Vol. 08, No. 09 [September 2022]

The most known of public key cryptosystem was introduced in 1978 by Rivest, Shamir and Adleman[19] and now called the RSA public key cryptosystem in their honor. Later, a few authors gave a simply extension of RSA over algebraic numbers field( see [20]-[22]), but they require that the ring of algebraic integers is Euclidean ring, this requirement is much more stronger than the class number one condition. In this paper, we introduce a high dimensional form of RSA by making use of the ring of algebraic integers of an algebraic number field and the lattice theory. We give an attainable algorithm (see Algorithm I below) of which is significant both from the theoretical and practical point of view. Our main purpose in this paper is to show that the high dimensional RSA is a lattice based on public key cryptosystem indeed, of which would be considered as a new number in the family of post-quantum cryptography(see [17] and [18]). On the other hand, we give a matrix expression for any algebraic number fields (see Theorem 2.7 below), which is a new result even in the sense of classical algebraic number theory
Key Words: RSA, The Ring of Algebraic Integers, Ideal Matrix, Ideal Lattice, HNF Basis

Multimedia streams usage increases nowadays and that creates the scope of development of efficient and effective methodologies for manipulating different image databases storing this type of information. Any content-based access to video data always requires parsing of each video stream into its building blocks. Any video stream consists of a number of shots; each one is a sequence of frames. Shot boundary detection is the very first step in any video stream-analysis system and there are numbers of proposed techniques are available for solving the problem of shot boundary detection, but the major limitation to them are their inefficiency, lack of reliability and less trustworthy. Here, proposes to learn shot boundary detection end-to-end, from pixels to final shot boundaries. For training such a model, we created our own dataset and automatically generated transitions such as cuts, dissolves and fades. Here we propose a Convolutional Neural Network (CNN) and Euclidean Distance algorithm and Change Point Analysis algorithm to make the system more efficient and accurate in nature.
Key Words: Convolutional Neural Network (CNN), Euclidean Distance algorithm