Faster Homomorphic Function Evaluation Using Non-integral Base Encoding

In this paper we present an encoding method for xed-point numbers tailored for homomorphic function evaluation. The choice of the degree of the polynomial modulus used in all popular somewhat homomorphic encryption schemes is dominated by security considerations, while with the current encoding techniques the correctness requirement allows for much smaller values. We introduce a generic encoding method using expansions with respect to a non-integral base, which exploits this large degree at the bene t of reducing the growth of the coe cients when performing homomorphic operations. In practice this allows one to choose a smaller plaintext coe cient modulus which results in a signi cant reduction of the running time. We illustrate our approach by applying this encoding in the setting of homomorphic electricity load forecasting for the smart grid which results in a speed-up by a factor 13 compared to previous work, where encoding was done using balanced ternary expansions.