Symmetric Ciphers for Fully Homomorphic Encryption

Abstract

Fully homomorphic encryption is the latest addition to the world of cryptography. It is a type of encryption that allows operations to be done on ciphertexts, which is not possible with traditional encryption. The field has gained a lot of traction since it was first theoretically proved possible in 2009. This thesis goes through how fully homomorphic encryption works, from making a somewhat homomorphic encryption scheme, into a fully homomorphic scheme. We also explain in detail the different aspects required, such as bootstrapping and noise. Since 2009 several schemes and libraries to optimize homomorphic encryption have been suggested, so that it one day may be feasible to implement it in regular modern-day applications. Some libraries target regular developers without an extensive cryptographic background, so they may still be able to use homomorphic encryption in applications, while others aim for researchers to implement and discover the possibilities that come with fully homomorphic encryption. With a focus on the use for fully homomorphic encryption within cloud computing, this thesis focuses on how symmetric ciphers can make fully homomorphic encryption possible, also for use with small IoT devices. We look at several such ciphers that have been suggested and focus on the family of stream ciphers called Rasta. We have implemented one variant of the Rasta cipher using the software library HElib and timed its performance.