{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T14:16:36Z","timestamp":1772892996332,"version":"3.50.1"},"publisher-location":"Cham","reference-count":37,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031828515","type":"print"},{"value":"9783031828522","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-82852-2_4","type":"book-chapter","created":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T13:02:16Z","timestamp":1741784536000},"page":"84-104","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Multi-key Homomorphic Encryption with\u00a0Threshold Re-encryption"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-4132-0914","authenticated-orcid":false,"given":"Akira","family":"Nakashima","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7349-1491","authenticated-orcid":false,"given":"Yukimasa","family":"Sugizaki","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0004-7500-3318","authenticated-orcid":false,"given":"Hikaru","family":"Tsuchida","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5869-2319","authenticated-orcid":false,"given":"Takuya","family":"Hayashi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8259-9958","authenticated-orcid":false,"given":"Koji","family":"Nuida","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0003-1950-1032","authenticated-orcid":false,"given":"Kengo","family":"Mori","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0004-2219-3779","authenticated-orcid":false,"given":"Toshiyuki","family":"Isshiki","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"4_CR1","unstructured":"Albrecht, M., et al.: Homomorphic Encryption Security Standard (2018). http:\/\/homomorphicencryption.org\/wp-content\/uploads\/2018\/11\/HomomorphicEncryptionStandardv1.1.pdf"},{"key":"4_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/978-3-642-29011-4_29","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"G Asharov","year":"2012","unstructured":"Asharov, G., Jain, A., L\u00f3pez-Alt, A., Tromer, E., Vaikuntanathan, V., Wichs, D.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 483\u2013501. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-29011-4_29"},{"key":"4_CR3","doi-asserted-by":"crossref","unstructured":"Ateniese, G., Fu, K., Green, M., Hohenberger, S.: Improved proxy re-encryption schemes with applications to secure distributed storage. In: NDSS. The Internet Society (2005)","DOI":"10.1145\/1127345.1127346"},{"key":"4_CR4","unstructured":"Badawi, A.A., et al.: OpenFHE: open-source fully homomorphic encryption library. Cryptology ePrint Archive, Paper 2022\/915 (2022). https:\/\/eprint.iacr.org\/2022\/915"},{"key":"4_CR5","doi-asserted-by":"publisher","unstructured":"Blaze, M., Bleumer, G., Strauss, M.: Divertible protocols and atomic proxy cryptography. In: EUROCRYPT. LNCS, vol.\u00a01403, pp. 127\u2013144. Springer, Heidelberg (1998). https:\/\/doi.org\/10.1007\/bfb0054122","DOI":"10.1007\/bfb0054122"},{"key":"4_CR6","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theory 6(3), 13:1\u201313:36 (2014)","DOI":"10.1145\/2633600"},{"key":"4_CR7","doi-asserted-by":"crossref","unstructured":"Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS, pp. 136\u2013145. IEEE Computer Society (2001)","DOI":"10.1109\/SFCS.2001.959888"},{"key":"4_CR8","doi-asserted-by":"crossref","unstructured":"Canetti, R., Hohenberger, S.: Chosen-ciphertext secure proxy re-encryption. In: CCS, pp. 185\u2013194. ACM (2007)","DOI":"10.1145\/1315245.1315269"},{"key":"4_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1007\/978-3-030-34621-8_16","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2019","author":"H Chen","year":"2019","unstructured":"Chen, H., Chillotti, I., Song, Y.: Multi-Key homomorphic encryption from TFHE. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11922, pp. 446\u2013472. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-34621-8_16"},{"key":"4_CR10","doi-asserted-by":"crossref","unstructured":"Chen, H., Dai, W., Kim, M., Song, Y.: Efficient multi-key homomorphic encryption with packed ciphertexts with application to oblivious neural network inference. In: CCS, pp. 395\u2013412. ACM (2019)","DOI":"10.1145\/3319535.3363207"},{"key":"4_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/978-3-319-70503-3_20","volume-title":"Theory of Cryptography","author":"L Chen","year":"2017","unstructured":"Chen, L., Zhang, Z., Wang, X.: Batched multi-hop multi-key FHE from Ring-LWE with compact ciphertext extension. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 597\u2013627. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70503-3_20"},{"key":"4_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1007\/978-3-030-00015-8_2","volume-title":"Cloud Computing and Security","author":"X Chen","year":"2018","unstructured":"Chen, X., Liu, Y., Li, Y., Lin, C.: Threshold proxy re-encryption and its application in blockchain. In: Sun, X., Pan, Z., Bertino, E. (eds.) ICCCS 2018. LNCS, vol. 11066, pp. 16\u201325. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-00015-8_2"},{"key":"4_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/978-3-319-70694-8_15","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2017","author":"JH Cheon","year":"2017","unstructured":"Cheon, J.H., Kim, A., Kim, M., Song, Y.: Homomorphic encryption for arithmetic of approximate numbers. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 409\u2013437. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70694-8_15"},{"issue":"1","key":"4_CR14","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/s00145-019-09319-x","volume":"33","author":"I Chillotti","year":"2020","unstructured":"Chillotti, I., Gama, N., Georgieva, M., Izabach\u00e8ne, M.: TFHE: fast fully homomorphic encryption over the torus. J. Cryptol. 33(1), 34\u201391 (2020)","journal-title":"J. Cryptol."},{"key":"4_CR15","unstructured":"Community, Foundation: Fully Homomorphic Encryption $$|$$ We are a community of researchers and developers interested in advancing homomorphic encryption and other secure computation techniques. (2023). https:\/\/fhe.org\/"},{"key":"4_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/978-3-319-70972-7_7","volume-title":"Financial Cryptography and Data Security","author":"D Derler","year":"2017","unstructured":"Derler, D., Ramacher, S., Slamanig, D.: Homomorphic proxy re-authenticators and applications to verifiable multi-user data aggregation. In: Kiayias, A. (ed.) FC 2017. LNCS, vol. 10322, pp. 124\u2013142. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70972-7_7"},{"key":"4_CR17","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.tcs.2021.04.008","volume":"871","author":"P Dutta","year":"2021","unstructured":"Dutta, P., Susilo, W., Duong, D.H., Roy, P.S.: Collusion-resistant identity-based proxy re-encryption: lattice-based constructions in standard model. Theor. Comput. Sci. 871, 16\u201329 (2021)","journal-title":"Theor. Comput. Sci."},{"key":"4_CR18","unstructured":"Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. IACR Cryptol. ePrint Arch, p.\u00a0144 (2012)"},{"key":"4_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/978-3-642-40041-4_5","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"C Gentry","year":"2013","unstructured":"Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 75\u201392. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40041-4_5"},{"key":"4_CR20","unstructured":"Benchmark (2023). https:\/\/github.com\/google\/benchmark\/"},{"key":"4_CR21","unstructured":"ICO: Homomorphic encryption (HE) | ICO (2023). https:\/\/ico.org.uk\/for-organisations\/uk-gdpr-guidance-and-resources\/data-sharing\/privacy-enhancing-technologies\/what-pets-are-there\/homomorphic-encryption-he\/"},{"key":"4_CR22","unstructured":"ISO\/IEC: ISO\/IEC WD 18033-8 - Information security \u2014 Encryption algorithms \u2014 Part 8: Fully Homomorphic Encryption (2023). https:\/\/www.iso.org\/standard\/83139.html"},{"issue":"5","key":"4_CR23","doi-asserted-by":"publisher","first-page":"2090","DOI":"10.1137\/090755886","volume":"39","author":"E Kushilevitz","year":"2010","unstructured":"Kushilevitz, E., Lindell, Y., Rabin, T.: Information-theoretically secure protocols and security under composition. SIAM J. Comput. 39(5), 2090\u20132112 (2010)","journal-title":"SIAM J. Comput."},{"key":"4_CR24","doi-asserted-by":"crossref","unstructured":"L\u00f3pez-Alt, A., Tromer, E., Vaikuntanathan, V.: On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption. In: STOC, pp. 1219\u20131234. ACM (2012)","DOI":"10.1145\/2213977.2214086"},{"key":"4_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-13190-5_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"V Lyubashevsky","year":"2010","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1\u201323. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_1"},{"key":"4_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/978-3-319-47422-9_21","volume-title":"Provable Security","author":"C Ma","year":"2016","unstructured":"Ma, C., Li, J., Ouyang, W.: A homomorphic proxy re-encryption from\u00a0lattices. In: Chen, L., Han, J. (eds.) ProvSec 2016. LNCS, vol. 10005, pp. 353\u2013372. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-47422-9_21"},{"key":"4_CR27","doi-asserted-by":"crossref","unstructured":"Mohassel, P., Rindal, P.: ABY3: a mixed protocol framework for machine learning. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security. p. 35\u201352. CCS 2018, Association for Computing Machinery, New York, NY, USA (2018). https:\/\/doi.org\/10.1145\/3243734.3243760","DOI":"10.1145\/3243734.3243760"},{"key":"4_CR28","doi-asserted-by":"crossref","unstructured":"Mohassel, P., Zhang, Y.: SecureML: a system for scalable privacy-preserving machine learning. Cryptology ePrint Archive, Paper 2017\/396 (2017)","DOI":"10.1109\/SP.2017.12"},{"issue":"4","key":"4_CR29","doi-asserted-by":"publisher","first-page":"291","DOI":"10.2478\/popets-2021-0071","volume":"2021","author":"C Mouchet","year":"2021","unstructured":"Mouchet, C., Troncoso-Pastoriza, J.R., Bossuat, J., Hubaux, J.: Multiparty homomorphic encryption from ring-learning-with-errors. Proc. Priv. Enhancing Technol. 2021(4), 291\u2013311 (2021)","journal-title":"Proc. Priv. Enhancing Technol."},{"key":"4_CR30","unstructured":"NIST: Multi-party threshold cryptography $$|$$ CSRC (2023). https:\/\/csrc.nist.gov\/Projects\/threshold-cryptography"},{"key":"4_CR31","unstructured":"NTL: A library for doing number theory (2021). https:\/\/libntl.org\/"},{"key":"4_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/978-3-030-01446-9_7","volume-title":"Provable Security","author":"A Paul","year":"2018","unstructured":"Paul, A., Srinivasavaradhan, V., Sharmila Deva Selvi, S., Pandu Rangan, C.: A CCA-secure collusion-resistant identity-based proxy re-encryption scheme. In: Baek, J., Susilo, W., Kim, J. (eds.) ProvSec 2018. LNCS, vol. 11192, pp. 111\u2013128. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-01446-9_7"},{"key":"4_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/978-3-662-53644-5_9","volume-title":"Theory of Cryptography","author":"C Peikert","year":"2016","unstructured":"Peikert, C., Shiehian, S.: Multi-key FHE from LWE, revisited. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 217\u2013238. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_9"},{"key":"4_CR34","doi-asserted-by":"publisher","unstructured":"Raghav, Andola, N., Verma, K., Venkatesan, S., Verma, S.: Proactive threshold-proxy re-encryption scheme for secure data sharing on cloud. J. Supercomput. 79, 1\u201329 (2023). https:\/\/doi.org\/10.1007\/s11227-023-05221-3","DOI":"10.1007\/s11227-023-05221-3"},{"key":"4_CR35","unstructured":"Microsoft SEAL (release 4.1). https:\/\/github.com\/Microsoft\/SEAL (Jan 2023), microsoft Research, Redmond, WA"},{"key":"4_CR36","unstructured":"Standardization, H.E.: Homomorphic Encryption Standardization \u2013 An Open Industry \/ Government \/ Academic Consortium to Advance Secure Computation (2023). https:\/\/homomorphicencryption.org\/"},{"key":"4_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1007\/978-3-319-99136-8_18","volume-title":"Information Security","author":"S Yasuda","year":"2018","unstructured":"Yasuda, S., Koseki, Y., Hiromasa, R., Kawai, Y.: Multi-key homomorphic proxy re-encryption. In: Chen, L., Manulis, M., Schneider, S. (eds.) ISC 2018. LNCS, vol. 11060, pp. 328\u2013346. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-99136-8_18"}],"container-title":["Lecture Notes in Computer Science","Selected Areas in Cryptography \u2013 SAC 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-82852-2_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T13:02:24Z","timestamp":1741784544000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-82852-2_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031828515","9783031828522"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-82852-2_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"13 March 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SAC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Selected Areas in Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Montreal, QC","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 August 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31 August 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sacrypt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sacworkshop.org\/SAC24\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}