Volume of Square Pyramid Dependent Elliptic curve Cryptography

Abstract

The accelerated development in digital technology and network communica tions in the last few decades has enhanced the communications of electronic data in the wireless network. However, the secrecy of sensitive information’s during the transmission over the open network is doubtful and arise several questions on the issue. Cryptography is the study to overcome the problem of secure trans formation. Further cryptography is classified into two subfields, asymmetric key cryptography and symmetric key cryptography. This classification is made ac cording to the key. In asymmetric key cryptography dissimilar keys are used for encryption and decryption. In symmetric key cryptography the same key is used for encryption and decryption. Advanced encryption standard (AES)[1], data en cryption standard (DES)[2] and triple data encryption standard (TDES)[3] are the examples of symmetric key cryptography. The scheme such as AES and TDES are the efficient cryptographic algorithm and suitable for the security of small data’s, however these schemes are incapable to secure multimedia like digital image, audio and video data which contain large amount of data. The multimedia data is an important source to deliver information over the network, and widely used in many fields. The most important one of them is the digital image which has a signifi cant information panache and often used for the exchange of digital information. However, due to open network development the secrecy of the image which con tain sensitive information during transmission is a major issue. Chaotic systems are broadly used in the field of digital image security to prevent the privacy of secret information of the image during storing or transmitting over the open net work. In the last few decades numerous image encryption schemes were proposed. The chaos-based encryption schemes are usually based on low and high dimension chaotic sequences. The low dimensional chaotic sequences schemes have enough security issues due to low accuracy and short cord period. Thus, researcher pay attention to used high dimensional chaotic sequence in the encryption algorithm [4, 5, 24, 25]. However, the algorithm based on high dimension chaotic sequences are highly complex, required more space. The cryptosystems based on elliptic v curve have excellent cryptographic properties, depend on the discrete logarithmic problems. In this thesis is to discuss the Elliptic curve cryptography. Elliptic curve cryp tography (ECC) gain a considerable attention in the field of information security. The ECC based cryptosystems are more efficient as it is valuable against the side channel attacks. In this paper, we introduced a digital image encryption scheme based on isomorphic elliptic curves. In the proposed work, initially we split the pixels of an image into least significant bits (LSB) and the most significant bits (MSB) and then we transform the MSB of the image into elliptic curve points by using Koblitz method. Afterward, we map the obtained points into the other iso morphic elliptic curve to produce diffusion in the scheme. The diffusion process is performed through the small S-box construction scheme deployed in the proposed that generate a good quality S-box based on elliptic curve point. The analysis of the proposed scheme is compared with the existing scheme and found the results are specify batter than the existing scheme.