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arXiv · 2412.01641

Linearly Homomorphic Signature with Tight Security on Lattice

Heng Guo·Fengxia Liu·Kun Tian·Zhiyong Zheng
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Abstract

Constructing cryptographic schemes with tight or almost-tight security has long been one of the central problems in theoretical cryptography. At ASIACRYPT 2016, Boyen and Li posed an open problem: whether it is possible to construct a homomorphic signature scheme with tight or almost-tight security under the Short Integer Solution (SIS) assumption in the standard model. In 2024, Chen achieved the first construction with almost-tight security under a weaker security model. To further achieve tight security in the standard model, this paper introduces a new security model whose security requirements are weaker than those of the standard adaptive model but stronger than the model adopted by Chen. Under this model, we construct a linearly homomorphic signature scheme with tight security.

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Heng Guo, Fengxia Liu, Kun Tian, Zhiyong Zheng. 2024-12-02. Linearly Homomorphic Signature with Tight Security on Lattice. https://arxiv.org/abs/2412.01641

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