{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T20:02:12Z","timestamp":1778788932326,"version":"3.51.4"},"reference-count":44,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,4]],"date-time":"2023-03-04T00:00:00Z","timestamp":1677888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Proxy signature is one of the important primitives of public-key cryptography and plays an essential role in delivering security services in modern communications. However, existing post quantum proxy signature schemes with larger signature sizes might not be fully practical for some resource-constrained devices (e.g., Internet of Things devices). A signature scheme with message recovery has the characteristic that part or all of the message is embedded in the signature, which can reduce the size of the signature. In this paper, we present a new identity-based proxy signature scheme over an NTRU lattice with message recovery (IB-PSSMR), which is more efficient than the other existing identity-based proxy signature schemes in terms of the size of the signature and the cost of energy. We prove that our scheme is secure under a Short Integer Solution (SIS) assumption that is as hard as approximating several worst-case lattice problems in the random oracle model. We also discussed some application scenarios of IB-PSSMR in blockchain and Internet of Things (IOT). This paper provides a new idea for the design of lattice signature schemes in low resource constrained environments.<\/jats:p>","DOI":"10.3390\/e25030454","type":"journal-article","created":{"date-parts":[[2023,3,6]],"date-time":"2023-03-06T03:22:05Z","timestamp":1678072925000},"page":"454","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Identity-Based Proxy Signature with Message Recovery over NTRU Lattice"],"prefix":"10.3390","volume":"25","author":[{"given":"Faguo","family":"Wu","sequence":"first","affiliation":[{"name":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China"},{"name":"Institute of Artificial Intelligence, Beihang University, Beijing 100191, China"},{"name":"Zhongguancun Laboratory, Beijing 100194, China"},{"name":"Bejing Advanced Innovation Center for Future Blockchain and Privacy Computing, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Zhou","sequence":"additional","affiliation":[{"name":"Zhongguancun Laboratory, Beijing 100194, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics (LMIB), Beihang University, Beijing 100191, China"},{"name":"Zhongguancun Laboratory, Beijing 100194, China"},{"name":"School of Mathematical Sciences, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,4]]},"reference":[{"key":"ref_1","first-page":"1338","article-title":"Proxy Signatures: Delegation of the Power to Sign Messages","volume":"79","author":"Mambo","year":"1996","journal-title":"IEICE Trans. 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