A1 Eunkyung Kim

A1 Mehdi Tibouchi

PB iet

T1 FHE over the integers and modular arithmetic circuits

JN IET Information Security

VO 12

IS 4

SP 257

OP 264

AB Fully homomorphic encryption (FHE) over the integers, as proposed by van Dijk et al. in 2010 and developed in a number of papers afterwards, originally supported the evaluation of Boolean circuits (i.e. mod-2 arithmetic circuits) only. It is easily generalised to the somewhat homomorphic versions of the corresponding schemes to support arithmetic operations modulo Q for any Q > 2 , but bootstrapping those generalised variants into fully homomorphic schemes is not easy. Thus, Nuida and Kurosawa settled an interesting open problem in 2015 by showing that one could in fact construct FHE over the integers with message space Z / Q Z for any constant prime Q. As a result of their work, the authors can homomorphically evaluate a mod-Q arithmetic circuit with an FHE scheme over the integers in two different ways: one could either use their scheme with message space Z / Q Z directly, or one could first convert the arithmetic circuit to a Boolean one, and then evaluate that converted circuit using an FHE scheme with binary message space. In this study, they compare both approaches and show that the latter is often preferable to the former.

K1 integers

K1 arithmetic operations modulo

K1 modular arithmetic circuits

K1 mod-2 arithmetic circuits

K1 homomorphic versions

K1 message space

K1 fully homomorphic encryption

K1 mod-Q arithmetic circuit

K1 FHE scheme

K1 Boolean circuits

DO https://doi.org/10.1049/iet-ifs.2017.0024

UL https://digital-library.theiet.org/;jsessionid=ak4uhoifrodnt.x-iet-live-01content/journals/10.1049/iet-ifs.2017.0024

LA English

SN 1751-8709

YR 2018

OL EN