# Image Encryption Scheme Using Diffusion Technique Computer Science Essay

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With the proliferation of the Internet and maturation of the digital signal processing technology, applications of digital imaging are prevalent and are still continuously and rapidly increasing in recent years. Yet the main hurdle in the widespread deployment of digital image services has been enforcing security and ensuring authorized access to sensitive data. Compared with text encryption, which most existing encryption standards aim at, image encryption (or more generally, multimedia encryption) has its own intrinsic characteristics and special features with many unique specifications. In this regard, the chaos based cryptographic algorithms have suggested developing a new and efficient way of secure image encryption techniques.

In this regard, we propose a new algorithm for image based cryptosystem scheme based on chaotic maps in order to meet the security requirements of the multimedia content rich data. In the proposed image based encryption scheme, an external secret key of 15 decimal digits derived from chaotic logistic maps. The initial conditions for the both logistic maps are derived using the external secret key by providing different weight age to all its bits. Further, in the proposed encryption process, a simple operation is used to encrypt the pixels of an image and is decided by the outcome of the logistic map. In the proposed method, the cipher image is robust against any malicious attack, the secret key may be modified after encrypting and twice a time logistic map is used. From the results of statistical analysis test shows that the proposed image cryptosystems provides a secure way for real-time systems and information transferring system from the network security viewpoint.

## KEYWORDS: Chaos, Logistic map, Image Encryption and Cipher.

## 1. INTRODUCTION

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In Today's world all communication system, including wireless networks, satellite, and inter networks, it is impossible to prevent unauthorized people from malicious activity and masquerade attacks. When information is communicated via satellite or transferred through the internet, there is a high risk of information threat and interception. It is essential to protect data, still image, video, and multimedia and it has become prime important for many applications including video conferencing, medical, e-commerce, e-banking and military applications. The image cryptosystem have been developed for this purpose has two important aspects. The first one is conversion process technique i.e., changing the intelligible information (plain text) in to unintelligible information (cipher text) and it is performed by encryption, for which a key is required to decrypt the information. In the second one is watermarking, it is the process of embedding a message into the multimedia content rich data. The above said systems are complementary to each other.

The main focus of the current trend is secured communications using encryption, the information is converted to an unintelligible structure using certain basic and primitive operations at the transmitter .In this context, the exiting classical encryption technique is mainly performed by scrambling the content of information, such as video, audio, text and image so forth to make the data not legible, fathom or incomprehensible during broadcast of information. The cipher is then transmitted through the insecure channel, i.e. internet, satellite, etc to the receiver. At the receiver, the information is again transformed to an intelligible form using a reverse operation and thus the information is conveyed in a safe and secure manner. The same key is used in both these (sender) forward and reverse (receiver) process. Such system is classified as symmetric key cryptography.

However, an image scrambling method transforms an intelligible image into another form an unintelligible image, based on some keys only known to the transmitter and the receiver. The fundamental encryption process in an image is to encrypt a group of pixels (called block) by performing combination of Shannon's fundamental operation like, substitution and permutation technique. The substitution technique replaces one pixel with another pixel; permutation technique the sequence of the pixels order is changed in a block to make them uncipherable.

In current years, a chaotic map is a best alternative for key generation and they have been employed for image based cryptosystems. Most widely used chaotic image cryptosystems uses the permutation-substitution process. For several rounds these two techniques are repeated, to obtain the final cipher image. In [4], Fridrich suggested an image encryption by chaotic method and it is composed of substitution and permutation. By using 2D chaotic map all the image pixels are moved. The new pixels movements to the present position are considered as a permutation of the original image pixel positions. The pixel values are changed sequentially in the substitution process. Chen et. al. used a three-dimensional (3D) Arnold cat map [5] and a 3D Baker map [6] for performing the permutation process. Gao et. al[10]. Present the image encryption technique based on a new nonlinear chaotic algorithm by using a two functions power function and tangent and also it uses a chaotic logistic sequence generated by a nonlinear chaotic map to encrypt an image data using exclusive - OR operation.

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Pareek et al. extended the classical encryption scheme to image encryption scheme by using two chaotic maps and a key [13].In this paper, new permutation-substitution architecture is performed by using chaotic logistic map. In the permutation phase, a bit sequence is generated by using a logistic map. The permutation and substitution operation requires two keys, Key-P and Key-S, respectively. In the substitution phase, a pseudo random image is produced by using tent map and they are mixed it with the permutation process.

Many aspects of non linear chaotic maps have analogous but different characteristics as compared with conventional cryptographic algorithms [1, 2, 3, and 4]. As early as in 1989 [5], a non -linear function (chaotic) was already used to design a cryptosystems. Although dedicated chaos-based image encryption techniques won't appear in the literature very often, there does exist some, which are discussed here. For example [6], chaotic key-based algorithm (CKBA) was proposed. In this scheme first generates a time series based on a chaotic map, and then uses it to create a binary sequence as a key. The binary sequence so generated, image pixels are rearranged and then XOR or XNOR operated with the selected key. This method is very simple but has obvious defects in security, as pointed out lately in [14]: this method is very weak to the chosen/known-plaintext attack using only one plain-image, and moreover its security is questionable with brute-force attack. In [7] a chaotic Kolmogorov flow-based image encryption algorithm was designed. In this scheme, the whole image is considered as a single block and permuted through a key-controlled chaotic system based on the Kolmogorov flow. In order to protect the data, a substitution based on a shift-registered pseudo-random number generator is applied, which alters the statistical property of the cipher-image. In [8], a systematical method was suggested for adapting an invertible 2 D chaotic map on a torus or on a square, so as to create a symmetric block encryption scheme. Most image scrambling scheme make use of the quantization strategy of coefficient. But it is unknown weather the map keeps chaos property after quantization.

In this paper, we perform a simple diffusion operations aims at reducing time complexity and applicability in low power devices. The chaotic sequence is generated from logistic map, using secret key arrangement, initial seed, by using two chaos maps which extends the key space. The algorithm reduces iterative number and makes use of non deterministic chaotic property of map. Because of the strong irregularity of the new algorithm, the encrypted image possesses high-level security. The proposed method gives high level of security protection in one iteration round and hence the total elapsed time is very short. In section 2, a chaotic map system is discussed. We analyze the dynamics action of the logistic map in finite precision. In section 3, the detail of image encryption is described. In section 4, we test the new algorithm and show the high level security. Section 5 is a conclusion.

2. CHAOTIC MAPS

The chaos can be generated by using various chaotic maps. Here 1 D chaotic map is used to produce the chaotic sequence which is used to control the encryption process.

Logistic Map

A simple and well-studied example of a 1D map that exhibits complicated behavior is the logistic map from the interval into, parameterized by Î¼:

Where 0 â‰¤ Î¼ â‰¤ 4. This map constitutes a discrete-time dynamical system in the sense that the map generates a semi-group through the operation of composition of functions. The state evolution is described by .we denote

(ntimes)-(2)

For all, a "discrete-time" trajectory, where, can be generated. The set of points is called the (forward) orbit of x. A periodic point of g is a point such that for some positive integer n. The least positive integer n is called the period of x. A periodic point of period 1 is called a fixed point.

For differentiable g, a periodic point x with period n is stable if

and unstable if

Where .

In the logistic map, as Î¼ is varied from 0 to 4, a period-doubling bifurcation occurs. In the region, the map gÎ¼ possesses one stable fixed point. As Î¼ is increased past 3, the stable fixed point becomes unstable and two new stable periodic points of period 2 are created. As Î¼ is further increased, these stable periodic points in turn become unstable and each spawns two new stable periodic points of period 4. Thus the period of the stable periodic points is doubled at each bifurcation point. Each period-doubling episode occurs in a shorter "parameter" interval, decreasing at a geometric rate each time. Moreover, at a finite Î¼, the period-doubling episode converges to an infinite number of period doublings at which point chaos is observed.

## 3. ALGORITHM FOR BIT XOR:

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Examples of our work1. Reading of Original image (Im) :

The original image is converted to gray scale if it is color image.

Im = {Im i,j}, where and , H and W, respectively, are height and width of the Original image in pixels.

2. The secret key:

The secret key in the proposed encryption technique is a set of two floating point numbers and one integer XINT=(Âµ ,Xo, rw),

Where value is 3.987654321000001, Xo is initial value of the chaotic map, it is key and its typical value is 0.123456789000001; and W is width of the image.

y=(Âµ,X(row),column)

Where its typical value is 3.963852741000001,X(row) is last value of x map and column is Height of the image.

Y k/R is the logistic map generated with the value said above and it is multiplied with the number of columns and fixed as Column.

Similarly Y k/c is the logistic map generated with the value said above and multiplied with the number of rows and fixed as row.

3. Then chaotic key value Y k is XOR'ed with original image.

FOR i=1 to row

y=(Âµ,Y(i),col)

y = y * column;

Y k = integer(Y)

FOR j=1 to column

Im(i,j) = Im(i,j) Yk( j)

END

END

4.Again chaotic key value Y k is XOR' ed with original image.

FOR i=1 to row

y=(Âµ,Y(i),col)

y = y * row;

Y k = integer(Y)

FOR j=1 to column

Im(i,j) = Im(i,j) Yk( i)

END

END

The Proposed Scheme:

Original Image

Secret Key

15 digit floating point number

Ykey /col

Pixel values are XOR'ed with Chaotic sub key

Initialization

For chaotic Maps

Transmitted through unsecured channel

Cipher

Ykey /row

Chaotic Map- Logistic Map Y/Col

Chaotic Map- Logistic Map X/Row

4. EXPERIMENTAL RESULTS

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Conclusion

The proposed image based crypto system has a simple two chaotic logistic maps. In this algorithm, a bit sequence is generated by a logistic map , which was in turn used to generate another logistic map and image pixels are transformed by simple diffusion processes.

The security of the algorithm needs two different keys, YK-Row and YK-Column, respectively. The total key length was 45 bits. Therefore, the key space was 245, which is large enough to protect the information against any malicious and brute-force attacks.

The image was a 2-D array of pixels, each with 256 gray scales and the histogram of the cipher image could be uniform.

The proposed method is simulated using a MATLAB 7.6 version. It is desired that the histogram of the cipher image should be uniform and the proposed method produces histogram approximately a uniform distribution. Hence the proposed encryption system is highly resistant to any statistical attack. To quantify the difference between encrypted image and corresponding plain-image, two measures were used; Correlation and key space analysis is performed. It is concluded that the correlation and KSA criteria of the proposed system were satisfactory for the real time systems .It can be implemented and tested in real time by using FPGA.