Accelerating Homomorphic Encryption using Approximate Computing Techniques

This research proposes approximate computing techniques to accelerate homomorphic encryption (HE). In particular, the CKKS encryption scheme for approximate numbers is targeted. There is a requirement for HE in services dealing with confidential data, however current constructions are not efficient enough for real-time applications. A homomorphic encryption scheme which uses approximate arithmetic (showing faster results than previous HE schemes) already exists, the CKKS scheme, and this research applies a variation of the approximate computing techniques of task skipping and depth reduction (derived from loop perforation) to determine whether further approximating the functions evaluated using CKKS scheme can have a positive impact on performance of homomorphic evaluation. This is demonstrated via the evaluation of the logistic and exponential functions that this is possible, showing positive results. The speed up in running time for HE with task skipping is between 12.1% and 45.5%, depth reduction gives 35-45.5% speed-up with a small error difference than task skipping alone. The combination of both techniques corresponds to a halving of the running time, at the cost of increased error. This novel approach to further approximate homomorphic encryption shows that it is possible for certain functions, where running time is of paramount importance, that further approximations can be made with a lower-impacting greater error.