{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:21:08Z","timestamp":1760239268864,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T00:00:00Z","timestamp":1604275200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shandong Provincial Key Research and Development 512 Program of China","award":["2018CXGC0701"],"award-info":[{"award-number":["2018CXGC0701"]}]},{"name":"National Natural Science Foundation of China (NSFC)","award":["No. 61972050"],"award-info":[{"award-number":["No. 61972050"]}]},{"name":"BUPT Excellent Ph.D. Students Foundation","award":["No. CX2019119"],"award-info":[{"award-number":["No. CX2019119"]}]},{"DOI":"10.13039\/501100013314","name":"111 Project","doi-asserted-by":"publisher","award":["No. B08004"],"award-info":[{"award-number":["No. B08004"]}],"id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Identity-based encryption (IBE), and its hierarchical extension (HIBE), are interesting cryptographic primitives that aim at the implicit authentication on the users\u2019 public keys by using users\u2019 identities directly. During the past several decades, numerous elegant pairing-based (H)IBE schemes were proposed. However, most pairing-related security assumptions suffer from known quantum algorithmic attacks. Therefore, the construction of lattice-based (H)IBE became one of the hot directions in recent years. In the setting of most existing lattice-based (H)IBE schemes, each bit of a user\u2019s identity is always associated with a parameter matrix. This always leads to drastic but unfavorable increases in the sizes of the system public parameters. To overcome this issue, we propose a flexible trade-off mechanism between the size of the public parameters and the involved computational cost using the blocking technique. More specifically, we divide an identity into l\u2032 segments and associate each segment with a matrix, while increasing the lattice modulo slightly for maintaining the same security level. As a result, for the setting of 160-bit identities, we show that the size of the public parameters can be reduced by almost 89.7% (resp. 93.8%) while increasing the computational cost by merely 5.2% (resp. 12.25%) when l\u2032 is a set of 16 (resp. 8). Finally, our IBE scheme is extended to an HIBE scheme, and both of them are proved to achieve the indistinguishability of ciphertexts against adaptively chosen identity and chosen plaintext attack (IND-ID-CPA) in the standard model, assuming that the well-known ring learning with error (RLWE) problem over the involved ideal lattices is intractable, even in the post-quantum era.<\/jats:p>","DOI":"10.3390\/e22111247","type":"journal-article","created":{"date-parts":[[2020,11,2]],"date-time":"2020-11-02T19:51:31Z","timestamp":1604346691000},"page":"1247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Adaptively Secure Efficient (H)IBE over Ideal Lattice with Short Parameters"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6963-0594","authenticated-orcid":false,"given":"Yuan","family":"Zhang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3619-0099","authenticated-orcid":false,"given":"Yuan","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yurong","family":"Guo","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shihui","family":"Zheng","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Licheng","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,2]]},"reference":[{"key":"ref_1","unstructured":"Shamir, A. 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