{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T01:42:35Z","timestamp":1772070155202,"version":"3.50.1"},"reference-count":51,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T00:00:00Z","timestamp":1686614400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T00:00:00Z","timestamp":1686614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100009572","name":"University of St.Gallen","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100009572","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Cryptol"],"published-print":{"date-parts":[[2023,7]]},"abstract":"Abstract<\/jats:title>Predicate inner product functional encryption (P-IPFE) is essentially attribute-based IPFE (AB-IPFE) which additionally hides attributes associated to ciphertexts. In a P-IPFE, a message $${\\textbf {x}}$$<\/jats:tex-math>\n x<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is encrypted under an attribute $${\\textbf {w}}$$<\/jats:tex-math>\n w<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and a secret key is generated for a pair $$({\\textbf {y}}, {\\textbf {v}})$$<\/jats:tex-math>\n \n (<\/mml:mo>\n y<\/mml:mi>\n ,<\/mml:mo>\n v<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> such that recovery of $$\\langle {{\\textbf {x}}}, {{\\textbf {y}}}\\rangle $$<\/jats:tex-math>\n \n \u27e8<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n \u27e9<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> requires the vectors $${\\textbf {w}}, {\\textbf {v}}$$<\/jats:tex-math>\n \n w<\/mml:mi>\n ,<\/mml:mo>\n v<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to satisfy a linear relation. We call a P-IPFE unbounded<\/jats:italic> if it can encrypt unbounded length attributes and message vectors. $$\\bullet $$<\/jats:tex-math>\n \u2219<\/mml:mo>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>zero predicate IPFE<\/jats:italic>. We construct the first<\/jats:italic> unbounded zero predicate IPFE (UZP-IPFE) which recovers $$\\langle {{\\textbf {x}}}, {{\\textbf {y}}}\\rangle $$<\/jats:tex-math>\n \n \u27e8<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n \u27e9<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> if $$\\langle {{\\textbf {w}}}, {{\\textbf {v}}}\\rangle =0$$<\/jats:tex-math>\n \n \u27e8<\/mml:mo>\n w<\/mml:mi>\n ,<\/mml:mo>\n v<\/mml:mi>\n \u27e9<\/mml:mo>\n =<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. This construction is inspired by the unbounded IPFE of Tomida and Takashima (ASIACRYPT 2018) and the unbounded zero inner product encryption of Okamoto and Takashima (ASIACRYPT 2012). The UZP-IPFE stands secure against general attackers capable of decrypting the challenge ciphertext. Concretely, it provides full attribute-hiding security in the indistinguishability-based semi-adaptive model under the standard symmetric external Diffie\u2013Hellman assumption. $$\\bullet $$<\/jats:tex-math>\n \u2219<\/mml:mo>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>non-zero predicate IPFE<\/jats:italic>. We present the first<\/jats:italic> unbounded non-zero predicate IPFE (UNP-IPFE) that successfully recovers $$\\langle {{\\textbf {x}}}, {{\\textbf {y}}}\\rangle $$<\/jats:tex-math>\n \n \u27e8<\/mml:mo>\n x<\/mml:mi>\n ,<\/mml:mo>\n y<\/mml:mi>\n \u27e9<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> if $$\\langle {{\\textbf {w}}}, {{\\textbf {v}}}\\rangle \\ne 0$$<\/jats:tex-math>\n \n \u27e8<\/mml:mo>\n w<\/mml:mi>\n ,<\/mml:mo>\n v<\/mml:mi>\n \u27e9<\/mml:mo>\n \u2260<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. We generically transform an unbounded quadratic FE (UQFE) scheme to weak attribute-hiding UNP-IPFE in both public and secret key setting. Interestingly, our secret key simulation<\/jats:italic> secure UNP-IPFE has succinct<\/jats:italic> secret keys and is constructed from a novel succinct<\/jats:italic> UQFE that we build in the random oracle model. We leave the problem of constructing a succinct public key UNP-IPFE or UQFE in the standard model as an important open problem.<\/jats:p>","DOI":"10.1007\/s00145-023-09458-2","type":"journal-article","created":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T21:01:42Z","timestamp":1686690102000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Unbounded Predicate Inner Product Functional Encryption from Pairings"],"prefix":"10.1007","volume":"36","author":[{"given":"Uddipana","family":"Dowerah","sequence":"first","affiliation":[]},{"given":"Subhranil","family":"Dutta","sequence":"additional","affiliation":[]},{"given":"Aikaterini","family":"Mitrokotsa","sequence":"additional","affiliation":[]},{"given":"Sayantan","family":"Mukherjee","sequence":"additional","affiliation":[]},{"given":"Tapas","family":"Pal","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,13]]},"reference":[{"key":"9458_CR1","doi-asserted-by":"crossref","unstructured":"M. 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