Ομομορφική κρυπτογραφία με ιδεώδη δικτυώματα
Homomorphic encryption using ideal lattices
In this Master’s Thesis we do a survey about the development of fully homomorphic encryption. We study Gentry’s scheme which is the first fully homomorphic encryption scheme, solving a central open problem in cryptography. Gentry with his construction allows us to compute arbitrary functions over encrypted data without decrypt them first. Fully homomorphic encryption has numerous applications. For example allows to us to make private queries to a search engine. Suppose that a user wants to search for something so he commits a query in encrypted format to the search engine. The engine implements a fully homomorphic scheme so it can handle the query in absolutely encrypted mode and return the result in also encrypted format without knowing what it returned or what the engine searched about. This provides the users with full search privacy. Gentry’s construction begins with a somewhat homomorphic encryption scheme. Gentry then shows how to slightly modify this scheme to make it bootstrappable. Finally, he shows that any bootstrappable somewhat homomorphic encryption scheme can be converted into a fully homomorphic encryption through a recursive self-embedding. Gentry based the security of his scheme on hard problems over ideal lattices and the sparse subset sum problem.