An application of Rossby wave triads in information security

Abstract

In recent decades, the protection of sensitive data has achieved a lot of attention from cryptographers. The researchers have suggested di erent types of security informative techniques. The main principle of cryptographic approach is to use key(s) to transform critical data into an unreadable form. Shannon [30] proved that confusion and di usion in the data up to a certain level is essential for a secure security system. The di usion is composed in dispersed the impact of plaintext bits to ciphertext bits to di cult to understand the statistical con guration of the plaintext. Confusion is the process of conversion in which statistics of ciphertext change in line with the alteration of the plaintext information. There are various sort of cryptosystems which are based upon di erent concepts in mathematics. An S-box is primarily responsible for confusion and di usion 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, di erential approximation probability. In substitution permutation cipher structures S-boxes are used as important nonlinear components that guarantee the confusion property of block ciphers [8, 23, 36]. Rossby waves, also known as planetary waves, are a type of inertial wave naturally occurring in rotating uids. They were rst identi ed by Carl-Gustaf Arvid Rossby. Atmospheric Rossby waves on Earth are giant meanders in highaltitude winds that have a major in uence on weather. These waves are associated with pressure systems and the jet stream. Oceanic Rossby waves move along the thermocline: the boundary between the warm upper layer and the cold deeper part of the ocean. Rossby waves are also a solution of simpli ed form of the equations governing the dynamics of the atmosphere and oceans. In 2013, Hayat et al. [15] had prove that the Rossby wave triads lie on an elliptic surface. In [33], rstly has used Rossby wave triads in cryptography. Elliptic curves (EC) are also used in the development of powerful cryptosystems. The notion of elliptic curve was rstly introduced in cryptography in [25]. ii In addition, a cryptosystem is suggested that's 20% e cient than Di e-Hellman algorithm. A cryptosystem primarily depends on elliptic curve is shown in [26]. A relation between both the hyper elliptic curve points and the nonlinearity of the S-box is shown in [17]. In [19], the idea of a discrete logarithmic issue is utilized to build a highly safe, fast, and e cient security system. In [1], a comparison between elliptic curve cryptography and RSA is given. It is observed that ECC with a smaller key lengths is more secure as compared to RSA with larger key length. The programs and merits of ECC are mentioned in [34]. In [13, 14], presents a new technique for construction of S-boxes primarily based on points on elliptic curve over a prime eld. 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 resistant against di erent cryptographic attacks. This thesis comprises of three chapters which are brie y described below. Chapter 1, we outlined some concepts related to elliptic curve cryptography and Rossby wave triads. The de nitions of elliptic curve, Mordell elliptic curve and isomorphism between two elliptic curves are also discussed. We also study resonant triads, quasi-resonant triads, and a brief introduction of a relation between quasi-resonant triads and two auxiliary parameters has given. Chapter 2, represents an image encryption scheme that works on the base of the Mordell elliptic curve and Rossby wave triads. Chapter 3, describes the main aim of this thesis, that is, the S-boxes generation scheme using Rossby wave triads.