Fully Homomorphic Encryption Without Noise

In this paper, the authors present a novel fully homomorphic encryption scheme operating between and capable of arbitrarily performing additions and multiplications. The new scheme is compact and each operation (addition or multiplication) performed on any two ciphertexts produces a fresh ciphertext without any associated noise. Thus, the scheme does not need any bootstrapping procedure or noise reduction technique to refresh ciphertexts. In the absence, to the best of the knowledge of the authors, of any existing fully, partially or leveled homomorphic encryption scheme using as the set of plaintexts, the new cryptosystem has been implemented and has had its performance compared to the identity encoding.