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An Exploration of One-Way Functions and their Cryptographic Implications

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A one-way function (OWF) is a function that is computationally feasible to compute in one direction, but infeasible to invert. Many current cryptosystems make use of properties of OWFs to provide ways to send secure messages. This paper reviews some

A one-way function (OWF) is a function that is computationally feasible to compute in one direction, but infeasible to invert. Many current cryptosystems make use of properties of OWFs to provide ways to send secure messages. This paper reviews some simple OWFs and examines their use in contemporary cryptosystems and other cryptographic applications. This paper also discusses the broader implications of OWF-based cryptography, including its relevance to fields such as complexity theory and quantum computing, and considers the importance of OWFs in future cryptographic development

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2020-05

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Branching Worlds: Quantum Mechanics and Hugh Everett's Many-Worlds Interpretation

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This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make u

This thesis attempts to explain Everettian quantum mechanics from the ground up, such that those with little to no experience in quantum physics can understand it. First, we introduce the history of quantum theory, and some concepts that make up the framework of quantum physics. Through these concepts, we reveal why interpretations are necessary to map the quantum world onto our classical world. We then introduce the Copenhagen interpretation, and how many-worlds differs from it. From there, we dive into the concepts of entanglement and decoherence, explaining how worlds branch in an Everettian universe, and how an Everettian universe can appear as our classical observed world. From there, we attempt to answer common questions about many-worlds and discuss whether there are philosophical ramifications to believing such a theory. Finally, we look at whether the many-worlds interpretation can be proven, and why one might choose to believe it.

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2021-05

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Entanglement, Locality, and Hidden Variables

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The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as

The purpose of this paper is to provide an analysis of entanglement and the particular problems it poses for some physicists. In addition to looking at the history of entanglement and non-locality, this paper will use the Bell Test as a means for demonstrating how entanglement works, which measures the behavior of electrons whose combined internal angular momentum is zero. This paper will go over Dr. Bell's famous inequality, which shows why the process of entanglement cannot be explained by traditional means of local processes. Entanglement will be viewed initially through the Copenhagen Interpretation, but this paper will also look at two particular models of quantum mechanics, de-Broglie Bohm theory and Everett's Many-Worlds Interpretation, and observe how they explain the behavior of spin and entangled particles compared to the Copenhagen Interpretation.

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2021-05