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However, the limited resources of some terminal devices make multi-signature, which based on bilinear map, is not suitable for multi-cloud computing environment. In addition, the signers are disclosure in multi-signature so there is the risk of attack. To solve this issues, this paper proposes a certificateless designated verifier multi-signature scheme based on multivariable public key cryptography (MPKC). Firstly, the formalized definition and security model of the proposed scheme are given. Secondly, it is proved that the proposed scheme is against adaptive chosen-message attacks. Finally, the analysis shows that the proposed scheme is more efficiency and suitable for multi-cloud. Moreover, the proposed scheme can hidding signature source to achieve privacy protection.<\/jats:p>","DOI":"10.1186\/s13677-022-00333-2","type":"journal-article","created":{"date-parts":[[2022,10,1]],"date-time":"2022-10-01T11:02:44Z","timestamp":1664622164000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A designated verifier multi-signature scheme in multi-clouds"],"prefix":"10.1186","volume":"11","author":[{"given":"Chaoyue","family":"Tan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuling","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongtang","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaochuan","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,10,1]]},"reference":[{"issue":"1","key":"333_CR1","doi-asserted-by":"publisher","first-page":"37","DOI":"10.23919\/ICN.2020.0002","volume":"1","author":"Y Zhang","year":"2020","unstructured":"Zhang Y, Zhang H, Cosmas J, Jawad N, Ali K, Meunier B et al (2020) Internet of radio and light: 5G building network radio and edge architecture. 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