Linearly Homomorphic Ring Signature Scheme over Lattices
Heng Guo, Jia Li, Yanan Wang, Fengxia Liu, Zhiyong Zheng, Kun Tian
TL;DR
This work addresses the absence of practical homomorphic ring signatures by introducing the first lattice-based linearly homomorphic ring signature (LHRS) scheme. It achieves quantum-resistant security in the standard model under the small integer solution ($SIS$) assumption and provides strong anonymity under full key exposure along with existential unforgeability under insider corruption. The construction unifies ring signatures with linear homomorphic signatures, leveraging lattice tools such as TrapGen, the Decompose algorithm, and discrete Gaussian sampling to enable verifiable linear computations on signed data. This LHRS delivers post-quantum privacy-preserving capabilities for applications like confidential blockchain transactions and secure multiparty computation, while outlining avenues for future improvements in efficiency and expressive power.
Abstract
Homomorphic ring signature schemes combine the strong anonymity of ring signatures with the computability of homomorphic signatures, demonstrating significant potential in scenarios requiring both anonymous data provenance and verifiable homomorphic computation (e.g., confidential blockchain transactions and secure multi-party computation). However, no feasible homomorphic ring signature scheme currently exists. In this work, we propose the first lattice-based linearly homomorphic ring signature scheme. Proven secure in the standard model under the small integer solution (SIS) assumption, our scheme achieves strong anonymity under full key exposure and unforgeability against insider corruption attacks. As the first unified framework for ring signatures and linear homomorphic signatures, this construction provides a post-quantum-secure solution for the aforementioned applications, advancing the development of privacy-enhanced homomorphic computation.