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However, ensuring the security of EHR cloud system remains a critical issue. Some patients require regular remote medical services, and controlling access to medical data involving patient privacy during specific times is essential. Timed-release encryption (TRE) technology enables the sender to preset a future time <jats:italic>T<\/jats:italic> at which the data can be decrypted and accessed. It is a cryptographic primitive with time-dependent properties. Currently, mainstream TRE schemes are based on non-interactive single time server methods. However, if the single time server is attacked or corrupted, it is easy to directly threaten the security applications of TRE. Although some research schemes \u201cdistribute\u201d the single time server into multiple ones, they still cannot resist the single point of failure problem. To address this issue, we propose a multiple time servers TRE scheme based on Shamir secret sharing and another variant derived from it. In our proposed schemes, the data receiver does not need to interact with the time servers; instead, they only need to obtain the time trapdoors that exceed or equal the preset threshold value for decryption, which ensures the identity privacy of the data sender and tolerates partial downtime or other failures of some time servers, significantly improving TRE reliability. Security analysis indicates that our proposed schemes demonstrate data confidentiality, verifiability, anti-advance decryption, and robust decryption with multiple time trapdoors, making them more practical. Efficiency analysis indicates that although our schemes have slightly higher computational costs than most efficient existing TRE schemes, such differences are insignificant from a practical application perspective.<\/jats:p>","DOI":"10.1186\/s13677-024-00676-y","type":"journal-article","created":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T14:02:16Z","timestamp":1718200936000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Multiple time servers timed-release encryption based on Shamir secret sharing for EHR cloud system"],"prefix":"10.1186","volume":"13","author":[{"given":"Ke","family":"Yuan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziwei","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keyan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bozhen","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junyang","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sufang","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunfu","family":"Jia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,6,12]]},"reference":[{"key":"676_CR1","doi-asserted-by":"publisher","first-page":"101966","DOI":"10.1016\/j.cose.2020.101966","volume":"97","author":"S Shi","year":"2020","unstructured":"Shi S, He D, Li L, Kumar N, Khan MK, Choo KKR (2020) Applications of blockchain in ensuring the security and privacy of electronic health record systems: A survey. 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