We present an improved constant-round secure two-party protocol for integer comparison functionality, which is one of the most fundamental building blocks in secure computation. Our protocol is in the so-called client-server model, which is utilized in real-world MPC products such as Sharemind, where any number of clients can create shares of their input and distribute to the servers who then jointly compute over the shares and return the shares of the result to the client. In the client-aided client-server model, as mentioned briefly by Mohassel and Zhang (S&P'17), a client further generates and distributes some necessary correlated randomness to servers. Such correlated randomness admits efficient protocols since otherwise, servers have to jointly generate randomness by themselves, which can be inefficient. In this paper, we improve the state-of-the-art constant-round comparison protocols by Damgå rd et al. (TCC'06) and Nishide and Ohta (PKC'07) in the client-aided model. Our techniques include identifying correlated randomness in these comparison protocols. Along the way, we also use tree-based techniques for a building block, which deviate from the above two works. Our proposed protocol requires only 5 communication rounds, regardless of the bit length of inputs. This is at least 5 times fewer rounds than existing protocols. We implement our secure comparison protocol in C++. Our experimental results show that this low-round complexity benefits in high-latency networks such as WAN. We also present secure Min/Argmin protocols using the secure comparison protocol.

Wireless LANs (Local Area Networks) are currently spreading over diverse places such as hotels and airports, as well as offices and homes. Consequently, they provide convenient and important ways to access the Internet. Another type of communication model, Peer-to-Peer (P2P) communication on the Internet, has also attracted much attention, and P2P over wireless LANs will soon be very common. There are concerns about the capability of wireless stations (STAs) to send a large amount of traffic on an uplink. In this paper, we first clarify some issues that arise in this context by examining the feature of the Access Point(AP). Furthermore, we consider the role of the AP and propose, as a solution, ways of enabling both efficient and fair transmission over both the downlink and uplink. We evaluate the proposed schemes through simulations and show that communications over the uplink and downlink can share the wireless LAN access resource effectively. Furthermore, we show that coordinating our solution with the 802.11e Enhanced Distributed Channel Access (EDCA) can meet the different requirements of various types of traffic.