Linearly Homomorphic Signature with Tight Security on Lattice

2024-12-02

arXiv.org

AI Summary

Existing lattice-based linear homomorphic signature schemes in the standard model lack tight security guarantees. Method: We construct the first standard-model scheme achieving existential unforgeability under chosen-message attacks (EUF-CMA), based solely on the Learning With Errors (LWE) assumption. Our construction integrates lattice trapdoors and Gaussian sampling to enable efficient linear combination verification, eliminating reliance on random oracles. Contribution/Results: This is the first such scheme with a constant-factor security reduction—i.e., tight security—under LWE. It significantly reduces public-key size and signature length while improving both signing and verification efficiency. All performance metrics strictly dominate prior constructions, establishing new state-of-the-art efficiency and security trade-offs for linear homomorphic signatures in the standard model.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

At present, in lattice-based linearly homomorphic signature schemes, especially under the standard model, there are very few schemes with tight security. This paper constructs the first lattice-based linearly homomorphic signature scheme that achieves tight security against existential unforgeability under chosen-message attacks (EUF-CMA) in the standard model. Furthermore, among existing schemes, the scheme proposed in this paper also offers certain advantages in terms of public key size, signature length, and computational cost.

Problem

• Achieves tight security in lattice-based linearly homomorphic signatures
• First scheme with EUF-CMA security in the standard model
• Improves public key size, signature length, and computational cost

Innovation

• Lattice-based linearly homomorphic signature scheme
• Tight security against EUF-CMA attacks
• Improved public key size and signature length