International Association
for Cryptologic Research

<p> Multi-key fully homomorphic encryption (MKFHE), a generalization of fully homomorphic encryption (FHE), enables a computation over encrypted data under multiple keys. The first MKFHE schemes were based on the NTRU primitive, however these early NTRU based FHE schemes were found to be insecure due to the problem of over-stretched parameters. Recently, in the case of standard (non-multi key) FHE a secure version, called FINAL, of NTRU has been found. In this work we extend FINAL to an MKFHE scheme, this allows us to benefit from some of the performance advantages provided by NTRU based primitives. Thus, our scheme provides competitive performance against current state-of-the-art multi-key TFHE, in particular reducing the computational complexity from quadratic to linear in the number of keys. </p>

This paper examines multi-party computation protocols in the presence of two major constraints present in deployed systems. Firstly, we consider the situation where the parties are connected not by direct point-to-point connections, but by a star-like topology with a few central post-office style relays. Secondly, we consider MPC protocols with a strong honest majority ($t \gg n/2$) in which we have stragglers (some parties are progressing slower than others). We model stragglers by allowing the adversary to delay messages to and from some parties for a given length of time. We first show that having only a single honest relay is enough to ensure consensus of the messages sent within a protocol; secondly, we show that special care must be taken to describe multiplication protocols in the case of relays and stragglers; thirdly, we present an efficient honest-majority MPC protocol which can be run ontop of the relays and which provides active-security with abort in the case of a strong honest majority, even when run with stragglers. We back up our protocol presentation with both experimental evaluations and simulations of the effect of the relays and delays on our protocol.