A Simple Chaos Based 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 approach for image encryption scheme based on chaotic logistic maps in order to meet the requirements of the secure image transfer. In the proposed image encryption scheme, an external secret key of 15 decimal digit and two chaotic logistic maps are employed. The initial conditions for the both logistic maps are derived using the external secret key by providing different weightage to all its bits. Further, in the proposed encryption process, simple type of operations is used to encrypt the pixels of an image and is decided by the outcome of the logistic map. To make the cipher more robust against any attack, the secret key may be modified after encrypting and logistic map is used twice a time. From the results of several experimental, key space analysis, statistical analysis, and key sensitivity tests show that the proposed image cryptosystems provides an efficient and secure way for real-time image encryption and transmission from the network security viewpoint.

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


In recent years all communication system, including satellite and internet, it is impossible to prevent unauthorized people from eavesdropping. When information is broadcasted from a satellite or transmitted through the internet, there is a high risk of information interception. Security of still image, video, multimedia and data has become increasingly important for many applications including video conferencing, secure facsimile, medical, and military applications. Two main groups of technologies have been developed for this purpose. In the first group is content protection through encryption, for which a key is required for proper decryption of the data. In the second group is digital watermarking, which aims to embed a message into the multimedia data. These two technologies could be used complementary to each other.

In secured communications using encryption, which is the focus of the recent work, the information under consideration is converted from the intelligible form to an unintelligible structure using certain primitive operations at the transmitter .In the exiting Data encryption technique is mainly performed by scrambling the content of data, such as text, image, audio, video and so forth to make the data unreadable, invisible or incomprehensible during transmission. The encrypted form of the information is then transmitted through the insecure channel, i.e. internet, satellite, etc to the receiver. At the intended recipient side, however, the information is again converted back to an intelligible form using decryption or reverse operation and thus the information is conveyed securely. It should be noted that the same keys guide both these encryption and decryption operations. Such encryption system is grouped under private key cryptography.

In particular, an image-scrambling scheme transforms an image into another unintelligible image, based on keys only known to the senders and the receivers. The fundamental techniques to encrypt a block of pixels are substitution and permutation. Substitution replaces a pixel with another one; permutation changes the sequence of the pixels in a block to make them unreadable.

In recent years, chaotic maps have been employed for image encryption. Most chaotic image encryptions (or encryption systems) use the permutation-substitution architecture. These two processes are repeated for several rounds, to obtain the final encrypted image. For example, in [4], Fridrich suggested a chaotic image encryption method composed of permutation and substitution. All the pixels are moved using a 2D chaotic map. The new pixels moved to the current position are taken as a permutation of the original pixels. In the substitution process, the pixel values are altered sequentially. Chen et. al. employed a three-dimensional (3D) Arnold cat map [5] and a 3D Baker map [6] in the permutation stage. Guan et al. used a 2D cat map for pixel position permutation and the discretized Chen's chaotic system for pixel value masking [7]. Lian et al. [8] used a chaotic standard map in the permutation stage and a quantized logistic map in the substitution stage. The parameters of these two chaotic maps are determined by a key-stream generated in each round. Mao et. al. construct a new image encryption scheme based on the extended chaotic Baker map [6]. Zhang et. al. first permute the pixels of images with discrete exponential chaotic map, and then use ''XOR plus mod'' operation for substitution [9]. Gao et. al. present the image encryption algorithm based on a new nonlinear chaotic algorithm using a power function and a tangent function instead of a linear function. It also uses a chaotic sequence generated by a nonlinear chaotic algorithm to encrypt image data using XOR operation [10]. Zhou et. al., propose a parallel image encryption algorithm using discretized kolmogorov flow map. All the pixels are first permuted with a discretized chaotic map and then encrypted under the cipher block chain mode [11].

There are however, some other chaotic image encryption systems with different structures. For example, Pisarchik et al. suggested an algorithm to convert image pixels to chaotic maps coupled to form a chaotic map lattice. The encrypted image is obtained by iterating the chaotic map lattice with secret system parameters and number of cycles [12]. Pareek et al. extended the concept of their text encryption to image encryption by using two logistic maps and a key [13].

In this paper, a new permutation-substitution architecture using chaotic maps and Tompkins-Paige algorithm is proposed. Our designed technique for speech scrambling [14] is extended to two-dimensional (2-D) permutation, and is applied to image permutation [15]. We have improved our work by using chaotic maps and adding a substitution part to an image encryption system. In the permutation phase, a logistic map is used to generate a bit sequence, which is used to generate pseudo random numbers in Tompkins-Paige algorithm. A tent map is also used in the substitution phase to product a pseudo random image that is used to mix it with the permuted image. The permutation and substitution operations need two different keys, Key-P and Key-S, respectively. Satisfactory security performance of the proposed system is achieved in only one round and therefore the total encryption time is short .

It has been proved that in many aspects chaotic maps have analogous but different characteristics as compared with conventional encryption algorithms [1, 2, 3, 4]. As early as in 1989 [5], a chaotic function was already used to design a cryptographic algorithm. Although dedicated chaos-based image encryption schemes do not often appear in the literature, there does exist some, which are briery discussed here. In [6], an encryption method called CKBA (chaotic key-based algorithm) was proposed. The algorithm first generates a time series based on a chaotic map, and then uses it to create a binary sequence as a key. According to 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 to brute-force attack is also questionable. In [7] a chaotic Kolmogorov flow-based image encryption algorithm was designed. In this scheme, the whole image is taken as a single block and permuted through a key-controlled chaotic system based on the Kolmogorov flow. In order to confuse the data, a substitution based on a shift-registered pseudo-random number generator is applied, which alters the statistical property of the cipher-image. It was advocated that the scheme is computationally secure and superior to contemporary bulk encryption systems when aiming at efficient image and video data encryption. In [8], a systematical method was suggested for adapting an invertible two-dimensional chaotic map on a torus or on a square, so as to create a symmetric block encryption scheme. Most image scrambling algorithms 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. 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.


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 μ:

Where 0 ≤ μ ≤ 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


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 μ is varied from 0 to 4, a period-doubling bifurcation occurs. In the region, the map gμ possesses one stable fixed point. As μ is increased past 3, the stable fixed point becomes unstable and two new stable periodic points of period 2 are created. As μ 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 μ, the period-doubling episode converges to an infinite number of period doublings at which point chaos is observed.


1. 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=(µ ,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.


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 = y * column;

Y k = integer(Y)

FOR j=1 to column

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



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

FOR i=1 to row


y = y * row;

Y k = integer(Y)

FOR j=1 to column

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



Original Image

Secret Key

15 digit floating point number


For chaotic Maps

Chaotic Map- Logistic Map X/Row

Pixel values are XOR'ed with Chaotic sub key

Transmitted through unsecured channel


Ykey /col

Ykey /row

Chaotic Map- Logistic Map Y/ColThe Proposed Scheme:




The proposed crypto system has a simple two chaotic maps. A logistic map was used to generate a bit sequence, which was in turn used to generate another logistic map, in this algorithm; 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 was large enough to protect the system against any brute-force attacks.

The image was a 2-D array of pixels, each with 256 gray scales. To improve security of the proposed encryption system, the histogram needed to become uniform.

All parts of the proposed chaotic encryption system were simulated using a MATLAB 7.6 version. The histogram of the encrypted image was approximated a uniform distribution. Therefore, the proposed encryption system was resistant against any statistical attack. To quantify the difference between encrypted image and corresponding plain-image, three measures were used: Correlation and key space analysis is performed. It was concluded that the correlation and KSA criteria of the proposed system were satisfactory when compared to other research results as was the security performance of the proposed system.