Memory and Round-Efficient MPC Primitives in the Pre-Processing Model from Unit Vectorization

Abstract

In this paper, we propose memory-and round-efficient protocols for securely evaluating arithmetic primitives. We focus on secure twoparty computation over the ring Z 2 𝑘 that achieves security against semi-honest adversaries and works in the pre-processing model. Our protocols rely on the unit vectorization technique introduced by Boyle et al. (TCC 2019). The unit vectorization technique provides online-optimal protocols for several fundamental operations in the pre-processing model. However, a relatively large memory cost for correlated randomness is required, which might become an obstacle in a large-scale application. In order to achieve both memory and communication efficiency, we propose a size reduction method that uses unit vectorization only for short-length inputs, and based on this, construct two-round protocols for equality test, detecting the most significant non-zero bit, detecting wrap-around, and less-than comparison. In addition, as applications of these results, we provide practically efficient protocols for integer division, integer square root, integer logarithm, and modular exponentiation. CCS CONCEPTS• Theory of computation → Cryptographic protocols.