A novel chaotic block image encryption algorithm based on dynamic random growth technique
Introduction
Nowadays more and more images and videos are transmitted through Internet. This brings great convenience to people in daily life as they can obtain what they want on the Internet conveniently. But there are some problems: the information transmitted on the Internet can be intercepted, tampered and destroyed illegally. So the secure transmission of images has become urgent. Due to some intrinsic features of images, such as bulk data capacity and high correlation among pixels, traditional encryption methods like DES, IDEA and RSA are not suitable for image encryption. Since chaos has the characters of non-periodicity, non-convergence, ergodicity and sensitive dependence on initial conditions, chaos-based image encryption system attracts more and more people׳s attentions.
The classic encryption frame is the permutation–diffusion pattern suggested by Shannon. Many encryption methods use Arnold cat map or generalized cat map in the permutation section [1], [2]. But since short periodic and easy to be cracked by chosen plaintext attack, cat map is not secure to be used in the common way [3], [4]. Some proposed image encryption schemes only do XOR operation on the original or scrambling images [5], [6], [7], [8]. It is also easy to be cracked by chosen plaintext attack [9], [10], since the key stream only depends on the key not related to the plaintext. Recently, some image encryption schemes using double images are proposed to get a good encryption effect [11], [12], while other people proposed method using genetic algorithm and DNA sequence [13].
Many other algorithms are also proposed [14], [15], [16], [17], [18], [19], [20], and some of them are analyzed [21], [22]. In this paper, a new chaos-based block image encryption method is proposed, which is a two rounds algorithm based on permutation–diffusion architecture. Both theoretical and computer simulations show that the algorithm is secure enough to be used in image transmission system.
This paper is organized as following: Section 2 describes Arnold cat map; Section 3 shows the proposed image encryption scheme; Section 4 presents the computer simulation results; Section 5 discusses the security analyses; finally, Section 6 concludes this paper.
Section snippets
Arnold cat map
The classical Arnold cat map is a two-dimensional invertible chaotic map defined by
But in permutation process of image encryption scheme, it is more common to use the generalized cat map as following:
Here N is the number of rows or columns. That is to say the image is of the size N×N. (xn, yn) is the original position of a pixel, and (xn+1, yn+1) is the new position.
It is very fast to permute an image using cat map, which is very
The proposed encryption method
The encryption method consists of two processes: permutation and diffusion.
Experimental results
We use Microsoft VC++6.0 to run the encryption and decryption process in computer with 2.66 GHz CPU, 512 MB memory and Microsoft Windows XP operation system. The plaintext image we choose is Lena.bmp of size 256×256, the keys we select are , , , , , , p=4, and q=8. And we choose . In Fig. 6, we show the results of encryption and decryption.
In our proposed encryption scheme, after one round of encryption, the cipher is secure
Key space analysis
A good image encryption system should be sensitive to cipher keys, and the key space needs to be large enough to make the brute-force impossible. To our proposed encryption algorithm, the key consists of the initial values , of logistic map, control parameter of logistic map , , initial value and control parameter of Tent map , parameters of Arnold cat map p, q, and . The precision is 10−16, so the key space is larger than 1096. So the key space is large enough to resist all
Conclusions
In this paper, a new block image encryption scheme based on cat map with permutation–diffusion architecture is proposed. In the permutation process, we use Arnold cat map and dynamic random growth technique to confuse the original image to keep the advantages of fast encryption of cat map, but eliminate its fatal drawback. In the diffusion section, we change the gray value of scrambling image using image division technique. For security analysis, we employ various methods such as key space
Acknowledgment
This research is supported by the National Natural Science Foundation of China (Nos. 61370145, 61173183 and 60973152), the Doctoral Program Foundation of Institution of Higher Education of China (No. 20070141014), Program for Liaoning Excellent Talents in University (No. LR2012003), the National Natural Science Foundation of Liaoning province (No. 20082165) and the Fundamental Research Funds for the Central Universities (No. DUT12JB06).
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