Blockchain, valued for its decentralized and tamper-proof features, has sprung up as a predominant paradigm in numerous security applications. To facilitate massive trustworthy retrieval services, blockchain-assisted clouds, combining immutable on-chain storage and scalable off-chain storage, offer a data-reliable and storage-flexible platform. Based on the blockchain-assisted cloud model, existing studies have focused on several types of authenticated retrievals including verifiable skyline queries, graph queries, range queries, e.t.c., however, currently, few of them can directly support efficient query processing and result verification for trajectory similarity retrieval. To the best of our knowledge, this paper is the first attempt to address the problem of authenticated trajectory similarity retrieval on the blockchain-assisted cloud. To this end, we first propose novel authenticated data structures, \(\mathcal {PMB}\) -Tree, to enable authenticated trajectory similarity retrieval, and \(\mathcal {SPMB}\) -Tree, to save gas consumption on the blockchain. To reduce the client-side verification costs, we further optimized the index as \(\mathcal {PMB^*}\) -Tree to improve the verification efficiency. In addition, we propose a gas-efficient index maintenance for ADS updates on the blockchain. Finally, we provide a theoretical analysis of the complexity and verification guarantees of the proposed authenticated approaches and conduct extensive experiments on both real and synthetic datasets to demonstrate the efficient performance of our approaches.