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The interesting characteristics of blockchain are decentralized ledger and strong security, while non-repudiation is the important property of information security in blockchain. A digital signature scheme is an effective approach to achieve non-repudiation. In this paper, the characteristics of blockchain and the digital signature to guarantee information non-repudiation are firstly discussed. Secondly, the typical digital signature schemes in blockchain are classified and analyzed, and then the state-of-the-art digital signatures are investigated and compared in terms of application fields, methods, security, and performance. Lastly, the conclusions are given, and some future works are suggested to stir research efforts in this field. 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