International Association
for Cryptologic Research

\par Topology-hiding computation (THC) enables $n$ parties to perform a secure multiparty computation (MPC) protocol in an incomplete communication graph while keeping the communication graph hidden. The work of Akavia et al. (CRYPTO 2017 and JoC 2020) shown that THC is feasible for any graph. In this work, we focus on the efficiency of THC and give improvements for various tasks including broadcast, sum and general computation. We mainly consider THC on undirected cycles, but we also give two results for THC on general graphs. All of our results are derived in the presence of a passive adversary statically corrupting any number of parties. \par In the undirected cycles, the state-of-the-art topology-hiding broadcast (THB) protocol is the Akavia-Moran (AM) protocol of Akavia et al. (EUROCRYPT 2017). We give an optimization for the AM protocol such that the communication cost of broadcasting $O(\kappa)$ bits is reduced from $O(n^2\kappa^2)$ bits to $O(n^2\kappa)$ bits. We also consider the sum and general computation functionalities. Previous to our work, the only THC protocols realizing the sum and general computation functionalities are constructed by using THB to simulate point-to-point channels in an MPC protocol realizing the sum and general computation functionalities, respectively. By allowing the parties to know the exact value of the number of the parties (the AM protocol and our optimization only assume the parties know an upper bound of the number of the parties), we can derive more efficient THC protocols realizing these two functionalities. As a result, comparing with previous works, we reduce the communication cost by a factor of $O(n\kappa)$ for both the sum and general computation functionalities. \par As we have mentioned, we also get two results for THC on general graphs. The state-of-the-art THB protocol for general graphs is the Akavia-LaVigne-Moran (ALM) protocol of Akavia et al. (CRYPTO 2017 and JoC 2020). Our result is that our optimization for the AM protocol also applies to the ALM protocol and can reduce its communication cost by a factor of $O(\kappa)$. Moreover, we optimize the fully-homomorphic encryption (FHE) based GTHC protocol of LaVigne et al. (TCC 2018) and reduce its communication cost from $O(n^8\kappa^2)$ FHE ciphertexts and $O(n^5\kappa)$ FHE public keys to $O(n^6\kappa)$ FHE ciphertexts and $O(n^5\kappa)$ FHE public keys.