Elliptic Curve Computation and Their Applications in Data Security

Abstract

In the recent era, the security of sensitive information has gained widespread attention. The multimedia data is one of the key sources of information, which can be agreements, photographs, medical reports, contracts, or other types of scanned papers, with the highest rank of sensitivity. The privacy of digital information is of utmost importance while communicated among authorized parties. To deal the security and privacy of multimedia data gave rise to the various efficient encryption algorithms. These algorithms are further based on two different ideas: symmetric and asymmetric key-algorithm. Various efficient algorithms are developed to generate substitution boxes (S-boxes) and pseudo-random number sequences. S-boxes have two major categories: Static and dynamic S-box. A static S-box depends on fixed operating as well as generating modes while a dynamic S-box has both variable modes of operations. As a result, dynamic S-boxes algorithms are preferred mostly to increase the computational cost for cryptanalysts. Recently, Razaq et al. [108], developed a novel algorithm with the help of group structure for secure S-box in terms of high nonlinearity. Toughi et al. [13], proposed an image encryption algorithm with core modules PRNG and advanced encryption standard AES. The authors in [14], used the chaotic model to design image encryption scheme with enough pseudo creation capability. Due to multiple advantages such as non-periodicity, high sensitivity to input parameters, ergodicity, key sensitivity, chaotic systems, and ECs are extensively adopted for S-box and pseudo-random number generation in image encryption algorithms. The authors in [19], designed a secure algorithm that can be suitable in either digital and optical environments. Wang et al. [20], suggested a cryptosystem based on multi-group techniques such as chaotic map, Fisher-Yates Shuffling, and DNA sequence encoding. The authors of this research study claimed to have high accuracy with fast convergence as an advantage of the encryption algorithm. In light of computational precision, chaotic maps can have the possibility to generate a random sequence with a short period. Reyad et al. [22], developed an idea based on ECs to get pseudo-random numbers that work efficiently in image cryptography. El-Latif et al. [23], utilized both cyclic ECs and hybrid-chaotic systems for developing an efficient image encryption scheme. The less computational effort with strong security, Elliptic curve based cryptographic architectures are more reliable as compared to the existing cryptographic methods. We introduced an efficient cryptosystem based on elliptic curves for digital image encryption. The designed scheme is consisting of three steps. Initially, the system uses the special type of i the isomorphic elliptic curves over a prime field and scrambles the pixel position of the plain image. Consequently, it disperses the intra-correlation among the pixels of the original image, and capable the scheme to be secure against statistical attacks. In the third step, the scheme generates multiple S-boxes with good cryptographic features by using isomorphic elliptic curves. The generated S-boxes are then used to substitute the scrambled data that produce optimum confusion in the ciphered data. Eventually, the encryption procedure generates PRNs through the arithmetic operation of the elliptic curves instead of elliptic curve group law; the operation used in the scheme creates high randomness as a result our proposed scheme shows high security against classical attacks. The simulation results and performance analysis divulge that the proposed scheme has excellent encryption performance with less computational effort, which indicates that the scheme has effective potential in real-time image encryption application. Secondly, we discuss the security strength of the elliptic curve cryptosystems (ECC) is due to its core operations-based group law. This aspect of the elliptic curve provides key service to ensure security against modern cryptanalysis. However, the excess use of group law in EC based algorithms make it computationally hard for real time applications. In this context, we presented a smart-like algorithm based on subgroup co-set operations. The suggested scheme uses all co-sets that generates multiple sequences that can smoothly be adopted in most promising communication architectures of the future such as internet of things (IoT). Besides, the subgroup structure on a small prime with possible embedding is managed to construct efficient S-box. Whereas, the performance of the proposed S-box is examined via standardized tests thus found significant for multimedia data security applications. Moreover, a small prime based EC subgroup coset model is designed, that generates a set of experimentally verified independent pseudo random streams. The atypical mathematical model for its application to image data encryption is established, by combining the S-box module (SM) and subgroup coset module (ECS-PRNSM). Several statistical tests revealed that the proposed technique is suitable for various cryptographic applications. Thirdly, in this dissertation, we discuss the Efficient multiple PRNS and S-boxes are one of the most significant building blocks, which are jointly adopted normally for secure data encryption. Multiple aspects pave the way to handle large-scale multimedia data. However, the computational work on multiple constructions may certainly lead to limits the required ciphering through-put. Therefore, reducing the computational time of multiple PRNS and S boxes is the main requirement for an efficient cryptosystem. For this achievement, we exploited the indexing technique over elliptic curves with small prime fields and introduce a ii computationally efficient mechanism for multiple PRNS and S-boxes. Statistical results of multiple S-boxes show that the proposed S-box mechanism is the most effective method that generates strong multiple S-boxes on minimum prime fields. Likewise, the PRNS’s assessment indicates that the proposed mechanism is the highly productive model for generating multiple verified patterns on small prime fields in a single round. Consequently, it might be smoothly formalized to diffused large-scaled image data. Subsequently, the experimental results and analysis show that the proposed algorithm provides desired keyspace, better statistical properties of encrypted data, and less computational effort.