Image compression and encryption scheme via satellite

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1 Article Image compression and encryption scheme via satellite Journal of Vibration and Control 2016, Vol. 22(13) ! The Author(s) 2014 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: / jvc.sagepub.com Azkar Hussain Abstract Satellite communication systems are now designed according to an outdated Shannon information theory where all data is transmitted in meaningless bit streams. In this article, a novel noise free digital image communication via satellite has been developed. The proposed scheme is based on fractional compression and a new block cipher cryptosystem based on S 8 substitution boxes transformation. The fractal compression technique is selected to compress the aerial images due to its high compression capability. The fractal image compression of the input aerial image is the first stage in the encoding phase. The fractal compression technique divides the original image into two different block sizes called range and domain blocks. The best match between the range and domain blocks is known as the transformation mapping. All the transformation mappings are recorded as the output-compressed file of the input aerial image. Keywords Cryptosystem, fractal compression, satellite communication, S-box transformation 1. Introduction In 1962, the American telecommunications giant AT&T launched the world s first true communications satellite, called Telstar. Since then, countless communications satellites have been placed into the earth s orbit, and the technology being applied to them is forever growing in sophistication. The satellite itself is also known as the space segment, and is composed of three separate units, namely the fuel system, the satellite and telemetry controls, and the transponder. The satellite model is shown in Figure 1. The transponder includes the receiving antenna to pick-up signals from the ground station, a broadband receiver, an input multiplexer, and a frequency converter, which is used to reroute the received signals through a high-powered amplifier for downlink. The primary role of a satellite is to reflect electronic signals. In the case of a telecom satellite, the primary task is to receive signals from a ground station and send them down to another ground station located a considerable distance away from the first. This relay action can be two-way, as in the case of a long distance phone call. Another use of the satellite is when, as is the case with television broadcasts, the ground station s uplink is then downlinked over a wide region, so that it may be received by many different customers possessing compatible equipment. Still another use for satellites is observation, wherein the satellite is equipped with cameras or various sensors, and it merely downlinks any information it picks up from its vantage point. Fractal compression is a very good compression method for digital images, based on fractals. The method is best suited for textures and natural images, relying on the fact that parts of an image often resemble other parts of the same image. Fractal algorithms convert these parts into mathematical data called fractal codes which are used to recreate the encoded image. Therefore, fractal image compression offers some interesting features which makes it an interesting candidate image compression technique for aerial images such as: resolution-independent, fast decoding and good image quality at low bit-rates. The concept of fractal was introduced by Hutchinson (2001) as an alternative to the traditional Euclidean geometry, mainly dealing with shapes generated by nature. In the recent years, (Anees et al., 2013; 2014; Hussain, 2013; Hussain and Shah, 2013; Hussain et al., 2013a,b,c,d,e,f,g; 2014; Jamal et al., 2013; Shah et al., 2013; Hussain and Gondal, 2014) proposed very interesting encryption algorithms. Iterated function Department of Electrical Engineering, HITEC University, Taxila, Pakistan Received: 19 May 2014; accepted: 29 May 2014 Corresponding author: Azkar Hussain, Federal Urdu University Islamabad Islamabad, Pakistan. [email protected]

2 Hussain 3119 decryption from Section 2. In Section 4, the security analyses are presented and Section 5 is about the conclusion of the proposed work. Figure 1. Satellite communication general model. system (IFS) has been used to generate and describe manmade fractal-like structures and natural images. Barnsley and Alan (2008) were the first to present the concept of fractal image compression using IFS. A fully automatic image compression algorithm for real-world gray-scale images called fractal block coding (FBC) was proposed by Jacquin (2010). Many important research results on this topic are collected in Fisher (2004). Sayood (2005) indicated that the main point of FBC is that it can capture and exploit a special kind of image redundancy: piecewise self-similarity in images, which is not used in traditional image coding techniques. In general, the natural images are not exactly self-similar thus some transformations are needed to reconstruct the image from transformed parts of itself. The fractal code of the image is actually the collection of these transformations, which are called fractal transformations. Since fewer bits of the fractal transformations can represent the original image, high compression ratios can be achieved. On the other hand, the fractal compressed image is encrypted by a S 8 advanced encryption scheme (SAES) as the second encoding stage of the proposed scheme. The advanced encryption standard (AES) belongs to the symmetric-key encryption techniques and works with linear transformation theory. The SAES algorithm is applied on the fractal transformations to achieve the required goal: secured compressed aerial images. The paper is organized as follows. In Section 2, the proposed encryption and decryption scheme is presented. Section 3 consists of the projected communication algorithm, which incorporates encryption and 2. Proposed communication system The encryption process relies on the use of nonlinear mapping subsystems to create confusion in the cipher text. The design of these nonlinear components is a challenging task and requires complex algebraic expression for their description. In an effort to increase the complexity of nonlinear mappings, several implementations exhibiting interesting properties are proposed in the literature. In particular, an affine-power-affine (APA) structure is designed for the AES, which improves the complexity of its algebraic expression by increasing the number of terms. Based on the characteristics of the APA structure, a new nonlinear component is proposed that uses the symmetric group permutation S 8 on the Galois field GF(2 8 ) elements and provides the possibility to incorporate unique instances. A rigorous analysis is presented in Hussain et al. (2012) to evaluate the properties of these new nonlinear components by applying nonlinearity analysis, linear approximation analysis, differential approximation analysis, bit independence criterion and a strict avalanche criterion Construction of S 8 Affine-power-affine S-boxes The S 8 APA S-boxes are constructed with the application of S 8 (symmetric group) permutation on the existing elements in binary form. The bytes are independently processed, and the transformation to the new S-box exhibits nonlinear properties. The resulting number of S-boxes is with different properties. The process of creating new S-boxes is shown in Hussain et al. (2012). The mathematical representation of the S 8 transformation process is given as: f : S 8 APAS box! S 8 APAS box: 2.2. Fractal image compression stage Fractal image compression exploits similarities within images. These similarities are described by a contractive transformation T of the image whose fixed point is close to the image itself. A transformation T is called contractive if the distance d between two arbitrary points X, Y is becoming smaller after applying T to them: d ðx, YÞ d ðtðxþ, TðYÞÞ

3 3120 Journal of Vibration and Control 22(13) Figure 2. One round of image encryption. Figure 3. One round of image encryption. The image transformation consists of block transformations, which approximate smaller parts of the image by larger ones using contractive affine transforms (Cormode et al., 2011). The smaller parts are called ranges and the larger ones are domains. Each range forms a partition of the image while the total ranges (range-pool) represent the whole image Proposed encryption and decryption scheme The encryption scheme is a modified version of the AES. In this algorithm changes are induced in the byte sub-step of AES by introducing S 8 8*8 APA S-boxes of Section 2.1, to improve the statistical analysis of the encrypted image. The method is explained in Figure 2. The process begins with the add round key step, after that byte sub transformation is applied together Figure 4. Generalized flow chart of proposed technique. with an application of S 8 APA on plaintext data. The byte sub-step is necessary to induce confusion in the data. Now this data will pass from the shift row and mixed column step to induce diffusion in the data, because according to Shannon theory the confusion

4 Hussain 3121 Table 1. Value of UACI and NPCR for ciphered Baboon image. Position UACI NPCR UACI: unified average changing intensity; NPCR: number of pixels change rate. and diffusion steps are necessary to encrypt and image. The basic mechanism of all steps such as byte sub, shift row, mixed column and add round key, are the same as in the AES, so here S 8 APA S-boxes are introduced in the byte sub-step. Now for the decryption process the author will move in reverse order to get the plaintext image of the decryption scheme which is explained in Figure Proposed algorithm The proposed algorithm consists of the following steps: Step 1. Consider plaintext image. Step 2. Apply fractional compression on plaintext image. Step 3. In this stage, apply the encryption scheme which is proposed in Section 2.3. Step 4. A cipher text image will be obtained from which insecure lines of communication from the satellite can be sent to the ground. Now for the decryption process the author will move in the reverse order and will get the original image. The scheme is explained in Figure Sensitivity analysis The average density between two images can be measured by unified average changing intensity (UACI) (Shatheesh et al., 2012). Two plain images differ in that they are different in only one pixel which can be encrypted and combined to obtain cipher images CA and CB. In this case UACI can be represented as: UACI ¼ 1 M N XMN i¼1 jca i cb i j 255 In the above mentioned equation ca i and cb i are the ith pixels of the cipher image. If an eight-bit is taken, the value of UACI comes out to be For experimenting purposes a set of eight different pixels have been chosen, yet one at a time, changing their value slightly by one. As shown in Table 1, all values of UACI in the second row are very close to ideal value. NPCR (Zhou and Liao, 2012), is a relatively better indicator of sensitivity of the algorithm corresponding to image encryption i.e. the change in the pixels of the cipher image if one of the pixels from the plain image is changed. The NPCR can be calculated by: NPCR ¼ # ica i 6¼ cb i M N For an ideal image encryption algorithm, NPCR is usually expected to turn out as (about ). During experimentation, around eight unique pixels are randomly chosen in each plain image and slightly altered their value. In Table 1, the values of NPCR are presented in the third row, all of which are close to Conclusions There is, therefore, a good image encryption algorithm as shown in Table 1. The value of NPCR and UACI analysis of the proposed algorithm are very close to the optimal value. Furthermore, this algorithm provides an extra confusion due to chaotic substitution box transformation. This algorithm directly hits the S-P network idea of Shannon due to the permutation and substitution operation. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. References Anees A, Khan WA, Gondal MA and Hussain I (2013) Application of mean of absolute deviation method for the selection of best nonlinear component based on video encryption. Z. Naturforsch Journal of Physical Sciences 68a: Anees A, Siddiqui AM, Ahmed J and Hussain I (2014) A technique for digital steganography using chaotic maps. Nonlinear Dynamics 75: Barnsley M and Alan D (2008) A better way to compress images Byte. Cormode G, Paterson M, Sahinalp SC and Vishkin U (2011) Communication complexity of document exchange. In Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, Jan , pp Fisher Y (2004) Fractal Image Compression - Theory and Application. New York: Springer-Verlag.

5 3122 Journal of Vibration and Control 22(13) Hussain I (2013) A novel approach of audio watermarking based on S-box transformation. Mathematical and Computer Modelling 57: Hussain I and Gondal MA (2014) An extended image encryption using chaotic coupled map and S-box transformation. Nonlinear Dynamics DOI: /s z. Hussain I and Shah T (2013) Literature survey on nonlinear components and chaotic nonlinear components of block ciphers. Nonlinear Dynamics 74: Hussain I, Azam NA and Shah T (2014) Stego optical encryption based on chaotic S-box transformation. Optics & Laser Technology 61: Hussain I, Shah T and Gondal MA (2013a) Application of S- box and chaotic map for image encryption. Mathematical and Computer Modelling 57: Hussain I, Shah T and Gondal MA (2013b) A group theoretic approach to construct cryptographically strong substitution boxes. Neural Computing & Application 23: Hussain I, Shah T and Mahmood H (2013c) A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Computing & Application 22: Hussain I, Shah T, Gondal MA and Mahmood H (2012) S8 affine-power-affine S-boxes and their applications. Neural Computing & Application 21: S377 S383. Hussain I, Shah T, Gondal MA and Mahmood H (2013d) A novel method for designing nonlinear component for block cipher based on TD-ERCS chaotic sequence. Nonlinear Dynamics 73: Hussain I, Shah T, Gondal MA and Mahmood H (2013e) Efficient method for designing chaotic S-boxes based on generalized Baker s map and TDERC chaotic sequence. Nonlinear Dynamics 74: Hussain I, Shah T, Gondal MA and Mahmood H (2013f) A novel image encryption algorithm based on chaotic maps and GF(2^8) exponent transformation. Nonlinear Dynamics 72: Hussain I, Shah T, Gondal MA and Mahmood H (2013g) An efficient approach for the construction of LFT S-boxes using chaotic logistic map. Nonlinear Dynamics 71: Hutchinson J (2001) Fractals and self-similarity. Indiana University Mathematics Journal. Jacquin AE (2010) Image coding based on a fractal theory of iterated contractive image transformations. IEEE Transaction on Image Processing Vol. 1, no. 1. Jamal SS, Shah T and Hussain I (2013) An efficient scheme for digital watermarking using chaotic map. Nonlinear Dynamics 73: Sayood K (2005) Introduction to Data Compression, 3rd edn. San Francisco, CA: Morgan Kaufmann, pp Shah T, Qamar A and Hussain I (2013) Substitution box on maximal cyclic subgroup of units of a Galois ring. Z. Naturforsch Journal of Physical Sciences 68a: Shatheesh S, Devaraj I and Bhuvaneswaran RS (2012) An intertwining chaotic maps based image encryption scheme. Nonlinear Dynamics 69: Zhou Q and Liao X (2012) Collision-based Fexible image encryption algorithm. Journal of System and Software 85: