Secure Multiparty Computation via Homomorphic Encryption Library

Abstract

Secure multiparty computation (MPC) is required when individuals want to privately evaluate a function over their inputs. While evaluating a common function, the participants do not reveal their inputs to each other. A homomorphic encryption (HE) scheme allows the evaluation of arbitrary computations on encrypted data without decrypting it. In theory, realizing MPC through a HE scheme is a simple and efficient approach. However, despite its promising theoretical power, the practical side of the approach remains underdeveloped. In this work, motivated by the rising MPC applications, e.g. cloud computation, a HE library is extended to provide the necessary methods for MPC. In particular HElib that implements Brakerski-Gentry-Vaikuntanathan (BGV), a HE scheme, is extended to support MPC protocols. This extension provides a broadcast protocol for the generation of a global public key by N parties, where each party maintains a share of the corresponding private key. In addition, the homomorphic evaluation of functions on ciphertexts encrypted by the public key is extended. Furthermore, a decryption broadcast protocol is provided where ciphertexts are decrypted using the individual shares of the private key. The proposed extension can be adapted to other HE libraries. A second contribution of this work, is a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> factorial experimental design and analysis to study the memory, computation, and communication costs of HElib and the proposed extension. Four main factors are identified: the security parameter, the plaintext space, the number of levels of the evaluation function, and the number of parties. The proposed extensions are shown to be effective and efficient. On the experimented setup, it takes about 0.2 sec for multiparty key generation and 0.06 sec for multiparty decryption.