Paper 2025/948

Resolving the Efficiency-Utility Dilemma of Threshold Linearly Homomorphic Encryption via Message-Space Adapter

Abstract

Threshold linearly homomorphic encryption (ThLHE) is a useful cryptographic tool for secure computation in multi-party settings, with applications in electronic voting, secure multiparty computation (MPC), and beyond. Although ThLHE offers significant advantages such as low communication overhead, its adoption in modern systems is hindered by a critical dilemma between efficiency and utility. Precisely, existing ThLHE schemes either suffer from high decryption complexity—typically $\mathcal{O}(N^2\log N)$ or worse for $N$ parties—or impose extra restrictions on the message space or participant set, limiting their practicality in large-scale and dynamic settings. In this work, we resolve this efficiency-utility dilemma for ThLHE by introducing a novel primitive termed message-space adapter (MeSA). By developing a lattice-based MeSA for exponential ElGamal (Exp-ElGamal), we mitigate the small-message restriction of Exp-ElGamal while preserving its efficient threshold decryption. This leads to the design of the first ThLHE scheme that achieves quasi-linear decryption complexity without restrictions on the message space or participant set. We implement a prototype of this new ThLHE scheme and validate the quasi-linear growth of its running time with respect to $N$. Beyond resolving this dilemma, we further extend the applications of our new ThLHE scheme. Specifically, we apply it to construct the first multi-party fully homomorphic encryption scheme with quasi-linear computation complexity and constant communication complexity, while supporting arbitrary threshold and dynamic participant set. This demonstrates the extra benefits of our ThLHE scheme with broader applicability.

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