Discrete mathematics topics in the secondary school curriculum

This thesis discusses two topics of discrete mathematics in a manner suitable for presentation at a secondary-school level. The introduction outlines the benefits of including discrete mathematics in the secondary-school curriculum. The two chapters which follow include detailed treatment of the two selected topics: the Traveling Salesman Problem and RSA encryption. The discussion of the Traveling Salesman Problem consists of introduction to the problem through several real-life scenarios, followed by a discussion of various methods for solving the problem. We discuss exact and approximate algorithms together with their computational complexity and practical limitations. The discussion of RSA encryption begins with an introduction to the necessary background in number theory, which includes the Chinese Remainder Theorem, Bezout\u27s Equation, and Fermat\u27s Little Theorem. Following this is a discussion of encryption and decryption techniques, which are illustrated through an example that is accessible to any student with a basic scientific calculator

SECURITY IMPROVEMENT AND TRUST ENHANCEMENT IN CLOUD-BASED SERVICES

Management of trust is one of the most challenging parts in cloud computing. Cloud service's features such as distributed, dynamic and nontransparentintroduces several challenges for availability, privacy, and security. A method is proposed to have trust as a service between cloud serviceprovider and customer by creating a cloud armor. This proposed methodology is used to make cloud server end and customer end system secure ofany intrusion to their privacy. In this methodology, we will have a user usage pattern log as ever user has its own unique way of using his/her system;hence, in case if any odd user pattern is being encountered it will automatically block the system and simultaneously shoots a message as well as a callto the user notifying him/her about this unauthorized access. This log is set a various small pattern log, for example, keylog, preferable website visited,and time of accessing the system. Further, we have secured these logs using Rivest-Shamir-Adleman algorithm with very large key size

Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations

In this paper we propose a definition and construction of a new family of one-way candidate functions ${\cal R}_N:Q^N \to Q^N$, where $Q=\{0,1,...,s-1\}$ is an alphabet with $s$ elements. Special instances of these functions can have the additional property to be permutations (i.e. one-way permutations). These one-way functions have the property that for achieving the security level of $2^n$ computations in order to invert them, only $n$ bits of input are needed. The construction is based on quasigroup string transformations. Since quasigroups in general do not have algebraic properties such as associativity, commutativity, neutral elements, inverting these functions seems to require exponentially many readings from the lookup table that defines them (a Latin Square) in order to check the satisfiability for the initial conditions, thus making them natural candidates for one-way functions.Comment: Submitetd to conferenc

Nation-State Attackers and their Effects on Computer Security

Nation-state intelligence agencies have long attempted to operate in secret, but recent revelations have drawn the attention of security researchers as well as the general public to their operations. The scale, aggressiveness, and untargeted nature of many of these now public operations were not only alarming, but also baffling as many were thought impossible or at best infeasible at scale. The security community has since made many efforts to protect end-users by identifying, analyzing, and mitigating these now known operations. While much-needed, the security community's response has largely been reactionary to the oracled existence of vulnerabilities and the disclosure of specific operations. Nation-State Attackers, however, are dynamic, forward-thinking, and surprisingly agile adversaries who do not rest on their laurels and are continually advancing their efforts to obtain information. Without the ability to conceptualize their actions, understand their perspective, or account for their presence, the security community's advances will become antiquated and unable to defend against the progress of Nation-State Attackers. In this work, we present and discuss a model of Nation-State Attackers that can be used to represent their attributes, behavior patterns, and world view. We use this representation of Nation-State Attackers to show that real-world threat models do not account for such highly privileged attackers, to identify and support technical explanations of known but ambiguous operations, and to identify and analyze vulnerabilities in current systems that are favorable to Nation-State Attackers.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143907/1/aaspring_1.pd

Molecular Spin Qudits for Quantum Algorithms

Presently, one of the most ambitious technological goals is the development of devices working under the laws of quantum mechanics. One prominent target is the quantum computer, which would allow the processing of information at quantum level for purposes not achievable with even the most powerful computer resources. The large-scale implementation of quantum information would be a game changer for current technology, because it would allow unprecedented parallelised computation and secure encryption based on the principles of quantum superposition and entanglement. Currently, there are several physical platforms racing to achieve the level of performance required for the quantum hardware to step into the realm of practical quantum information applications. Several materials have been proposed to fulfil this task, ranging from quantum dots, Bose-Einstein condensates, spin impurities, superconducting circuits, molecules, amongst others. Magnetic molecules are among the list of promising building blocks, due to (i) their intrinsic monodispersity, (ii) discrete energy levels (iii) the possibility of chemical quantum state engineering, and (iv) their multilevel characteristics, leading to the so called Qudits (d > 2), amongst others. Herein we review how a molecular multilevel nuclear spin qubit (or qudit, where d = 4), known as TbPc2, gathers all the necessary requirements to perform as a molecular hardware platform with a first generation of molecular devices enabling even quantum algorithm operations.Comment: Chem. Soc. Rev., 2017, Advance Articl