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Proof of storage (PoS) is an interactive protocol allowing a client to verify that the server possesses the original data without retrieving it. All of the existed PoS protocols are based on the hardness of factoring or discrete-log problems, which cannot resist quantum attacks. In this paper, we first propose a linearly homomorphic signature scheme(LHHS) from lattice assumption, and generate HTVs from LHSS. Then we construct the first lattice-based PoS protocol from the new HTVs. Our PoS protocol is public verifiable and can be proved unforgeable in random oracle model assuming that SIS problem is hard. Complexity analysis shows that the mainly computation cost in LPoS are occur in Encode phase. The communication cost in prove and verify phases is independent to the scale of the file. The client or the verifier only needs to store the verifiable tags rather than the original file blocks.