The Quality of the New Generator Sequence Improvent to Spread the Color System ’ s Image Transmission

This paper shows a new technic applicable for the digital devices that are the result of the finite’s effect precision in the chaotic dynamics used in the coupled technic and the chaotic map’s perturbation technics used for the generation of a Pseudo-Random Number Generator (PRNGs).The use of the pseudochaotic sequences coupled to the orbit perturbation method in the chaotic logistic map and the NewPiece-Wise Linear Chaotic Map (NPWLCM). The pseudo random number generator’s originality proposed from the perturbation of the chaotic recurrence. Furthermore the outputs of the binary sequences with NPWLCM are reconstructed conventionally with the Bernoulli’s sequences shifts map to change the shapes with the bitwise permetation then the results in simulation are shown in progress.After being perturbed, the chaotic system can generate the chaotic binary sequences in uniform distribution and the statistical properties invulnerable analysis. This generator also has many advantages in the possible useful applications of spread spectrum digitalimages, such as sensitive secret keys, random uniform distribution of pixels in Crypto system in secure and synchronize communication.


Introduction
The chaotic secure communication is one important application of chaos theories .So how can we secure and synchronize a communication system in using the chaotic system with the direct spread spectrum sequence (DS-SS)?Initially in the field of the chaotic secure communication we've two types of the chaotic encryption systems: one is the analogue chaotic secure system based on the chaotic synchronization.The other is the digital encryption system based on the chaotic pseudo-random sequence [3] with many uses as in the military communication [2].The pseudo chaotic generations sequences of the random numbers based on a chaotic map are important in every aspect of the hiding information whith the cryptography [1] and the spread spectrum [4].A random number generator (RNG) is a deterministic algorithm that seed outputs a longer sequence on in put that are computationally distinguishable from an uniform chosen random sequence.Different methods exist for generating chaotic sequences of the chaotic map's type.It is the logistic map which is the most studied discrete nonlinear map has been used in many scientific fields.Also this discrete map has a known mathematic distribution.Here also the logistic map makes a good parameter for using in the designs of the random bits generators.In the Chaotic spread spectrum communication systems a different user can be assigned to different generated sequences.
A number of the spreding technics images have been proposed-including the chaosbased image spreding-to provide a better solution for the security problem of the digital image.These technics give a good combination of speed and security.The use of the chaotic sequence as the spreading sequences has been proposed as it must seem absolutely random.These generator's (CPRNG) chaotic pseudo-random number has been analyzed in [5].So we need a digital chaotic generator with important cryptographic properties such as balance on {0, 1} long-cycle length, high linear complexity, like function of the auto-correlation and the function cross-correlation near to zero [6].According to these properties, chaos sequence can be used as the random numbers generator.One of the simple systems are used to generate chaotic sequence is in the logistic map [7].The digital new system implementation gave more problems TELKOMNIKA ISSN: 1693-6930  The Quality of a New Generator Sequence Improvent for Spreading the… (Mohamed Krim)

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because of the finite precision of the digital representation.The methods have been proposed to find out the problems of the finite representation [8].In this study we followed this condition: The cascading of several chaotic systems: the improvement is not significant because it gets another chaotic function that will in turn have the specific problems in the finite representation.The application of a perturbation presents an efficient solution to avoid redundancy in the cycles of the chaotic sequences.Several sources of disturbance are used for this purpose, such as the linears feedback shifts registers (LFSRs) .The number of the sequence generated by (LFSR) may be insufficient to wideband the direct spread spectrum sequence (DS-SS ( in a very large number of users [7].Also the LFSR technics provide particular flexibility in incorporating security into multiple user systems [9].The study in the non-linear dynamical system has developed the chaotic theories.This last is caracterized by: a well done function of the auto-correlation by spreadingas uniformal as, bya cycle of the maximal lenght which is the Hardwar implementation orthe easy device [9].Practicly ananalysis of the periodicity of chaotic requires full search over all possible initial values [31].With these proprities; we propose chaos function can be used as a random number generator [11]- [12].Indeed the chaos's properties functions ensure the properties of the chaotic sequence such as the sensitivity determined in the initial values and the control parameters.They are used for the different applications such as: pseudo-random sources, communications and securities.These generators gave the pseudo-chaotics sequences and have a uniform distributed with long orbites.The proposed generator is done with structures that integrate a random technic and the copling technics between the perturbed chaotics maps in ordering the newpiece-wise linear chaotic map (NPWLCM), Bernoulli map.This technic improves randomness of the generated sequence but causes a down value speed performance.We established a chaotic pseudo number generator based on three weakly-coupled discrete chaotic maps perturbed in ordering the new (NPWLCM), Bernoulli map combined with permutation Bitwise (XOR) technic.Testing of algorithm was done based on the spreding and despreding average time, size of the key space, and the key sensitivity analysis.Beside that, we conducted a randomness analysis of the key stream which generated by these algorithm, and uniform distribution analysis of pixel values in the color images that has been spreding.Our algorithm provides very important tests stastics the peak of the signal-to-noise ratio (PSNR) and the Mean in the similarity structure (MSSIM).The best solution of the system of the finite precision of the digital chaotic.
The proposed name for the technic is the direct spread spectrum's sequence based on the cryptography.The second is descuted according to the method of the synchronization of the chaotic systems for the information's transmission applications.This synchronization approach is then used in a new pattern of the chaotic secure communication, which aims to increase the number and the amplitude of the transmitted messages and to improve the level of the security and robustness in the communication channel existed noise.

The Spread Spectrum Direct Sequence (DS-SS)
The spread spectrum's direct sequence is one of the spread spectrum technics.Eventually a pseudo random sequence code symbols called (Chips) isused for the direct sequence code division multiple access (DS-CDMA) systems, but it lacks in the security due to the fact that there are a limited number of an available pseudo random sequence generator and they show the periodic correlation properties.A DS-ss system is the most common version usede today due to the simplicity implementation.In actual practice the base band informations digitized and Modulo-2 added to the code sequence and then modulated by Binary Phase-Shift Keying (BPSK) [7], [13]- [14].System as illustrated in Figure1.
They are in these processes: a.The pseudo-random sequence generator to spread the input signal.b.The spreading is given the signal-spread for a Larger Band.
The despeeding processes are similar to the speeding processes but inreverse order.This dispread signal 0 () Nb an is writen by equation ( 2) :

The Dynamic Modeling System (DMS)
The Dynamic Modeling System (DMS) has been used as a method of synchronization and generating sequence in this section .At the beginning the main idea of the based method dynamic system is given then a menu method for the initial condition perturbation for the chaotic is proposed and its performance is also shown in he Dynamic Modeling System (DMS).

The Chaotic Dynamic Secret Keys Generator
The finite precision's effect of the of the chaotic dynamics aim to use two technics: the coupling and the perturbation chaotic orbit's technic.The first technic effectively allows an expansion of the cycle length but without any control.The second technic allows not only a long cycle, but also imposing a minimum cycle length directly dependenty on the disturbance signal.This section is a new algorithm to generate random binary sequence (RBSG), using the-New Piece Wise Linear Chaotic Map-(NPWLCM) coupling with the logistic maps.Figure .2shows the structure of the dynamic Secret Keys generator proposed [14].

The Perturbation Principles
This section is a new algorithm to generate random binary sequence (RBSG), using the -New Piece Wise Linear Chaotic Map-(NPWLCM) combined with the block perturbation and is introduced.The structure the Figure 2 is composed by a new algorithm to generate pseudo chaotic the -New Piece Wise Linear Chaotic Map-(NPWLCM) -a generator bloc about perturbation which role is to disrupt the orbit of the chaotic generator allowing it to access a new orbit and to establish synchronization based symbolic dynamics between transmitter and receiver and an effective solution to avoid redundancy and expand the cycles in the chaotic sequences.The Quality of a New Generator Sequence Improvent for Spreading the… (Mohamed Krim) The input parameter for generating the matrix secret key is considered with the one seed input secret as a key K 0 .So based on the value of K 0 a set of secret keys are generated using a combination of the logistic map and -New Piece Wise Linear Chaotic Map-(NPWLCM) In this value of K 0 , the initial condition Step 2: Generator chaotic the New pice-wise linear chaotic map (PWLCM), x(n) is used to : x n x n i (4) Step 3: Generate the key stream Step 4: The output sequence function the in length (L) are automatically generated and will be transformed into the binary sequences {0,1}.

Generate of the Binary Sequence
The proposed method consists of the following steps: First, the sequence {X n } is generated by the chaotic map method which must be amplified by a scale factor (n') and to integer part subsequence .
  method, we can use floor (f(x)) in matlab software [5,6].The resulting sequence B n has a finite level equal to (m') defined over (mod m') and is transformed to the binary sequence as it is shown in Figure 3.The equation of the scheme is: We generate another   x n pseudo-random sequence B n of natural numbers n bit sequence given by the binary chaotic sequence encoding (LSB: Least Signification Bit).

The Chaotic Functions
The chaos has been successfully implemented in the analog communication systems following the work of Pecora and Carroll 1990 [8].The digital implementation gave more problems because of the finite precision of the digital representation.When the chaotic systems are represented with a finite precision, they become inevitably cyclic functions and their distribution and correlation deteriorate.The methods have been proposed to address the problems of the finite representation [8]: a. Cascading of several chaotic systems.b.Use of higher accuracy: brings significant improvements but the high cost of implementation.c.Disruption of the chaotic orbit.

The Chaotic Sequence Generator Bits
Various nonlinear of the dynamical systems are used to generate the chaotic sequence.All the chaotic systems must have following properties [15]: Sensitivity to the initial conditions, the topological mixing , the topological Ergodicity and the density periodic orbits.
The discrete-time of the dynamical systems is the particular type of the non-linear dynamical systems generally described as an iterative the map : Where n is the discrete-time,  k n xR  is the time's state system at n, while 1 n x  shows the next state and k is the dimension of the state-space.

The Used Chaotic Map
The applications of the logistic map all of them are about the image incryption [16].The properties of a logistic map can be quantitatively analyzed by methods of the statistical probability and the Lyponov exponent.Practically an analysis of the probability density of Logistic map sequences is not uniform [17].Prac Piece Wise Linear Chaotic Map-(PWLCM) is called also a tent map and Piece Wise Linear Chaotic Map-(PWLCM) can produce the pseudo random sequences with the good statistical properties even under the condition of finite word length computing [18].Piece Wise Linear Chaotic Map-(PWLCM) system has an uniform invariant distribution and good ergodicity so it can provide excellent random sequence, which is suitable for our cryptosystem, then to produce the pseudorandom sequences with good stastical prooprites [19].The characteristics of Piece Wise Linear Chaotic Map-(PWLCM) are suitable for the design system of encryption.It is reported that some findings on the new series of dynamical indicators that can quantitatively reflected in the degradation effects on a digital the Piece Wise Linear Chaotic Map-(PWLCM) realized with a fixed-point finite precision.The Bernouli shift is an algorithm that gives a complex chaotic behaviour .It is characterized by the exponential growth and disorder [20].Table 1 New Piece Wise Linear Chaotic Map (NPWLCM) Or frac: fractional part or   x ,λ>1 :frac(x) for  xR is defined a: Where x   is the floor function (i.e. the integer nearest to  ).The new piecewise linear chaotic map (NPWLCM maps) is given by:  Figure 5 showssample results (NPWLCM) sensitivity for two initial conditions a 200 iterations.The sensitivity of the initial value of chaotic specifically, for f (x) application begins with two initial values that are close, say (x) and (y) such that (a large amount), and generate the orbits of the first two points is given by: In this study the generation of the chaotic sequences is studied by analyzing the bifurcation diagram and in analyzing the Lyapunov Exponent (LE) also the Probability Density.a.The Lyapunov Exponent: The Lyapunov exponent (  L ) [23],of a 1D map x n+1 =f(x n ) is: As shown in Figure 6, Figure 7 and Figure 8 the sensitivity of the chaotic maps towards its initial value x 0 also indicates that: Depending on the value of (λ), the dynamic in the system can change attractively giving periodicity or chaos.A diagram of bifurcation is a visual summary in the succession of the doubling time shown: as (λ) increases.The probability density permits a determination of the spreading function F X [24]: The histograms of Figure 9 and  The structure of the proposed generator is shown in the Figure 12.The output are third of key K 1 ,K 2 ,K 3 .The first one the input data for generating matrix secret key K 1 is done with the one seed input secret key K 0 .Then based on the value of K 0 which is a set of secret keys is generated by using a combination of the logistic and the -New Piece Wise Linear Chaotic Map-(NPWLCM) methods.The second generating matrix secret key K 2 is done with the one seed input secret key K 0 .Then based on the value of K 0 a set of secret keys is generated by using a combination of the logistic and the first Bernoulli map (Bernoulli map (1)) chaotic map methods.The third generating matrix secret key K 3 is done with the one seed input secret key K 0 .After that based on the value of K 0 a set of secret keys which is generated by using a combination of logistic and second Bernoulli map (Bernoulli map (2)) methods of the chaotic map.Finally, the output of the chaotic sequence is given in ascending order and forms combined with the Following standard based with block non-linear Boolean functions with permutation Bitwise XOR block., Z→f i (seed x3 , λ 3).Setup 2:Permutation bitwise xor.The initial state is initialized with input with tow chaotic perturbed .We apply "X" stapes, where "X" is the bit size of the input of the input parameter "X"For each step i: Extract bit "i" form "X", If X[i]=0, apply the bitwise permeation WithY, The structure of our pseudo random number generator has been designed to be used as to the disturbance technic .Notice that the output of the proposed pseudo-random number generator depends on several chaotic recurrences.Also all the chaotic sequences intervening in the generation of the encoding sequences are transformed into the dynamic symbolic sequences which provide a partial description of the corresponding chaotic orbites.The dynamic symbolic sequences are difficult to locate their values.So that the observation of the used encrypting sequences does not provide any useful information.

The Spread Spectrum Color Image Resarch Method
An image spreading experiment is designed by using the proposed the algorithms system, where the generated chaotic sequence is employed to spread the image.Suppose that the size of RGB image is (M × N),or (M, N): The numbers of rows and column of pixels.The spreading processes as shown in Figure13 are described in the step 1 to step 5: Step 1: Firstly, we choose M=N=256.The color images are represented by three distincts color's of [25]: The red R; the green G and the blue B colors.
Step 2: The spreading of each color apart a color mixing step is used to mix data from different colors and to provide further confusion aspect in the resulting speeded image.

Evaluation's Criteria and Basic Experiment Simulation
The signal-to-noise ratio peak (PSNR) and the structural similarity (SSIM) are the evaluation of the qualities of the spreading image.Till here we have to know how to evaluate the image quality of the Pseudo Noise (PN) code.Let H(i 1 ,j 1 ) or H(i 1 =1,2,…,N ; j 1 =1,2,…,M) be the ideal image, S(i 1 ,j 1 ) or S(i 1 =1,2,…,N ; j 1 =1,2,…,M) be image in the Pseudo noise .The total difference is can be written as: The formula for the Mean Square Error (MSE) [26] is: The formula for the signal-to-noise ratio peak (PSNR) [27], [28] (17) The Structural Similarity Index (SSIM): The similarity compared the brightness, the contrast and the structure between every pair of vectors when the structural similarity (SSIM) between two Iimages (H) and (S) is given by the Equation (18) [27]- [28]:

The Experimental Results on Color Noisy Image Based on RGB Color Model
The applied proposed algorithms were : 1 st generator (New Piece-Wise Linear Chaotic Map (NPWLCM) combined with the block perturbation the logistic map). 2 nd generator( Bernoulli map combined with the block perturbation the logistic map).Three qualities and similarities measures (1 st generator, 2 nd generator and 3 rd generator) The Figure 35, Figure 36 and Figure 37 show the performance compared with execution: MSE, PSNR and MSSIM of the orginal and spreading image for the thres generated typs.These results are obtained with a noise RNS=0.01 to 25 bite-rates.An exponential decrease in Mean Square Error (MSE) is observed in Figure17 as the power increases in the first step.The15 db refers to a decrease in power; MSE is approaching oppositly nearly zero with 1 st generator, 2 nd generator and 3 rd generator.In the absence of noise the two images are identical, and thuse the MSE is Zero.In this case the PSNR is infinite(See Figure 16).The results obtained are also ploted in Figure 16 and 17 it is observed from the resulted images and data, the 3 rd generator is better than the other generators with the increase of the noise intensity.However the SSIM is better for the orginal one at some SNR .Then we are showing the comparaison forthe 1 st generator ,the 2 nd generator and the 3 rd generator algorithms .The experiments are performed with the 3 rd generator.The image spreading quality with the help PSNR is very simple as compared to SSIM.The efficiency of the proposed algorithm about the speeded image quality of the low bit-rate.It is shown that the difference in (PSNR, MSSIM) is greater and lower for the first algorithm, the second and the third algoritm.Hence the chaotic performance and the key size of the third (3 rd ) generator .These properties are suitable for different applications such as security.

Conclusion
Finally the obtained results are satisfactory in terms of the spreading quality's image.The digital communication system pseudo generator chaos is based in the (DS-SS) and is very important.They have different strong point and are equally important.They are based on a unique combination of the coupled technics and NPWLCM sequence of the perturbed logistic map which has been used the proposed system and must be protected from droppers in the case of the use of the different methods.All these features make the system robust and feasible to provide the required security in the synchronize communication system based for the digital sense of DS-SS system.

Figure 2 .
Figure 2. The first structure of the chaotic generator proposed (1 st generator)

Figure 3 .
Figure 3. Subclass generation of the binary sequence.

Figure 4
Figure 4 shows cobweb diagram (left) and time domain waveform (right) for the (NPWLCM).

Figure 5 . 409 Figure 8 .
Figure 5. Sample results (NPWLCM) sensitivity for two initial conditions a 200 iterations Figure 10 denote that the distribution of the Bernoulli map and New PWCLM density function have the better uniform distribution and have the better qualitative & quantitative properties.The Figure 11 has a bad distributed probability function which is required for random number generation.

Figure 9 .
Figure 9. Simulation of the probability density for the New PWCLM

Figure 12 .
Figure 12.The structure of the chaotic proposed generator (3 rd generator)

Step 3 :
This resulting data is show into the near 256 bit blocks(8 byte per block).Every pixel is represented in a given color by1 byte so we collect them one by one from one color to ISSN: 1693-6930  The Quality of a New Generator Sequence Improvent for Spreading the… (Mohamed Krim) 411 another using following mechanism.The first byte is the blue and is spread by multiplying it with a long sequence of PN (Pseudo Noise) code, each information bit contains a number ofchips (First spread of The 8 chips) to obtain the spreader image S R and first byte is the green which is spread by multiplying it with a long sequence of PN (Pseudo Noise) code.Each information of bit contains anumber ofchips (Second spread of The 8 chips S G ) that obtain the spreader image S G and the first bytes is thered spread by multiplying it with a long sequence of PN (Pseudo Noise) code .Each information of bit contains number of chips (Third spread of The 8 chips) and obtain the spreader image S B and then we'll take the second blue byte spread by multiplying it with first spread The 8 chips S R .The green byte spreads by multiplying it with Second spread of The 8 chips and red byte spread by multiplying it with Third spread of The 8 chips.Step 4: The signal spreding additive with the channel of the Additive White Gaussian Noise (AWGN).Step 5: The synchronously received sgnal (Ciperd-image).The despeeding processes are similar to the speeding processes but in reverse order.

Figure 13 .
Figure 13.Complete steps image spreading technic 3 rd generator (Describded in section 4.4) .In the test color image (JPEG)of size (256*256 x 3) encoded into 8 bpp of colors.The analysis shows the possibility of reducing the speeding chips so that the image quality remains acceptable.The result images are shown in Figure 14.The below results exist in MATLAB 7.2.

Figure 14 .
Figure 14.Original image andthe speeding image with different the signal-to-noise ratio (SNR).Three qualities and similarities measures (1 st generator, 2 nd generator and 3 rd generator)

Table 1 .
shows the formulat of the Piece Wise Linear Chaotic Map-(PWLCM), New Piece Wise Linear Chaotic Map-(NPWLCM) and Bernoulli's Shift Map.The Formulat of the Logistics Map, Piece Wise Linear Chaotic Map-(PWLCM), Piece Wise Linear Chaotic Map-(NPWLCM) and Bernoulli's Shift Map

Table 1 .
The Formulat of the Logistics Map, Piece Wise Linear Chaotic Map-(PWLCM), Piece Wise Linear Chaotic Map-(NPWLCM) and Bernoulli's Shift Map The Quality of a New Generator Sequence Improvent for Spreading the… (Mohamed Krim) 407 is: