### Accelerating Homomorphic Evaluation on Reconfigurable Hardware

Thomas Pöppelmann, Michael Naehrig, Andrew Putnam, and Adrian Macias

##### Abstract

Homomorphic encryption allows computation on encrypted data and makes it possible to securely outsource computational tasks to untrusted environments. However, all proposed schemes are quite inefficient and homomorphic evaluation of ciphertexts usually takes several seconds on high-end CPUs, even for evaluating simple functions. In this work we investigate the potential of FPGAs for speeding up those evaluation operations. We propose an architecture to accelerate schemes based on the ring learning with errors (RLWE) problem and specifically implemented the somewhat homomorphic encryption scheme YASHE, which was proposed by Bos, Lauter, Loftus, and Naehrig in 2013. Due to the large size of ciphertexts and evaluation keys, on-chip storage of all data is not possible and external memory is required. For efficient utilization of the external memory we propose an efficient double-buffered memory access scheme and a polynomial multiplier based on the number theoretic transform (NTT). For the parameter set (n=16384,log_2(q)=512) capable of evaluating 9 levels of multiplications, we can perform a homomorphic addition in 48.67 and a homomorphic multiplication in 0.94 ms.

Available format(s)
Category
Implementation
Publication info
A major revision of an IACR publication in CHES 2015
Contact author(s)
thomas poeppelmann @ rub de
mnaehrig @ microsoft com
anputnam @ microsoft com
History
Short URL
https://ia.cr/2015/631

CC BY

BibTeX

@misc{cryptoeprint:2015/631,
author = {Thomas Pöppelmann and Michael Naehrig and Andrew Putnam and Adrian Macias},
title = {Accelerating Homomorphic Evaluation on Reconfigurable Hardware},
howpublished = {Cryptology ePrint Archive, Paper 2015/631},
year = {2015},
note = {\url{https://eprint.iacr.org/2015/631}},
url = {https://eprint.iacr.org/2015/631}
}

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