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Different to that, the security loss of our schemes is only dependent on\nthe security parameter. Our schemes are adaptively secure based on the Matrix Diffie-Hellman\nassumption, which is a generalization of standard Diffie-Hellman assumptions such as k-Linear. We\nhave two tightly secure constructions, one with constant ciphertext size, and the other with tighter\nsecurity at the cost of linear ciphertext size. Among other things, our schemes imply the first tightly\nsecure identity-based signature scheme by a variant of the Naor transformation.<\/jats:p>","DOI":"10.1007\/s00145-020-09356-x","type":"journal-article","created":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T15:04:02Z","timestamp":1600182242000},"page":"1787-1821","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Tightly Secure Hierarchical Identity-Based Encryption"],"prefix":"10.1007","volume":"33","author":[{"given":"Roman","family":"Langrehr","sequence":"first","affiliation":[]},{"given":"Jiaxin","family":"Pan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,15]]},"reference":[{"key":"9356_CR1","series-title":"Part II, volume 10402 of LNCS","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1007\/978-3-319-63715-0_19","volume-title":"CRYPTO 2017","author":"Masayuki Abe","year":"2017","unstructured":"Abe, Masayuki, Hofheinz, Dennis, Nishimaki, Ryo, Ohkubo, Miyako, Pan, Jiaxin: Compact structure-preserving signatures with almost tight security. 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