In this paper we don’t simply integrate **chaotic** maps hoping that the implemented algo- rithm remains **chaotic**. The PRNG algorithms we conceive are constituted by discrete **chaotic** **iterations** that we mathematically proved in [3], that produce topological chaos as defined by Devaney. In the same paper, we raised the question of their implementa- tion, proving in doing so that it is possible to design a **chaotic** algorithm and a **chaotic** computer program. In conclusion, the **generator** proposed in this paper does not inherit its **chaotic** properties from a continuous real **chaotic** map, but from discrete **chaotic** it- erations defined in Section 2.2. As quoted above, it has been proven in [3] that **chaotic** **iterations** behave as chaos, as it is defined by Devaney: they are regular, transitive and sensitive to initial conditions. This famous definition of a **chaotic** behavior for a dy- namical system implies unpredictability, mixture, sensitivity and uniform repartition. This allows the conception of a new generation of **chaotic** PRNGs. Because only inte- gers are manipulated in discrete **chaotic** **iterations**, the **chaotic** behavior of the system is preserved during computations, and these computations are fast.

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ost of the research work that has been done in this field looks at increasing the output speed in computing the cryptographic results in on TRNG platform[1]. As we read other research related work in Research and Implementation of RSA Algorithm in Java[9]and Text **Watermarking** Using Combined Image- plus-Text Watermark[2,3]. These two papers discuss two separate independent studies on RSA algorithm in Java and text **watermarking** using combined image **based** **watermarking**. So far, the limited research studies of text- **based** digital **watermarking** techniques **based** on **Pseudo**- **Random** Number **Generator** (PRNG) for Cryptography **application**. Therefore, we need to do research and experimental undertaken within the context of design and implementation of text **based** **watermarking** combined with cryptographic techniques.

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logistic maps to generate the **chaotic** sequence of real **numbers**. The number of **iterations** should also be less to speed up the operation. This is the drawback of their algorithm. The organization of the paper is as follows: Section 1 deals with the introduction of the **random** generators, concept of logistic map and the statistical tests used for the validation of randomness of the sequences. Section 2 explains the proposed methodology **based** on the **Chaotic** **Random** Bit **Generator** and the uniqueness of the proposed work. Section 3 explains the statistical tests and their procedure in evaluating the randomness of the sequences. Section 4 involves the testing strategy to validate the sequences in randomness and the Statistical Analysis of the Randomness of the **Chaotic** Sequences. Section 4 involves the results and discussion of the sample sequence randomness and their validation. Section 5 concludes the unique features of the proposed **Random** Bit **generator** and the validation of the generated sequences.

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The tuning parameters provide a first level of security in the system. An attacker trying to erase, replace or extract the embedded watermark will not be able to perform these actions if he or she does not know the embedding frequency range and/or the frame size. However, even if an attacker knows or can guess these secret values, the embedded watermark can be further protected with cryptography. To increase security, a **pseudo**-**random** number **generator** (PRNG) can be used to change the secret bit stream to another stream which makes it more difficult for an attacker to extract the secret information. For example, the embedded bit stream can be constructed as the XOR sum of the real watermark and a **pseudo**-**random** bit stream. The seed of the PRNG would be required as a secret key both at the sender and the detector. There are many cryptography techniques that can be used to increase the security of the system. **Based** on the requirements of the **watermarking** system, a cryptographic method should be chosen. For example, if we want to increase security, AES encryption is a good choice in terms of complexity.

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In comparison with productive accidental natural number in which the range of the **numbers** cannot be produced again, the technique used for producing the accidental number in algorithm **based** on the **chaotic** function will prepare the ground that if we have the primary quantities and the drawn function, we can produce the **numbers** again. The main idea in the image encryption is to transmit the image securely over the network so that no unauthorized user can able to decrypt the image. The image data have special properties such as bulk capacity, high redundancy and high correlation among the pixels that imposes special requirements on any encryption technique [6]. The most common technique of secure the digital images is to scramble the digital data such that original message of the documents should not be known. There are several approaches to achieve this for example Steganography, compression, digital **watermarking** and cryptography. In this paper we focus on the encryption techniques of digital image **based** on the chaos mapping. Basically image encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key and the transforming information using “encryption algorithm” into a form that cannot be deciphered without a decryption key. On the other hand, decryption OF image retrieves the true information from the encrypted form image. There are several digital image encryption systems to encrypt and decrypt the image data, and there is not available the single encryption algorithm that satisfies the different image types. The encryption techniques **based** on the chaos mapping provides the encrypted digital images to hold the multilevel encryption method and also decreases the computational complexity of the encryption process. Most of the algorithms

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2) Interpretation of empirical results: P is the tail proba- bility that the chosen test statistic will assume values that are equal to or worse than the observed test statistic value when cosidering the null hypothesis. For each statistical test, a set of Ps is produced from a set of sequences obtained by our **generator** (i.e., 100 sequences are generated and tested, hence 100 Ps are produced). The interpretation of empirical results can be conducted in any number of ways. In this paper, the examination of the distribution of Ps to check for uniformity (PT ) is used.

At the sender side, a binary watermark of size (64x64) image is scrambled and encrypted using the steps stated earlier. Fig. 3 shows the original, scrambled, and ciphered watermark images. Then, after partitioning a standard Barbara (512x512 at 8bits/pixel ) cover image and applying the **watermarking** steps and inserting the ciphered scrambled watermark in each of the four parts of the divided cover image, four watermarked sub images are obtained. Next, the sub images are added together to form one watermarked image as fig. 4 shows. The process is reversed at the receiver side by doing the extraction and deciphering of the watermark. Fig. 4 shows four extracted deciphered unscrambled watermarks from each sub image and the combined weighted extracted watermark. A majority weight for each extracted pixel was taken (>2) meant a detection of a watermark pixel. The deciphering and unscrambling are an exact reversal of ciphering and scrambling shown in fig. 3.

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For a car ownership model, the complete choice set is the number of car owned: 0 car, 1 car… n Cars. Due to smaller sample size for households with 3 or more cars, we limit the choice set of our car ownership model to 0 car, 1 car and 2+ cars. In the current study, multiple car ownership is modeled **based** on a hierarchical structure, which involves two binary choice models: the first is the choice between zero car and one plus cars (noted as Model 1+ hereafter); then conditional on owning at least one car, choice between owning exactly one car and two plus car (noted as Model 2+|1+ hereafter). The advantage of such specification is that for each binary choice model, it does not require the IIA assumption and the assumption on the **random** term can be general. It also has the advantage of choice probability (of higher car ownership) increases monotonically with income. As a result, the hierarchical model structure is adopted for the current project, similar to other car ownership models such as NRTF (1997), Whelan (2001) and RAC (2002b). Normalizing the utility of owning no car to zero ( U 0 = 0 ), the utility of owning at least one car for household i in cohort c can be presented by equation (9). To turn the model into a readily tractable form, two assumptions on the **random** error components have been made. Firstly, under the asymptotic of

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Most applications require a floating point output u n in the interval [0,1). The conversion of the integer X n to a floating-point value u n has traditionally been done simply by multiplication with 2 -b . This involves the slow intermediate steps of converting the unsigned b-bit integer to a signed integer with more than b bits, and converting this signed integer to a normalized floating- point number. A much faster method can be implemented by manipulating the bits of a floating- point representation as follows: Set the binary exponent to 0 (+ bias) and the fraction part of the significand to **random** bits. This will generate a floating-point number with uniform distribution in the interval [1,2). A normalized floating-point number in the interval [0,1) is then obtained by subtracting 1. The binary representation of floating-point **numbers** usually follows the IEEE-754 standard (IEEE Computer Society 1985). If portability is important then you have to choose a floating-point precision that is available on all computers.

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encoded data is decoded back into 1 bit data under the condition: when MSB bit is at logic state 1. By utilizing FM0/Manchester encoding and decoding technique, the data will be secure; this process is facile and more expeditious to carry out. This paper develops a plenarily reused VLSI architecture, and additionally exhibits an efficient performance. Keywords:FM0/ Manchester encoder, Linear feedback shift register (LFSR), **Pseudo** **random** sequence **generator** (PRSG), Memory controller. 1. Introduction

In contrast, the occurrence of the pair “AE” is less common and the occurrence of “ZQT” is either a rare occurrence of an acronym or else indicates a terrible inability to spell. The frequencies with which these various N-grams appear in plaintext are used as the basis for determining the correctness of the key which produced that plaintext. The more the frequencies resemble expected frequencies, the closer the underlying decryption key is assumed to be to the actual key. With probabilistic encryption algorithms, a crypto analyst can no longer encrypt **random** plain texts looking for correct cipher text. Since multiple cipher texts will be developed for one plain text, even if he decrypts the message to plain text, he does not know how far he had guessed the message correctly. Also the cipher text will always be larger than plain text.

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In this section, we propose a secure communication system, called Asymptotic Synchronization of Modiﬁed Logistic Hyper-**Chaotic** System (ASMLHCS), which is **based** on the communication system (4.1)–(4.2). ASML- HCS utilizes an important property of the communication system (4.1)–(4.2); that is, the Transmitter and Receiver can realize synchronization. In the ASMLHCS, there are two phases — the asymptotical synchronization phase and the Encryption/Decryption phase. First, we need to make both sides (the Transmitter and Receiver) carry out asymptotic synchronization. We then utilize asymptotic synchronization to accomplish the secure communication. The communication scheme is sketched in Figure 5.1. In- formation is transmitted by the Transmitter through the channel after Encryption. The Receiver recovers the in- formation by Decryption.

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In last decade, highly integrated circuits make IP reuse technology be popular since it greatly cuts the cycle of IP design. In company with the popular utilization of IP reuse technology, the reused IP is easily to cause disputes on ownership. Meanwhile, chaos theory is introduced in IP **watermarking** scheme for its good performance on security. For example, literatures [17], [18] employed logistic mapping to generate a sequence as watermark. Furthermore, the **chaotic** mapping can be used to scramble image space and the watermarks are then inserted. For its effectiveness on digital watermark, **chaotic** mapping is widely used in recent IP **watermarking** schemes [19].

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The RK 4 algorithm **based** PBS **Chaotic** **generator** have been synthesized using the Nexus 4 DDR XC7A100TCSG-1 (Artix7) and Basys3 (Artix7) from the Xilinx Vivado v.2017.3 design suite. For the optimize result the clock period is set to 2.78 ns which uses2637 LUT’s and 4692 registers and the maximum frequency achieved is 359.71 MHz. The attractors generated for the FPGA **based** design are similar to PBSCS designed on analog platform.

The K constant obtained by sampling the **chaotic** signal according to the given parameters with 2 Hz sampling frequency is 0.9663. The change in mean square displacement over time is also given in Fig. 7.a. When this graph is obtained, the parametres change according to the randomly selected c values as in Fig.7.b.

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Nowadays, there is an ever increasing demand for **random** **numbers** in communication and cryptography. The applications of **random** **numbers** include symmetric key cryptography, Monte Carlo simulations, protection of transactions, and key distribution systems, which will be more significant in the age of quantum computers. In order to generate true **random** bits (TRB), quantum **random** number generators (QRNGs) need to be implemented. Pseudorandom number generators (PRNGs) are widespread; they are cost-efficient because they algorithmically create seemingly **random** **numbers**, but they are deterministic, therefore these **numbers** cannot be declared as truly **random**. There are some **random** number generators, which sample complex physical processes, but with suitable measurements others can obtain the same **numbers**. Nevertheless, the randomness of quantum mechanics can provide high bit generation rates. Some quantum process **based** generators, for instance the radioactivity **based** QRNG, come with several serious problems: for example, the radiation is only enough just for a few detections per second, decreasing the generation rate. Moreover, we need huge quantities of radioactive materials, for which serious security arrangements need to be implemented. There are different possible processes for **random** number generation (e.g. the noise of **chaotic** circuits or the Brown- motion of particles), but it is not possible to generate high bit generation rates using these phenomena. We can differentiate between optical **based** QRNG systems, too. The first group is that of is the branching path generators, when the photon goes to a semi-transparent mirror that transmits it along one of the paths. At the end of both paths there is one detector, and the number of the detector signalling the arrival of a photon determines the value of the bit. The semi-

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Discrete Cosine Transformation has been the most popular transform domain for various image processing. It allows an image to be broken up into different frequency bands viz. high frequency, middle frequency and low frequency, making it much easier to embed **watermarking** information in the desired frequency band. In general middle frequency bands are preferred over especially for **watermarking** The middle frequency bands are chosen such that they avoid the most visual important parts of the image (low frequencies) without over-exposing themselves to removal through compression and noise attacks (high frequencies). Embedding in the perceptually significant portion of the image has its own advantages because most compression schemes remove the perceptually insignificant portion of the image. In spatial domain it represents the LSB however in the frequency domain it represents the high frequency components[8].

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