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The concept of interval-valued intuitionistic fuzzy set was introduced by Atanassov and Gargov [2] in the year 1989.In this paper the Cartesian product of interval-valued intuitionistic fuzzy k-ideals is introduced. Also some basic properties are derived. The relationship between interval-valued intuitionistic fuzzy k-ideal A, B and A × B are proposed. Some theorems related to the above concepts are stated and proved.

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Resistive switching at the nanoscale is at the heart of the memristor devices technology. These switching devices have emerged as alternative candidates for the existing memory and data storage technologies. Memristors are also considered to be the fourth pillar of classical electronics; extensive research has been carried out for over three decades to understand the physical processes in these devices. Due to their robust characteristics, resistive switching memory devices have been proposed for neuromorphic computation, in-memory computation, and on-chip data storage. In this chapter, the effects of various external stimuli on the characteristics of resistive switching devices are comprehensively reviewed. The emphasis will be given on 2-dimensional (2D) materials, which are exciting systems owing to superior electrical characteristics combined with their high stability at room temperature. These atomically thin 2D materials possess unique electrical, optical and mechanical properties in a broad spectrum, and open the opportunity for developing novel and more efficient electronic devices. Additionally, resistive switching due to light has also grabbed the attention of optoelectronic engineers and scientists for the advancement of optical switches and photo tuned memristors. The variety of material systems used in the fabrication of memristors is comprehensively discussed.

Now a day's many people are connected to the internet with large amount of confidential information such as mails, transactions, being transmitted every day. Privacy and the confidentiality of this information can be achieved by encryption algorithms. The consequence is the significant improvement of cryptanalysis techniques. Phelix is one of the high-speed stream encryption cipher technique with built-in single-pass functionality. In Phelix We use a 2 8 -bit key, 2 7 -bit nonce to create design strength of 128 bits. This paper simulates and implements the function of Phelix stream cipher, wrote the codes to implement full algorithm that includes encryption and decryption using Very high speed hardware description language (VHDL) and provided the simulation and implementation results using Active HDL Simulation tool and Xilinx implementation tool respectively. The simulation result shows that the designed IP core meets the required protocol specifications for the proper functioning of Phelix stream cipher.

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