Towards the Construction of Reed-Muller Code Based Symmetric Key FHE

Abstract

Homomorphic encryption (HE) schemes became popular cryptographic primitives and very useful in variety of security applications. Homomorphic encryption based on coding theory have the advantages of faster computations due to the structural properties of the codes used. Several schemes are supporting unlimited Mod2 addition operations in literature. The present paper introduces Reed-Muller (RM) code based Mod2 multiplication operation thereby making RM code based HE scheme fully homomorphic. The representation of the codeword with necessary adaption to support unlimited number of Mod2​ multiplication operations is presented along with the scheme first. The correctness proof of the homomorphic operations along with experimental evaluation is also presented to demonstrate the practical aspects of the proposal.