Degree Name
Master of Science
Department or Program
Mathematics
Advisor
Spector Kathy
Abstract
This work provides a mathematical approach of the Fully homomorphic encryption (FHE) and its implementation in a wireless network. FHE has been presented as the "Holy Grail" by the cryptographers. This special encryption scheme enables one to perform complex operations(both addition and multiplication) on a cypher text without ever decrypting the text. An immediate application is the delegated computation, an untrusted party can process the data without endangering the privacy of the source and the integrity of the data. The first FHE scheme was introduced in 2009, by Craig Gentry. His scheme was based on the properties of rings especially on ideal lattices.As introduced by Gentry, FHE was not practical due to the length of ciphertext (per bit encrypted) and the keys, and its infeasible computational time. Many works have been done to make it somewhat practical(Shai-Halevi(2010), Smart-Vercauteren(2011)).The proposed schemes were based on algebra and number theory concepts. Following the idea of Smart-Vercauteren, and the implementation of Michael Brenner we design an implementation for wireless network. Such a system should allow operations on encrypted data that could result in reducing the computation load and the size of the packets in a wireless network. The most challenging part of this work will be to make the computational time of the FHE quasi real while preserving its security scheme. Since the strength of the FHE comes from the hardness to approximate short vector problems on arbitrary lattices within a slightly super polynomial factor, making that computational time logarithmic or less is quite challenging. This work attempts to design and implement fully homomorphic encryption for wireless networks.