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.

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