{"article_processing_charge":"No","scopus_import":"1","month":"05","date_updated":"2024-06-10T10:05:30Z","title":"Lower bounds for lattice-based compact functional encryption","acknowledgement":"We want to thank the anonymous reviewers of TCC and Eurocrypt for their very helpful comments and suggestions. This work has received funding from the Austrian Science Fund (FWF) and netidee SCIENCE via grant P31621-N38 (PROFET).","citation":{"mla":"Tairi, Erkan, and Akin Ünal. “Lower Bounds for Lattice-Based Compact Functional Encryption.” <i>Advances in Cryptology – EUROCRYPT 2024</i>, vol. 14652, Springer Nature, 2024, pp. 249–79, doi:<a href=\"https://doi.org/10.1007/978-3-031-58723-8_9\">10.1007/978-3-031-58723-8_9</a>.","ama":"Tairi E, Ünal A. Lower bounds for lattice-based compact functional encryption. In: <i>Advances in Cryptology – EUROCRYPT 2024</i>. Vol 14652. Springer Nature; 2024:249-279. doi:<a href=\"https://doi.org/10.1007/978-3-031-58723-8_9\">10.1007/978-3-031-58723-8_9</a>","ieee":"E. Tairi and A. Ünal, “Lower bounds for lattice-based compact functional encryption,” in <i>Advances in Cryptology – EUROCRYPT 2024</i>, Zurich, Switzerland, 2024, vol. 14652, pp. 249–279.","ista":"Tairi E, Ünal A. 2024. Lower bounds for lattice-based compact functional encryption. Advances in Cryptology – EUROCRYPT 2024. EUROCRYPT: International Conference on the Theory and Applications of Cryptographic Techniques, LNCS, vol. 14652, 249–279.","short":"E. Tairi, A. Ünal, in:, Advances in Cryptology – EUROCRYPT 2024, Springer Nature, 2024, pp. 249–279.","apa":"Tairi, E., &#38; Ünal, A. (2024). Lower bounds for lattice-based compact functional encryption. In <i>Advances in Cryptology – EUROCRYPT 2024</i> (Vol. 14652, pp. 249–279). Zurich, Switzerland: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-58723-8_9\">https://doi.org/10.1007/978-3-031-58723-8_9</a>","chicago":"Tairi, Erkan, and Akin Ünal. “Lower Bounds for Lattice-Based Compact Functional Encryption.” In <i>Advances in Cryptology – EUROCRYPT 2024</i>, 14652:249–79. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-58723-8_9\">https://doi.org/10.1007/978-3-031-58723-8_9</a>."},"type":"conference","date_created":"2024-06-09T22:01:03Z","status":"public","oa_version":"Submitted Version","department":[{"_id":"KrPi"}],"abstract":[{"lang":"eng","text":"Functional encryption (FE) is a primitive where the holder of a master secret key can control which functions a user can evaluate on encrypted data. It is a powerful primitive that even implies indistinguishability obfuscation (iO), given sufficiently compact ciphertexts (Ananth-Jain, CRYPTO’15 and Bitansky-Vaikuntanathan, FOCS’15). However, despite being extensively studied, there are FE schemes, such as function-hiding inner-product FE (Bishop-Jain-Kowalczyk, AC’15, Abdalla-Catalano-Fiore-Gay-Ursu, CRYPTO’18) and compact quadratic FE (Baltico-Catalano-Fiore-Gay, Lin, CRYPTO’17), that can be only realized using pairings. This raises the question if there are some mathematical barriers that hinder us from realizing these FE schemes from other assumptions.\r\n\r\nIn this paper, we study the difficulty of constructing lattice-based compact FE. We generalize the impossibility results of Ünal (EC’20) for lattice-based function-hiding FE, and extend it to the case of compact FE. Concretely, we prove lower bounds for lattice-based compact FE schemes which meet some (natural) algebraic restrictions at encryption and decryption, and have ciphertexts of linear size and secret keys of minimal degree. We see our results as important indications of why it is hard to construct lattice-based FE schemes for new functionalities, and which mathematical barriers have to be overcome."}],"year":"2024","publication_identifier":{"isbn":["9783031587221"],"issn":["0302-9743"],"eissn":["1611-3349"]},"publisher":"Springer Nature","author":[{"first_name":"Erkan","last_name":"Tairi","full_name":"Tairi, Erkan"},{"first_name":"Akin","full_name":"Ünal, Akin","last_name":"Ünal","orcid":"0000-0002-8929-0221","id":"f6b56fb6-dc63-11ee-9dbf-f6780863a85a"}],"doi":"10.1007/978-3-031-58723-8_9","_id":"17126","alternative_title":["LNCS"],"volume":14652,"conference":{"location":"Zurich, Switzerland","end_date":"2024-05-30","name":"EUROCRYPT: International Conference on the Theory and Applications of Cryptographic Techniques","start_date":"2024-05-26"},"date_published":"2024-05-08T00:00:00Z","publication_status":"published","day":"08","publication":"Advances in Cryptology – EUROCRYPT 2024","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"249-279","oa":1,"main_file_link":[{"open_access":"1","url":"https://eprint.iacr.org/2023/719.pdf"}],"intvolume":"     14652","language":[{"iso":"eng"}],"quality_controlled":"1"}