Nowadays, blockchain has become one of the most cutting-edge technologies, which has been widely concerned and researched. However, the quantum computing attack seriously threatens the security of blockchain, and related research is still less. Targeting at this issue, in this paper, we present the definition of post-quantum blockchain (PQB) and propose a secure cryptocurrency scheme based on PQB, which can resist quantum computing attacks. First, we propose a signature scheme based on lattice problem. We use lattice basis delegation algorithm to generate secret keys with selecting a random value, and sign message by preimage sampling algorithm. In addition, we design the first-signature and last-signature in our scheme, which are defined as double-signature. It is used to reduce the correlation between the message and the signature. Second, by combining the proposed signature scheme with blockchain, we construct the PQB and propose this cryptocurrency scheme. Its security can be reduced to the lattice short integer solution (SIS) problem. At last, through our analysis, the proposed cryptocurrency scheme is able to resist the quantum computing attack and its signature satisfies correctness and one-more unforgeability under the lattice SIS assumption. Furthermore, compared with previous signature schemes, the sizes of signature and secret keys are relatively shorter than that of others, which can decrease the computational complexity. These make our cryptocurrency scheme more secure and efficient.
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