Paper 2016/785
Optimization of Bootstrapping in Circuits
Fabrice Benhamouda, Tancrède Lepoint, Claire Mathieu, and Hang Zhou
Abstract
In 2009, Gentry proposed the first Fully Homomorphic Encryption (FHE) scheme, an extremely powerful cryptographic primitive that enables to perform computations, i.e., to evaluate circuits, on encrypted data without decrypting them first. This has many applications, in particular in cloud computing. In all currently known FHE schemes, encryptions are associated to some (non-negative integer) noise level, and at each evaluation of an AND gate, the noise level increases. This is problematic because decryption can only work if the noise level stays below some maximum level $L$ at every gate of the circuit. To ensure that property, it is possible to perform an operation called _bootstrapping_ to reduce the noise level. However, bootstrapping is time-consuming and has been identified as a critical operation. This motivates a new problem in discrete optimization, that of choosing where in the circuit to perform bootstrapping operations so as to control the noise level; the goal is to minimize the number of bootstrappings in circuits. In this paper, we formally define the _bootstrap problem_, we design a polynomial-time $L$-approximation algorithm using a novel method of rounding of a linear program, and we show a matching hardness result: $(L-\epsilon)$-inapproximability for any $\epsilon>0$.
Note: 2016-11-17: publication information + minor editorial improvements
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. SODA 2017
- Keywords
- DAGcircuitapproximation algorithmsinapproximabilitylinear programmingroundingfully homomorphic encryption (FHE)
- Contact author(s)
- fabrice benhamouda @ ens fr
- History
- 2016-11-17: revised
- 2016-08-18: received
- See all versions
- Short URL
- https://ia.cr/2016/785
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2016/785, author = {Fabrice Benhamouda and Tancrède Lepoint and Claire Mathieu and Hang Zhou}, title = {Optimization of Bootstrapping in Circuits}, howpublished = {Cryptology {ePrint} Archive, Paper 2016/785}, year = {2016}, url = {https://eprint.iacr.org/2016/785} }