DOI: https://doi.org/10.2174/1872212111666170223165916 Recent Patents on Engineering, 2016, Volume 12
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A Secure Image Encryption Scheme using Chaos and Wavelet Transformations Bhaskar Mondal*a, Tarni Mandal1, Danish Ali Khan2 and Tanupriya Choudhury3 a
Department Computer Science and Engineering, National Institute of Technology Jamshedpur, Jamshedpur, India; Department Mathematics, National Institute of Technology Jamshedpur, Jamshedpur, India; 2Department of Computer Applications, National Institute of Technology Jamshedpur, Jamshedpur, India 3Department Computer Science and Engineering – ASET, Faculty of Engineering & Technology, Amity University, Noida, India; 1
Abstract: Background: Images are widely stored and transform over public channel for communication,
medical purpose or organizational uses. Mostly the images are collected from the remote location, therefore the confidentiality of the data becomes the most important matter of concern. The most convenient way to protect the data (image) is to encrypt it right after the capturing the images from the sensors at remote locations. There are a large numbers of patents registered till date. We have covered all the benchmark and important patents on encryption. Objective: This paper furnish an enhanced secure encryption scheme to assure the confidentiality of images at the time of transmission or storage. There are numerous encryption algorithms proposed in the recent days, most of them are not suitable for image encryption due to their high computational overhead and design structure. The proposed scheme has comparatively low computational overhead as it uses 2D DWT for decomposition of the image and chaotic maps for generating pseudo random numbers sequence (PRNS). Method: The scheme is based on 2D DWT and chaotic maps. The scheme may divide into two basic phase. In the first phase It permute the image using pseudo-random numbers generated by Arnold’s cat map followed by a transformation in 2D DWT for diffusion based on enhanced piece wise linear chaotic map (EPWLCM). Results: The proposed scheme is tasted statistically and found promising in results. So the proposed scheme is secure to any attack, light weight and effective. Conclusion: The proposed scheme highly reduced the computational complexity, but without compromising with the security. A number of testes was done and the results were satisfactory. The scheme may simply modified for color image or any other kind of data encryption.
Keywords: Arnold cat map, DWT, encryption, enhanced piece wise linear chaotic map, permutation, PRNG.
1. INTRODUCTION As we became information and communication dependent in all aspects of life, and the information transmitted over the public (communication) media. The secret data on public media can be copied, tampered, and retransmitted which may disclose certain secret information, or may be used for illegal activity. With the increment of the volume of data as well user in the public network the security of confidential data became a significant issue. As a result study on information security is a necessary and on-going process of research. Techniques like cryptography, Steganography [1] or secret sharing [2] are used for protecting information from unauthorized access. Encryption makes information (image) * aDepartment Computer Science and Engineering, National Institute of Technology Jamshedpur, Jamshedpur, India, P.O. Box: 831014; E-mails:
[email protected]
5-14/18 $58.00+.00
meaningless to any unauthorized user by conversion of data into a secret code based on some key. Steganography is the technique of hiding messages or information within other nonsecret text or media. It has been proposed as a technique of transmitting data (image) by embedding into a cover (image) media like image, audio or video etc. So the Steganography techniques conceal the existence of secret data (image) from the undesired users [3], [4] on the other hand, encryption [5], [6] is the best way to protect data (text, image, audio or video) by converting it in some unrecognizable format. A variety of encryption schemes are proposed to meet the demand [7], [8], [9]. Martin E. Hellman and one of his graduate student together secured the landmark patent in cryptography in 1977 known as Diffie-Hellman patent [10], for a cryptographic key sharing[11] protocol, in the same year Another patent was © 2014 Bentham Science Publishers
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Recent Patents on Engineering, 2018, Vol. 12, No. 1
secured by Hellman and one of his colleague on public key infrastructure [12] known as Hellman- Merkle patent[13]. MIT filled and issued another patent for public key protocol called RSA [14]. Data Encryption Standard (DES) [15] patented by IBM in 1975 [16], International Data Encryption Algorithm (IDEA), a block cipher generator patented by Lai and Massey in 1992[17] and Advanced Encryption Standard (AES) [18] or the Rijndael’s algorithm was not patented by the developers. A list of patents in cryptographic schemes is available at [19]. The above algorithms are not suitable for image encryption due to the huge size and inherent redundancies of images. It also draws the attention of any undesired user who may intend to reveal the secret or alter the data. However, in literature [20], [5], [21], [22], [23] several image encryption algorithms have been proposed to secure the confidentiality of image data based on chaotic maps. The chaotic maps are nonlinear deterministic system. It has crypto-friendly properties, like highly sensitive to initial conditions, deterministic, ergodic. The chaotic maps often generate highly complex pseudorandom sequences, which are difficult to predict or analyze [24], [25] which provides high security to the encryption algorithms. For generating the pseudo random number generators (PRNG) researchers use one dimensional [20], two dimensional, three dimensional [26], [27], compound chaos map [28] or hyper chaos map [29], [30]. Fridrich [31] proposed the first work on chaos based image encryption [32]. In [33] proposed an image encryption technique for biometric image based on Cellular Automata to protect image storage. The technique is using a segmentation of Cellular Automata image with hidden secret keys generated by the Wolfram Cellular Automata which demonstrates chaotic patterns. Such segmented Cellular Automata binary image is diffused to the scrambled and bitplane decomposed of the plain image using XOR operations.
Bhaskar Mondal et al.
random growth. [45] proposed another image encryption scheme based on 2D Sine Logistic modulation map. R. Clayton et. al. in 2014 bagged a patent called ‘Data encryption system and method’[46] is a secret key based encryption method. In 2012 R.A. Stedron another patent on secret key based secure data transmission, named ‘Method of encrypting and transmitting data and system for transmitting encrypted data’[47]. This paper presents an effective light weight encryption algorithm based on chaos and DWT [48], [36] which makes the encrypted images non-vulnerable against attacks. The proposed encryption technique has been simulated and tested [49], [50] and the results were promising. In the next section preliminaries of Arnold map, EPWLCM, DWT and Haar Transformation are discussed. In section III the proposed scheme is discussed followed by the experimental results and security analysis are presented in section IV. Finally the conclusion in section V. 2. PRILIMINARIES 2.1 Arnold's cat map Arnold's cat map named by Vladimir Arnold, who found its effect like a cat's image in 1960. The map generates the torus into itself. It is represented as equation 1
𝑥 Γ ([𝑦]) = 1 1 1 [ ][ 0 1 1
[
2 1 𝑥 ] [ ] 𝑚𝑜𝑑 1 = 1 1 𝑦 0 𝑥 ] [ ] 𝑚𝑜𝑑 1 1 𝑦
(1)
Γ is area preserving, topologically transitive, ergodic and mixing, structurally stable, invertible as the determinant of the matrix is 1 and has a unique hyperbolic fixed point.
In [34] a chaotic logistic map [35] is used which will generate highly randomized number sequence. In the diffusion part, the scheme uses DNA computation as it is reversible. The DNA computation is like bit wise operations hence the encryption process becomes very fast. Therefore the encryption algorithm is a light weight and first process as well as resistive to any kind of known attack. As the encryption scheme has very low computational overhead the proposed model may be used on resource constrained devices like wireless sensor network nodes or in Internet of Things [36]. In [37] an image encryption scheme using chaotic maps and deoxyribonucleic acid (DNA) sequence computations is proposed.
Arnald’s cat map holds properties like sensitive dependency, topological transitivity and dense periodic points which are important properties for a chaotic map. It is very simple to scrambling the pixel coordinates using the Arnold’s cat map, which uses only mod functions linear and transformation to do so. After a number iterations, the correlation among the pixels can be disturbed completely. The remarkable fact about Arnold’s cat map is that if it is applied recurrently, after a certain number of iterations the plain image repeats. Hence it is not enough to use only Arnold’s cat map to achieve security. So, for improving the strength of the proposed scheme the diffusion phase is introduced in the proposed scheme.
In [38] a scheme is proposed a scheme to protect palm print images using Hessenberg decomposition, chaos and fractional wavelet packet transform (FrWPT). In [39], [40] authors have proposed another scheme to protect fingerprint data based on FrWPT and chaotic map. In [41] authors have presented a fingerprint protection scheme using 2D multiscroll attractors based pseudo-random sequence. In which all the initial parameters are generated from a binary fingerprint data. In [42] an image encryption scheme based on highdimension Lorenz chaotic map and perceptron model within a neural network. In [43] a permutation and diffusion based image encryption scheme is proposed. [44] proposed an image encryption algorithm based on chaotic maps and dynamic
2.2 Enhanced Piecewise Linear Chaotic Map Piecewise Linear Chaotic Map (PWLCM) can be defined as equation 2
𝑥𝑛+1 = 𝐹(𝑥𝑛 , 𝑝) = 𝑥𝑛 , 𝑖𝑓 𝑥𝑛 ∊ [0, 𝑞) 𝑞 𝑥𝑛 −𝑞 0.5−𝑞
, 𝑖𝑓 𝑥𝑛 ∊ [𝑞, 0.5)
{𝐹(1 − 𝑥𝑛 , 𝑞), (2)
𝑖𝑓 𝑥𝑛 ∊ (0.5,1)
A Secure Image Encryption Scheme using Chaos and Wavelet Transformations
where 𝑥𝑛 belongs to (0, 1) , when control parameter q belongs to (0; 0.5); (1) evolves into a chaotic state, and can be used as secret key. PWLCM demonstrates uniform invariant distribution and properties like randomness, determinacy, and uncertainty. Therefore the map is capable to generate highly random sequence, which is most important for cryptography. Based on the PWLCM, we propose an improved piecewise linear chaotic map (MPWLCM) model, which can be denoted by 3
𝑥𝑛+1 = 𝐹(𝑥𝑛 , 𝑝) =
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and terminating sum. The Haar wavelet's mother wavelet function 𝜓 (t) is described as equation 4 1 𝜓(𝑡) = {−1 1
1
0≤𝑡< , 2 1 2
≤ 𝑡
