Elsevier

Image and Vision Computing

Volume 24, Issue 9, 1 September 2006, Pages 926-934
Image and Vision Computing

Image encryption using chaotic logistic map

https://doi.org/10.1016/j.imavis.2006.02.021Get rights and content

Abstract

In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques. In this communication, we propose a new approach for image encryption 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 80-bit 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, eight different types of operations are used to encrypt the pixels of an image and which one of them will be used for a particular pixel is decided by the outcome of the logistic map. To make the cipher more robust against any attack, the secret key is modified after encrypting each block of sixteen pixels of the image. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.

Introduction

In recent years, owing to frequent flow of digital images across the world over the transmission media, it has become essential to secure them from leakages. Many applications like military image databases, confidential video conferencing, medical imaging system, cable TV, online personal photograph album, etc. require reliable, fast and robust security system to store and transmit digital images. The requirements to fulfill the security needs of digital images have led to the development of good encryption techniques. During the last decade, numerous encryption algorithms [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13] have been proposed in the literature based on different principles. Among them, chaos based encryption techniques are considered good for practical use as these techniques provide a good combination of speed, high security, complexity, reasonable computational overheads and computational power etc. The digital images have certain characteristics such as: redundancy of data, strong correlation among adjacent pixels, being less sensitive as compared to the text data i.e. a tiny change in the attribute of any pixel of the image does not drastically degrade the quality of the image and bulk capacity of data etc. Consequently, the traditional ciphers like IDEA, AES, DES, RSA etc. are not suitable for real time image encryption as these ciphers require a large computational time and high computing power. For real time image encryption only those ciphers are preferable which take lesser amount of time and at the same time without compromising security. An encryption scheme which runs very slowly, even may have higher degree of security features would be of little practical use for real time processes.

A number of chaos based image encryption scheme have been developed in recent years which we discuss in brief in this paragraph. In 1992, Bourbakis and Alexopoulos [1] have proposed an image encryption scheme which utilizes the SCAN language to encrypt and compress an image simultaneously. Fridrich [4] demonstrated the construction of a symmetric block encryption technique based on two-dimensional standard baker map. There are three basic steps in the method of Fridrich [4]: (a) choose a chaotic map and generalize it by introducing some parameter, (b) discretize the chaotic map to a finite square lattice of points that represent pixels, (c) extend the discretized map to three-dimensions and further compose it with a simple diffusion mechanism. Further, Scharinger [5] designed a chaotic Kolmogorov-flow-based image encryption technique, in which whole image is taken as a single block and which is permuted through a key-controlled chaotic system. In addition, a shift register pseudo random generator is also adopted to introduce the confusion in the data. Yen and Guo [6] proposed an encryption method called BRIE based on chaotic logistic map. The basic principle of BRIE is bit recirculation of pixels, which is controlled by a chaotic pseudo random binary sequence. The secret key of BRIE consists of two integers and an initial condition of the logistic map. Further, Yen and Guo [9] also proposed an encryption method called CKBA (Chaotic Key Based Algorithm) in which a binary sequence as a key is generated using a chaotic system. The image pixels are rearranged according to the generated binary sequence and then XORed and XNORed with the selected key. Later in 2002, Li and Zheng [11] pointed out some defects in the encryption schemes presented in the references [6], [9] and also discussed some possible improvements on them. Recently, Li et al. [12] have proposed a video encryption technique based on multiple digital chaotic systems which is known as CVES (Chaotic Video Encryption Scheme). In this scheme, 2n chaotic maps are used to generate pseudo random signals to mask the video and to perform pseudo random permutation of the masked video. Very recently, Chen et al. [13] have proposed a symmetric image encryption in which a two-dimensional chaotic map is generalized to three-dimension for designing a real time secure image encryption scheme. This approach employs the three-dimensional cat map to shuffle the positions of the image pixels and uses another chaotic map to confuse the relationship between the encrypted and its original image.

The characteristics of the chaotic maps have attracted the attention of cryptographers to develop new encryption algorithms. As these chaotic maps have many fundamental properties such as ergodicity, mixing property and sensitivity to initial condition/system parameter and which can be considered analogous to some cryptographic properties of ideal ciphers such as confusion, diffusion, balance and avalanche property etc. In this communication, a new image encryption scheme is proposed based on chaotic logistic maps in order to meet the requirements of the secure image transfer. Further in the proposed image encryption scheme an external secret key (as used by Chen et al. [13] for image encryption and by Pareek et al. [14], [15] for text ciphers) of 80-bit 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 its bits (see Eq. (6) for details). In the algorithm, the first logistic map is used to generate numbers ranging from 1 to 24 (numbers may be repeated). The initial condition of the second logistic map is modified from the numbers, generated by the first logistic map. By modifying the initial condition of the second logistic map in this way, its dynamics gets further randomized. In the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and which operation will be used for a particular pixel is decided by the outcome of the second logistic map. Thus, the second chaotic map further increases the confusion in the relationship between the encrypted and its original image. To make the cipher more robust against any attack, after each encryption of a block of sixteen pixels, the secret key is modified. In Section 2, we discuss the step by step procedure of image encryption and in Section 3, the security analysis of the proposed image encryption scheme such as statistical analysis, key and plaintext sensitivity analysis, key space analysis etc. to prove its security against the most common attacks. Finally, in Section 4, we conclude the paper.

Section snippets

The proposed image encryption procedure

In this section, we discuss the step by step procedure of the proposed image encryption as well as decryption process using two chaotic logistic maps.

  • 1

    The proposed image encryption process utilizes an external secret key of 80-bit long. Further, the secret key is divided into blocks of 8-bit each, referred as session keys.

K=k1k2k20(inhexadecimal),
  • here, ki's are the alphanumeric characters (0–9 and A–F) and each group of two alphanumeric characters represents a session key. Alternatively, the

Security analysis

A good encryption procedure should be robust against all kinds of cryptanalytic, statistical and brute-force attacks. In this section, we discuss the security analysis of the proposed image encryption scheme such as statistical analysis, sensitivity analysis with respect to the key and plaintext, key space analysis etc. to prove that the proposed cryptosystem is secure against the most common attacks.

Conclusions

In this communication, a new way of image encryption scheme have been proposed which utilizes two chaotic logistic maps and an external key of 80-bit. The initial conditions for both the logistic maps are derived using the external secret key by providing weightage to its bits corresponding to their position in the key. In the proposed encryption process, eight different types of operations are used to encrypt the pixels of an image and which operation will be used for a particular pixel is

Acknowledgements

The support from the special assistance programmed of the University Grants Commission (UGC), New Delhi to the Department of Physics, M.L.S. University is gratefully acknowledged. One of us (VP) also acknowledges to the University Grants Commission (UGC), New Delhi for providing senior research fellowship.

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