 [29] Ming Li, Yanqing Guo, Bo Wang, “Xiangwei Kong, Secure spread-spectrum data embedding with PN-sequence masking”, Signal Processing: Image Communication 39 (2015), pp 17–25.c [30] Thanh N.V, Quynh L C, “Multi Access Interference in CDMA and WCDMA Systems”, Master thesis, Hanoi University of Technology, 2013 [31] S P Maity, M K Kundu, “Performance Improvement in Spread Spectrum Watermarking Using Wavelets”, International Journal of Wavelets, Multi resolution and Information Processing, Vol 9, No (2011) 1–33 TÓM TẮT TẠO VÀ LỰA CHỌN DÃY CHO WATERMARKING TRẢI PHỔ VÀ STEGANOGRAPHY Bài báo đề xuất thảo luận tiêu chuẩn cho dãy sử dụng watermarking trải phổ steganography Những tiêu chuẩn bao gồm: hàm tự tương quan (ACF) nhọn, độ phức tạp tuyến tính (LC) cao, độ dài (L) lớn, phân bố chuẩn tính lưỡng cực Các lý cho việc lựa chọn tiêu chuẩn phương thức cho việc tạo đánh giá dãy thỏa mãn tiêu chuẩn giải thích phân tích việc sử dụng phép biến đổi D, đó, dãy biểu diễn dạng định hướng phần cứng Một số kết mô dẫn chứng để minh minh họa cho tính chất bật dãy tạo như: hàm tương quan (AFC) tốt độ phức tạp tuyến tính (LC) lớn nhằm sử dụng watermarking steganography Từ khóa: Dãy phi tuyến, Watermark trải phổ, Steganography Received date, Dec 26th, 2017 Revised manuscript, Jan 30 th, 2018 Published, Feb 26 th, 2018 Address: Electric Power University * Email: cuongnl@epu.edu.vn 60 Nguyen Le Cuong, “On the generation and selection of … watermark and steganography.” ... into the details of the watermarking process we concentrate on the issue of appropriate sequences selection The paper is organized as follows: at the end of this section, we will review the related... later in other contributions In the last section, some comparisons and conclusions are given It is clear that spread spectrum watermark is closely related to spreading sequences The sequences. .. sequence is not known Since the location, the spreading sequence and the content of the watermark are known to the watermark verification process, it is possible to concentrate these weak signals into