Computational Design of Block Cipher over Elliptic curve Point

Abstract

In recent decades, the protection of sensitive data has achieved a lot of at tention from cryptographers. The researchers have suggested different types of security informative techniques. The main principle of cryptographic approach is to use key(s) to transform critical data into an unreadable form. Shan-non [1] has proved that confusion and diffusion in the data up to a certain level is essential for a secure security system. The diffusion is composed in dispersed the impact of plaintext bits to ciphertext bits to difficult to understand the sta tistical configuration of the plaintext. Confusion is the process of conversion in which statistics of ciphertext change in line with the alteration of the plaintext 1 Contents information. There is various sort of cryptosystems which are based upon dif ferent concepts in mathematics. An S-box is primarily responsible for confusion and diffusion in the input data in many cryptographic techniques. An S-box is said to be good when it can produce high resistance against several cryptograhic attacks, which are measured by non-linearity, linear approximation probability, strict avalanche criterion, bit independence criterion, differential approximation probability and NIST SP 800-22. In substitution permutation cipher structures S-boxes are used as important nonlinear components that guarantee the confusion property of block ciphers [2, 3, 4, 5, 6]. Elliptical curves (EC) are also used in the development of powerful cryptosys tems. The notion of elliptic curve was firstly introduced in cryptography in [7]. In addition, a cryptosystem is supplied that’s 20% efficient than Diffie–Hellman algorithm. A cryptosystem primarily depends on elliptic curve is shown in [8]. Relation between both the hyper elliptic curve points and the non-linearity of the S-box is shown in [9]. In [10], the idea of a discrete logarithmic issue is utilized to build a highly safe, fast, and efficient security system. In [11], there is a com parison between elliptic curve cryptography and RSA is given. It is observed that ECC with a smaller key lengths has more secure as compared to RSA with larger key length. The programs and merits of ECC are mentioned in [12]. In [13, 14], presents a new technique for construction of S-boxes primarily based on points on elliptic curve over a prime field. Consistency of previously used S-boxes Experts still hasn’t had the most surprising ranking of S-box criteria. In this way, it is necessary to construct another special S-box design with the objective that the corresponding S-box is to be resistant against different cryptographic attacks. This thesis comprises of three chapters which are briefly described below. In Chapter 1, we study the basic concepts related to algebraic cyptography and elliptic curve cryptography. Chapter 2, represents the different techniques of construction of S-boxes such as construction over Galois field and Elliptic curves. Chapter 3 describes the main aim of this thesis, that is, the proposed S-box scheme using elliptic curve points.