Construct the first provably secure linear homomorphic ring signature scheme. Ring signatures allow a signer to anonymously sign a message on behalf of a user group (ring) and are widely applied in areas such as identity protection, electronic voting, and privacy enhancement in blockchain. Homomorphic signatures, on the other hand, support verifiable computations on signed data. The integration of anonymity and computability in homomorphic ring signatures holds the potential to create new application scenarios for privacy-preserving distributed systems. It is worth noting that Choi and Kim first introduced the concept of linear homomorphic ring signatures in 2017 and proposed a specific scheme. However, their scheme lacks a complete security proof, leaving its security theoretically unconfirmed. To address this research gap, this paper presents the first provably secure lattice-based linear homomorphic ring signature scheme, designed for scenarios where the ring size is O(log n). This scheme not only combines the anonymity of ring signatures with the malleability of homomorphic signatures but also achieves resistance against quantum attacks.

翻译：提出了首个可证明安全的线性同态环签名方案. 环签名允许签名者代表用户组（环）匿名签署消息, 广泛应用于身份保护、电子投票及区块链隐私增强等领域. 而同态签名则支持对已签名数据进行可验证计算. 同态环签名融合了匿名性与可计算性, 有望为隐私保护的分布式系统创造新的应用场景. 值得注意的是, Choi和Kim于2017年率先提出了线性同态环签名的概念并给出了一个具体方案, 然而该方案缺乏完整的安全证明, 其安全性在理论上尚未得到确认. 针对这一研究空白, 本文提出了首个可证明安全的基于格的线性同态环签名方案, 专为环规模为O(log n)的场景设计. 该方案不仅结合了环签名的匿名性与同态签名的可塑性, 还具备抵抗量子攻击的能力.