MORSE: An Efficient Homomorphic Secret Sharing Scheme Enabling Non-Linear Operation

TL;DR

MORSE is a novel homomorphic secret sharing scheme that enables efficient non-linear operations like addition, subtraction, multiplication, and comparison with small keys and low overhead, improving performance over existing solutions.

Contribution

MORSE introduces a new scheme supporting non-linear operations with small keys, no calculation errors, and low overhead, expanding the capabilities of homomorphic secret sharing.

Findings

Up to 9.3x faster secure multiplication

Up to 16.6% reduction in communication costs for comparison

Supports a range of operations including addition, subtraction, multiplication, and comparison

Abstract

Homomorphic secret sharing (HSS) enables two servers to locally perform functions on encrypted data directly and obtain the results in the form of shares. A Paillier-based HSS solution seamlessly achieves multiplicative homomorphism and consumes less communication costs. Unfortunately, existing Paillier-based HSS schemes suffer from a large private key size, potential calculation error, expensive computation and storage overhead, and only valid on linear operations (e.g., addition and multiplication). To this end, inspired by the Paillier cryptosystem with fast encryption and decryption, we propose MORSE, an efficient homomorphic secret sharing scheme enabling non-linear operation, which enjoys a small key size, no calculation error and low overhead. In terms of functions, MORSE supports addition, subtraction, multiplication, scalar-multiplication, and comparison. Particularly, we carefully design two conversion protocols achieving the mutual conversion between one Paillier ciphertext and two secret shares, which allows MORSE to continuously perform the above operations. Rigorous analyses demonstrate that MORSE securely outputs correct results. Experimental results show that MORSE makes a runtime improvement of up to 9.3 times in terms of secure multiplication, and a communication costs reduction of up to 16.6% in secure comparison, compared to the state-of-the-art.