{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:32:17Z","timestamp":1760059937746,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,20]],"date-time":"2025-07-20T00:00:00Z","timestamp":1752969600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62271496"],"award-info":[{"award-number":["62271496"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the era of big data, the security of information encryption systems has garnered extensive attention, particularly in critical domains such as financial transactions and medical data management. While traditional Shamir\u2019s Secret Sharing (SSS) ensures secure integer sharing through threshold cryptography, it exhibits inherent limitations when applied to floating-point domains and high-precision numerical scenarios. To address these issues, this paper proposes an innovative algorithm to optimize SSS via type-specific coding for real numbers. By categorizing real numbers into four types\u2014rational numbers, special irrationals, common irrationals, and general irrationals\u2014our approach achieves lossless transmission for rational numbers, special irrationals, and common irrationals, while enabling low-loss recovery for general irrationals. The scheme leverages a type-coding system to embed data category identifiers in polynomial coefficients, combined with Bernoulli-distributed random bit injection to enhance security. The experimental results validate its effectiveness in balancing precision and security across various real-number types.<\/jats:p>","DOI":"10.3390\/e27070769","type":"journal-article","created":{"date-parts":[[2025,7,21]],"date-time":"2025-07-21T10:35:31Z","timestamp":1753094131000},"page":"769","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["ApproximateSecret Sharing in Field of Real Numbers"],"prefix":"10.3390","volume":"27","author":[{"given":"Jiaqi","family":"Wan","sequence":"first","affiliation":[{"name":"College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China"},{"name":"Anhui Key Laboratory of Cyberspace Security Situation Awareness and Evaluation, Hefei 230037, China"}]},{"given":"Ziyue","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China"},{"name":"Anhui Key Laboratory of Cyberspace Security Situation Awareness and Evaluation, Hefei 230037, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9778-7783","authenticated-orcid":false,"given":"Yongqiang","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China"},{"name":"Anhui Key Laboratory of Cyberspace Security Situation Awareness and Evaluation, Hefei 230037, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6388-1720","authenticated-orcid":false,"given":"Xuehu","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China"},{"name":"Anhui Key Laboratory of Cyberspace Security Situation Awareness and Evaluation, Hefei 230037, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,20]]},"reference":[{"key":"ref_1","first-page":"1423","article-title":"Rivest-Shamir-Adleman algorithm optimized to protect iot devices from specific attacks","volume":"23","author":"Jenifer","year":"2024","journal-title":"Inform. 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