Constant Rounds Almost Linear Complexity Multi-party Computation for Prefix Sum

Abstract

One of research goals on multi-party computation (MPC) is to achieve both perfectly secure and efficient protocols for basic functions or operations (e.g., equality, comparison, bit decomposition, and modular exponentiation). Recently, for many basic operations, MPC protocols with constant rounds and linear communication cost (in the input size) are proposed. In this paper, we propose the first MPC protocol for prefix sum in general semigroups with constant 2d + 2dc rounds and almost linear O(l log^*(c) l) communication complexity, where c is a constant, d is the round complexity of subroutine protocol used in the MPC protocol, l is the input size, and log^*(c) is the iterated logarithm function. The prefix sum protocol can be seen as a generalization of the postfix comparison protocol proposed by Toft. Moreover, as an application of the prefix sum protocol, we construct the first bit addition protocol with constant rounds and almost linear communication complexity.