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.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Meissen, Rebecca M.

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-042612-132350

Advisor

• Martin, William J.

Year

• 2012

Date created

• 2012-04-26

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright