Replicated Additive Secret Sharing with the Optimized Number of Shares.

Replicated additive secret sharing (RSS) schemes introduce the threshold for additive secret sharing, and are known for computational efficiency and flexibility. While the traditional RSS schemes usually have a huge storage overhead with each server holding multiple shares, recent variations have tried reducing storage overhead but at the expense of computational performance. In this work, we focus on optimizing the number of shares to reduce storage overhead without introducing excessive computational cost. First, we construct a 2-of-n RSS (i.e., any two among n servers could reconstruct the secret value), which generates secret shares incrementally so that the storage increases almost linearly with n, and achieves the optimal number of shares as we proved. Then, we extend 2-of-n RSS to a general t-of-n RSS. Moreover, the incrementally-generate mechanism makes our scheme support a server to join dynamically that refrain existing shares from being modified. Our empirical study across 60 servers supports that our scheme largely reduces the storage overhead while obtaining an efficient runtime. Storage efficiency shows an improvement of up to two orders of magnitude and online runtime is within microsecond scale in our experimental settings.