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This survey explores lattice-based digital signatures, a promising post-quantum resistant alternative to traditional schemes relying on factoring or discrete logarithm problems, which face increasing risks from quantum computing. The study covers conventional paradigms like Hash-and-Sign and Fiat-Shamir, as well as specialized applications including group, ring, blind, and proxy signatures. It analyzes the versatility and security strengths of lattice-based schemes, providing practical insights. Each chapter summarizes advancements in schemes, identifying emerging trends. We also pinpoint future directions to deploy lattice-based digital signatures including quantum cryptography.<\/jats:p>","DOI":"10.1186\/s42400-023-00198-1","type":"journal-article","created":{"date-parts":[[2024,4,1]],"date-time":"2024-04-01T02:08:41Z","timestamp":1711937321000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["A survey on lattice-based digital signature"],"prefix":"10.1186","volume":"7","author":[{"given":"Fengxia","family":"Liu","sequence":"first","affiliation":[]},{"given":"Zhiyong","family":"Zheng","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0005-7059-5040","authenticated-orcid":false,"given":"Zixian","family":"Gong","sequence":"additional","affiliation":[]},{"given":"Kun","family":"Tian","sequence":"additional","affiliation":[]},{"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Zhe","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Jia","family":"Li","sequence":"additional","affiliation":[]},{"given":"Qun","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,4,1]]},"reference":[{"key":"198_CR1","first-page":"597","volume":"2012","author":"M Abdalla","year":"2015","unstructured":"Abdalla M, Fouque PA, Lyubashevsky V et al (2015) Tightly secure signatures from lossy identification schemes. 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