Reed-Muller code based symmetric key fully homomorphic encryption scheme

Abstract

Several number theoretic and algebraic homomorphic encryption schemes were proposed in the literature, which have been remained theoretical due to their high computational complexities. Coding theory is believed to be a promising alternative for the construction of homomorphic encryption schemes. A few of such schemes exist, but, they support limited operations of additions and multiplications over the ciphertexts. Based on a special class of linear codes called Reed-Muller codes, in this paper, a new symmetric key Fully Homomrphic Encryption (FHE) scheme is proposed, which employs a novel method of ciphertext post processing to achieve unlimited homomorphic multiplications. The security of the proposition is analysed with respect to all the known attacks.