Berekening op Beveiligd Data: in alle vormen

MPC is a primitive which allows for mutually distrusting parties to jointly compute the output of a function over their private inputs. This technology has many practical applications and, as such, has seen extensive research, which has generated several different methods for achieving MPC. In this thesis, we discuss and expand on three of the best known methods for achieving MPC. The first is based on Shamir's secret sharing scheme. We present a novel secret<br />sharing based scheme which achieves MPC under the following constraints. We allow for a malicious adversary that can arbitrarily delay any parties for a number of rounds. While these parties are delayed they can neither send nor receive messages. Furthermore, we assume that all messages between the parties are sent via a set of central parties called Relays. We provide a UC functionality and protocol for the relays, and for the MPC protocol. The second is based on Yao's garbled circuits protocol. Here we expand on the row reduction technology already present in maliciously secure two party garbled circuits and show how to achieve similar results in the multiparty setting. This reduces the number of ciphertexts that must be sent per AND gate in the multiparty Garbled Circuits setting from four to three.<br />The third is based on Fully Homomorphic Encryption. The particular protocol we introduce expands the FINAL FHE scheme and expands it to accept multiple keys, which can then be used by different parties to collectively outsource a computation to an untrusted server. We cover the various different obstacles that needed to be overcome in this expansion, and we show that our protocol has an asymptotic improvement in the efficiency of the bootstrapping over other multi-key FHE schemes. This now requires a number of polynomial multiplications which is linear in the number parties, rather than quadratic.