Cryptology ePrint Archive: Report 2017/996

Large FHE gates from Tensored Homomorphic Accumulator

Guillaume Bonnoron and Léo Ducas and Max Fillinger

Abstract: The main bottleneck of all known Fully Homomorphic Encryption schemes lies in the bootstrapping procedure invented by Gentry (STOC'09). The cost of this procedure can be mitigated either using Homomorphic SIMD techniques, or by performing larger computation per bootstrapping procedure.

In this work, we propose new techniques allowing to perform more operations per bootstrapping in FHEW-type schemes (EUROCRYPT'13). While maintaining the quasi-quadratic $\tilde O(n^2)$ complexity of the whole cycle, our new scheme allows to evaluate gates with $\Omega(\log n)$ input bits, which constitutes a quasi-linear speed-up. Our scheme is also very well adapted to large threshold gates, natively admitting up to $\Omega(n)$ inputs. This could be helpful for homomorphic evaluation of neural networks.

Our theoretical contribution is backed by a preliminary prototype implementation, which can perform $6$-to-$6$ bit gates in less than $10$ seconds on a single core, as well as threshold gates over $63$ input bits even faster.

Category / Keywords: Fully Homomorphic Encryption, Large Gates, Threshold Gates, Ideal lattices

Date: received 9 Oct 2017, last revised 24 Nov 2017

Contact author: guillaume bonnoron at imt-atlantique fr

Available format(s): PDF | BibTeX Citation

Note: Add link to implementation on github

Version: 20171124:125107 (All versions of this report)

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