This paper provides an overview of the basic principles, types, recent works, and applications of quantum digital signatures. The security of traditional digital signature schemes is compromised by the rise of quantum computing, leading to a need for post-quantum cryptography. Quantum digital signatures, which rely on the principles of quantum mechanics, offer a potential solution to this problem. This paper aims to provide a comprehensive overview of quantum digital signatures and post-quantum digital signatures. The paper introduces the basic principles of quantum mechanics, then explains key distribution in quantum digital signatures. The paper then provides a detailed description of both quantum and post-quantum digital signatures, including their differences and applications. Finally, the paper summarizes the main findings in the field, highlights potential future directions, and discusses challenges that humans must address. In addition, the paper examines the widespread applications of quantum digital signatures and post-quantum digital signatures in various fields such as Bitcoin, smart city blockchain, and finance. Finally, the paper summarizes the key findings in the field, highlighting potential future directions and discussing challenges that humans must address. Overall, this paper aims to provide readers with a comprehensive understanding of quantum digital signatures and post-quantum digital signatures and their applications in various domains.
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