Cryptanalysis of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system

doi:10.1016/j.ijleo.2014.08.129

Optik

Volume 126, Issue 2, January 2015, Pages 223-229

https://doi.org/10.1016/j.ijleo.2014.08.129 Get rights and content

Abstract

We studied the security features of a recently proposed image encryption scheme [Zhang et al., Optik 124(18) (2013) 3596] based on DNA sequence operation and hyper-chaotic system. We showed that all kinds of DNA encoding and decoding schemes used in this encryption scheme are equivalent to each other, which makes it a confusion-only encryption scheme. This paper successfully broke the scheme with the chosen plaintext attack method.

Introduction

The chaotic systems are widely used in image encryption systems [1], [2], [3], [4], [5] due to its strong sensitivity to initial values and parameters, the unpredictability of long-term evolution, easy producing pseudo-random sequences and other characteristics. However, some chaotic image encryption systems [6], [7], [8] are vulnerable to chosen plaintext or known plaintext attacks [9], [10], [11] because their cipher code streams, also known as equivalent secret keys are independent with the plain image. Consequently, some scholars began to explore plaintext related image encryption systems [12], [13], [14], [15], [16].

Recently, several novel image encryption systems integrated with chaotic systems and other systems are proposed to improve the security of image encryption systems. Ref. [17] presented an encryption system based on the hyper-chaotic Lorenz system and Choquet fuzzy integral, which employed the Choquet fuzzy integral to integrate the sequences generated by the hyper-chaotic system to obtain the cipher code streams, then applied them using the “add - modulo - xor” operations to encrypt plain image and produce the cipher image. Ref. [18] suggested an image encryption system based on the hyper-chaotic Chen's system and DNA sequence operations. We will refer to it as ZGW2013 hereinafter. In this paper, we pointed out that in ZGW2013, the cipher code streams used for encryption are unrelated with the plain image. We showed that the scheme of ZGW2013 is equivalent to a permutation-only image encryption system without diffusion. We also developed a chosen plaintext method to break the ZGW2013. The rest of the paper is organized as follows: Section 2 briefly describes the encryption scheme of ZGW2013; Section 3 elaborates the chosen plaintext attack method to break ZGW2013; Section 4 gives the simulation results; Section 5 concludes the paper.

Section snippets

Encryption scheme of ZGW2013

The ZGW2013 used the hyper-chaotic Chen's system and DNA encoding and decoding schemes, where the hyper-chaotic Chen's system can be formulated as follows: $\{\begin{array}{c} \dot{x} = a (y - x) \\ \dot{y} = - x z + d x + c y - q \\ \dot{z} = x y - b z \\ \dot{q} = x + k \end{array}$ here, a = 36, b = 3, c = 28, d = 16, and k = 0.2. Discretize (1) according to the fourth order Runge–Kutta method with the step size of 0.001 and transient iterations of 8000.

There are 8 kinds of DNA encoding and decoding schemes in ZGW2013, listed in Table 1. The DNA XOR operations are identical to the binary XOR

Chosen plaintext attack

According to the algorithm description of ZGW2013 described in Section 2, we can conclude the following given two plain images P⁽¹⁾ and P⁽²⁾ and their corresponding cipher images C⁽¹⁾ and C⁽²⁾:

(1)
When the DNA encoding and decoding schemes are known, we can get the matrices Pe⁽¹⁾ and Pe⁽²⁾ from P⁽¹⁾ and P⁽²⁾, respectively, and get the matrices O⁽¹⁾ and O⁽²⁾ from C⁽¹⁾ and C⁽²⁾,respectively. Then we have Ps⁽¹⁾XORPs⁽²⁾ = O⁽¹⁾XORO⁽²⁾. On the other hand, Ps⁽¹⁾XORPs⁽²⁾ can also be obtained by scrambling Pe

Simulation results

The computer used is configured with Intel Duo CPU T5450 @1.66 GHz, 2GB DDR2 RAM, Windows 7 and MATLAB 7.1. We found that the randomness of lx and ly generated by the method in [18] is not good, so we used mod(x*10,1) and mod(y*10,1) to replace the x ad y in Step 3 of ZGW2013 in Section 2, respectively, to produce the new lx and ly. Without loss of generality, the secret keys used in ZGW2013 are {0.3, −0.4, 1.2, 1}, and key matrix K of size M × N, whose elements range from 0 to 255, is generated

Conclusion

In ZGW2013, the DNA encoding and decoding schemes used are known, so ZGW2013 can be considered as a permutation-only scheme without diffusion, whose security is very vulnerable as pointed out in [19]. Our study shows that the ZGW2013 cannot resist chosen plaintext attack whether the combination scheme of DNA encoding and decoding is known or not. This paper indicates that the equivalent secret key pKs of Ks can be found, which makes the 28 possible combinations of DNA encoding and decoding

Acknowledgement

This work was fully supported by the Natural Science Foundations of Jiangxi Province (Grant nos. 20122BAB201036 and 20114BAB211011).

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Citation Excerpt :
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Cryptanalysis of a novel image fusion encryption algorithm based on DNA sequence operation and hyper-chaotic system

Abstract

Introduction

Section snippets

Encryption scheme of ZGW2013

Chosen plaintext attack

Simulation results

Conclusion

Acknowledgement

Phys. Lett. A

Chaos, Solitons Fractals

Chaos, Solitons Fractals

Opt. Commun.

Chaos, Solitons Fractals

Phys. Lett. A

Opt. Commun.

Chaos, Solitons Fractals

Chaos, Solitons Fractals