On the Equality Test and Comparison for Replicated Secret Sharing

In this paper, we propose an equality test protocol and a comparison protocol based on replicated shares, and precisely determine their communication complexities in exact bit counts (not asymptotic $\mathcal{O}$ (. ) -notation). Our secure comparison$ protocol achieves a communication complexity comparable to prior work, while our equality determination protocol reduces communication complexity by at least 2/3 compared to existing methods.