© 2019 Mustafa K. Ramadhan and Adil AL-Rammahi. This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license. Journal of Computer Science Original Research Paper Image Cryptography with Least Squares Approximations 1 Mustafa K. Ramadhan and 2 Adil AL-Rammahi 1 Department of Computer Techniques Engineering, Al-Safwa College University, Iraq 2 Department of Mathematics, Faculty of Mathematics and Computer Science, University of Kufa, Iraq Article history Received: 22-08-2019 Revised: 12-10-2019 Accepted: 19-11-2019 Corresponding Authors Adil AL-Rammahi Department of Mathematics, Faculty of Mathematics and Computer Science, University of Kufa, Iraq Email: adilm.hasan@uokufa.edu.iq Abstract: Security of digital images has become one of the most important issues in network technologies. Different techniques have been evolved over the past few years to provide security for digital images through concealing information, image scrambling and image encryption. The aim of this work is to enhance the network security level by using the cryptographic method based on the Least Square Approximation technique (LSA). This work is one of the first attempts due to the use of the least squares polynomial of fifth degree technique as data interpolation in the image cryptography process. It has been proven in this study that a high level of correlation exists amongst the original and the corresponding decrypted images. The achieved high values of the measured Peak Signal to Noise Ratio (PSNR) for the decrypted images in this study are an indication to the high accuracy of the proposed technique in comparison to other cryptographic techniques. The output of the encrypted technique in this study reveals its reliability and robustness against security attacks. Keywords: Index Terms-Image Encryption, Least Squares Approximations, Peak Signal to Noise Ratio, Coefficient Correlations Introduction Information security is an increasingly important concern in the social networking era. Cryptography plays a crucial role in different popular applications of multimedia technology such as smart phones communications, electronic commerce, exchange of private emails, ATM security, transmitting financial information, etc. Cryptography can be described as a process of converting particular data into unreadable format for secure electronic transmitting and then retransforming it back to its original form. Different encryption methods have been proposed to protect the confidential data from unauthorized use such as discrete logarithm (Odlyzko, 2000), Rivest-Shamir- Adleman (RSA) public key (Rivest et al., 1970), knapsack (Merkle and Hellman 1978) and the alike. Those techniques depended on the Galio field construction technique which is considered a difficult one to employ (Merkle and Hellman, 2017). They are based on highly complicated concepts represented in algebra modular, prime number, operators, vector spaces and orthogonal basis. To overcome those difficulties and complexities, different methods have been introduced, such as a hybrid chaotic map for image encryption and hiding problems. In that method, the ciphered image is embedded into several carrier images (Cao, 2013). Based on the composition of the three classic chaotic maps: The logistic map, the Henon map and the Ikeda map, the hybrid chaotic map demonstrates a more complex chaotic characteristic than that of the single chaotic maps. Younes and Jantan presented a block-based transformation algorithm. They combined the process of image transformations and the well known Blowfish encryption and decryption algorithm (Younes and Jantan, 2008). That technique introduced lower correlations and higher entropies due to the increase in the number of blocks owing to the use of smaller block sizes. El Abbadi et al. (2014) introduced an image encryption using the Singular Values Decomposition (SVD). Elabbadi utilised the spectral diagonal matrices of two images to produce a new third one. Al-Rammahi (2015) used mutual two images for crypto one image via SVD technique. Mutual singular value decomposition approach can perform well with simple images, but it is not an appropriate method to be employed with complex images due to the simplicity of the SVD method. To overcome the associated drawbacks with that method, (Al-Rammahi, 2014a; 2014b) proposed another two methods for image encryption/decryption operation, see. However, limitations still associated with those two methods when they were applied to the very complex digital images.