Symmetric Fully Homomorphic Encryption Scheme with Polynomials Operations

Feasible homomorphic encryption schemes are being proposed in literature regularly, yet the message space is very restricted or limited. This makes the existing schemes costly to adopt for practical use where data is too large. This paper proposes a homomorphic encryption scheme that has very large message space. Polynomials are used to assemble chunks of data and encrypt them. The coefficients of polynomials are the encrypted messages. Addition and multiplication of the polynomials are the homomorphic functions to achieve functions on messages. Decryption and Refresh Primitives consists of single mathematical operations, which makes them fast. This meets the requirement of a feasible FHE.