A Mathematical Approach to Fully Homomorphic Encryption

The homomorphic properties of various encryption schemes have been a fascination of the cryptographic community for decades. With the rise of cloud computing and decentralized processing, the need for security in such applications is increasing. Only recently, however, has the construction of a fully homomorphic encryption scheme been realized. I present a mathematical approach to Craig Gentry\u27s proposed fully homomorphic scheme. I start with an overview of other homomorphic encryption schemes, followed by an examination of polynomial rings and their relation to lattices. Finally, I explore the scheme itself and provide a foundation from which to understand the challenges faced when constructing a fully homomorphic encryption scheme

Capturing the Changing Face of the Venetian Retail Sector

The retail sector of Venice has been evolving considerably since World War II, with a high number of store closures. Theories as to the cause of this phenomenon include population decline, high levels of tourism, rise of supermarkets, or a combination of these factors. This project intended to explore this phenomenon by examining and collecting current shop information and analyzing past data. Additionally, residential comfort in the city of Venice was to be examined using current shop information. Finally, this project developed a mechanism for making all of our work sustainable so that past and future shop information can be collected and inserted with ease