A robust hybrid method for image encryption based on Hopfield neural network q Nooshin Bigdeli, Yousef Farid ⇑ , Karim Afshar EE Department, Imam Khomeini International University, Qazvin, Iran article info Article history: Received 23 January 2011 Received in revised form 22 November 2011 Accepted 23 November 2011 Available online 30 December 2011 abstract In this paper, a robust hybrid image encryption algorithm with permutation–diffusion structure is proposed, based on chaotic control parameters and hyper-chaotic system. In the proposed method, a chaotic logistic map is employed to generate the control parame- ters for the permutation stage which results in shuffling the image rows and columns to disturb the high correlation among pixels. Next, in the diffusion stage, another chaotic logistic map with different initial conditions and parameters is employed to generate the initial conditions for a hyper-chaotic Hopfield neural network to generate a keystream for image homogenization of the shuffled image. The new hybrid method has been com- pared with several existing methods and shows comparable or superior robustness to blind decryption. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Information security plays a significant role in all fields such as internet communication, multimedia systems, medical imaging, telemedicine, and so on [1]. Recently, this topic has attracted increasing research attention [2–10]. The main obsta- cle in designing effective image encryption algorithms is that it is rather difficult to swiftly shuffle and diffuse such image data by traditional cryptographic means. In spatial domain, the basic ideas for image encryption can be classified into three major types: the position permutation, the value transformation, and their compounding form. Many fundamental charac- teristics of chaos, such as the ergodicity, mixing and exactness property and the sensitivity to initial conditions, can be con- nected with the ‘‘confusion’’ and ‘‘diffusion’’ property in cryptography [11]. So it is a natural idea to use chaos to enrich the design of new ciphers [12–15]. In the recent years, various image encryption algorithms based on the permutation–diffusion architecture have been pro- posed (see Fig. 1) [16–19]. In this architecture, permutation and diffusion are considered as two separate stages, both requir- ing image-scanning to obtain pixel values. The permutation stage changes the position of image pixels but does not alter their values. In the diffusion stage, the pixel values are modified sequentially so that a tiny change in one pixel is spread out to almost all pixels in the whole image. The whole permutation–diffusion round repeats for a number of times so as to achieve a satisfactory level of security. However, the control parameters used in the permutation and/or diffusion stages are usually fixed in the whole encryption process, which favors attacks [20]. In this study, chaotic keys are used to control, automatically, the permutation–diffusion stages, in which the complexity is increased and the algorithm can effectively resist all known attacks against permutation–diffusion architectures. In the pro- posed algorithm, chaotic control parameters of Arnold Cat map [11] has been used for image shuffling. Next the discrete out- put signals of the fourth order hyper chaotic Hopfield neural network [21] is preprocessed to be suitable for the image encryption, and the shuffled image is encrypted by the preprocessed signals pixel by pixel. There are two logistic maps with 0045-7906/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compeleceng.2011.11.019 q Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek. ⇑ Corresponding author. Address: EE Department, Imam Khomeini International University, Norouzian Street, Qazvin, Iran. Tel./fax: +98 281 8371155. E-mail addresses: bigdeli@ikiu.ac.ir (N. Bigdeli), yousef.farid@ikiu.ac.ir (Y. Farid), afshar@ikiu.ac.ir (K. Afshar). Computers and Electrical Engineering 38 (2012) 356–369 Contents lists available at SciVerse ScienceDirect Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng