Date of Award


Document Type


Degree Name

Master of Science (MS)


Mathematical Sciences

Committee Chair/Advisor

Shuhong Gao

Committee Member

Ryann Cartor

Committee Member

Felice Manganiello

Committee Member

Hui Xue


In 2009, Craig Gentry introduced the first fully homomorphic encryption scheme using bootstrapping. In the 13 years since, a large amount of research has gone into improving efficiency of homomorphic encryption schemes. This includes implementing leveled homomorphic encryption schemes for practical use, which are schemes that allow for some predetermined amount of additions and multiplications that can be performed on ciphertexts. These leveled schemes have been found to be very efficient in practice. In this thesis, we will discuss the efficiency of various homomorphic encryption schemes. In particular, we will see how to improve sizes of parameter choices in homomorphic encryption schemes with a variety of techniques to include modulus leveling and techniques of error bound control.



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