Symmetric Fully Homomorphic Encryption Using Decidable Matrix Equations

Abstract

We propose a new fully homomorphic encryption (FHE) scheme. Unlike previous ones, our FHE scheme is effective and simple enough for practical applications. Our FHE essentially exploits mathematical body of matrix polynomials which are matrix equations of a particular form. This makes the scheme both faster and (we believe) easier to understand than ancestors. Also, the paper gives the formal definitions of new framework for secure cloud computing -- the primitive of compact symmetric fully homomorphic encryption scheme whose security relies on the difficulty of some NP-complete problem. We consider organization and infrastructure of secure cloud computations using such symmetric fully homomorphic encryption.Construction of the proposed encryption scheme introduces a new hardness assumption. Some basic ideas explain the security of such FHE against known plaintext attacks. We give theoretical evaluation of scheme's overhead (both in time and size).The paper provides experimental investigation on fully homomorphic encryption of our type. Our implementation uses NTL library by Victor Shoup, and we present a real life efficiency of the encryption scheme.