Faculty Advisor

Martin, William J.

Abstract

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's 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.

Publisher

Worcester Polytechnic Institute

Date Accepted

April 2012

Major

Mathematical Sciences

Project Type

Major Qualifying Project

Accessibility

Unrestricted

Advisor Department

Mathematical Sciences

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