{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T17:12:50Z","timestamp":1778087570866,"version":"3.51.4"},"publisher-location":"Cham","reference-count":55,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032253262","type":"print"},{"value":"9783032253279","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"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":[[2026]]},"DOI":"10.1007\/978-3-032-25327-9_8","type":"book-chapter","created":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T16:32:55Z","timestamp":1778085175000},"page":"214-242","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["HERDS: Multi-key Fully Homomorphic Encryption with\u00a0Sublinear Bootstrapping"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-8163-3987","authenticated-orcid":false,"given":"Binwu","family":"Xiang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1151-2453","authenticated-orcid":false,"given":"Seonhong","family":"Min","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-3870-2096","authenticated-orcid":false,"given":"Intak","family":"Hwang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8150-1792","authenticated-orcid":false,"given":"Zhiwei","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-8270-4442","authenticated-orcid":false,"given":"Haoqi","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-6778-9794","authenticated-orcid":false,"given":"Yuanju","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7453-4043","authenticated-orcid":false,"given":"Kang","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4787-0316","authenticated-orcid":false,"given":"Jiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5948-0780","authenticated-orcid":false,"given":"Yi","family":"Deng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9278-4521","authenticated-orcid":false,"given":"Yu","family":"Yu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,5,7]]},"reference":[{"key":"8_CR1","doi-asserted-by":"publisher","unstructured":"Akin, Y., Klemsa, J., \u00d6nen, M.: A practical TFHE-based multi-key homomorphic encryption with linear complexity and low noise growth. In: ESORICS 2023. Lecture Notes in Computer Science, vol. 14344, pp. 3\u201323. Springer (2023). https:\/\/doi.org\/10.1007\/978-3-031-50594-2_1","DOI":"10.1007\/978-3-031-50594-2_1"},{"key":"8_CR2","doi-asserted-by":"crossref","unstructured":"Albrecht, M.R., Player, R., Scott, S.: On the concrete hardness of learning with errors. J. Math. Cryptol. 9(3), 169\u2013203 (2015). http:\/\/www.degruyter.com\/view\/j\/jmc.2015.9.issue-3\/jmc-2015-0016\/jmc-2015-0016.xml","DOI":"10.1515\/jmc-2015-0016"},{"key":"8_CR3","doi-asserted-by":"publisher","unstructured":"Angel, S., Chen, H., Laine, K., Setty, S.T.V.: PIR with compressed queries and amortized query processing. In: 2018 IEEE Symposium on Security and Privacy, SP 2018, Proceedings, pp. 962\u2013979, 21\u201323 May 2018, San Francisco, California, USA. IEEE Computer Society (2018). https:\/\/doi.org\/10.1109\/SP.2018.00062,","DOI":"10.1109\/SP.2018.00062"},{"key":"8_CR4","doi-asserted-by":"publisher","unstructured":"Asharov, G., et al.: Multiparty computation with low communication, computation and interaction via threshold FHE. In: EUROCRYPT 2012. Lecture Notes in Computer Science, vol.\u00a07237, pp. 483\u2013501. Springer (2012). https:\/\/doi.org\/10.1007\/978-3-642-29011-4_29","DOI":"10.1007\/978-3-642-29011-4_29"},{"key":"8_CR5","doi-asserted-by":"publisher","unstructured":"Badawi, A.A., et al.: OpenFHE: Open-Source Fully Homomorphic Encryption Library. In: Proceedings of the 10th Workshop on Encrypted Computing & Applied Homomorphic Cryptography, Los Angeles, CA, USA, 7 November 2022, pp. 53\u201363. ACM (2022). https:\/\/doi.org\/10.1145\/3560827.3563379","DOI":"10.1145\/3560827.3563379"},{"key":"8_CR6","doi-asserted-by":"publisher","unstructured":"Belorgey, M.G., Carpov, S., Gama, N., Guasch, S., Jetchev, D.: Revisiting key decomposition techniques for FHE: simpler, faster and more generic. In: ASIACRYPT 2024. Lecture Notes in Computer Science, vol. 15484, pp. 176\u2013207. Springer (2024). https:\/\/doi.org\/10.1007\/978-981-96-0875-1_6","DOI":"10.1007\/978-981-96-0875-1_6"},{"key":"8_CR7","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theory. 6, 13:1\u201313:36 (2014). https:\/\/doi.org\/10.1145\/2633600","DOI":"10.1145\/2633600"},{"key":"8_CR8","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: FOCS 2011, pp. 97\u2013106. IEEE Computer Society (2011). https:\/\/doi.org\/10.1109\/FOCS.2011.12","DOI":"10.1109\/FOCS.2011.12"},{"key":"8_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.array.2021.100118","volume":"13","author":"L Brenna","year":"2022","unstructured":"Brenna, L., Singh, I.S., Johansen, H.D., Johansen, D.: TFHE-RS: a library for safe and secure remote computing using fully homomorphic encryption and trusted execution environments. Array 13, 100118 (2022)","journal-title":"Array"},{"key":"8_CR10","doi-asserted-by":"publisher","unstructured":"Chen, H., Chillotti, I., Song, Y.: Multi-key homomorphic encryption from TFHE. In: ASIACRYPT 2019. Lecture Notes in Computer Science, vol. 11922, pp. 446\u2013472. Springer (2019). https:\/\/doi.org\/10.1007\/978-3-030-34621-8_16","DOI":"10.1007\/978-3-030-34621-8_16"},{"key":"8_CR11","doi-asserted-by":"publisher","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 2019, pp. 395\u2013412. ACM (2019). https:\/\/doi.org\/10.1145\/3319535.3363207","DOI":"10.1145\/3319535.3363207"},{"key":"8_CR12","doi-asserted-by":"publisher","unstructured":"Chen, H., Huang, Z., Laine, K., Rindal, P.: Labeled PSI from fully homomorphic encryption with malicious security. In: CCS 2018, pp. 1223\u20131237. ACM (2018). https:\/\/doi.org\/10.1145\/3243734.3243836","DOI":"10.1145\/3243734.3243836"},{"key":"8_CR13","doi-asserted-by":"publisher","unstructured":"Chen, H., Laine, K., Rindal, P.: Fast private set intersection from homomorphic encryption. In: CCS 2017, pp. 1243\u20131255. ACM (2017). https:\/\/doi.org\/10.1145\/3133956.3134061","DOI":"10.1145\/3133956.3134061"},{"key":"8_CR14","doi-asserted-by":"publisher","unstructured":"Chen, L., Zhang, Z., Wang, X.: Batched multi-hop multi-key FHE from ring-LWE with compact ciphertext extension. In: TCC 2017. LNCS, vol. 10678, pp. 597\u2013627. Springer (2017). https:\/\/doi.org\/10.1007\/978-3-319-70503-3_20","DOI":"10.1007\/978-3-319-70503-3_20"},{"key":"8_CR15","doi-asserted-by":"publisher","unstructured":"Cheon, J.H., Kim, A., Kim, M., Song, Y.S.: Homomorphic encryption for arithmetic of approximate numbers. In: ASIACRYPT 2017. Lecture Notes in Computer Science, vol. 10624, pp. 409\u2013437. Springer (2017). https:\/\/doi.org\/10.1007\/978-3-319-70694-8_15","DOI":"10.1007\/978-3-319-70694-8_15"},{"key":"8_CR16","doi-asserted-by":"publisher","unstructured":"Chillotti, I., Gama, N., Georgieva, M., Izabach\u00e8ne, M.: Faster packed homomorphic operations and efficient circuit bootstrapping for TFHE. In: ASIACRYPT 2017. Lecture Notes in Computer Science, vol. 10624, pp. 377\u2013408. Springer (2017). https:\/\/doi.org\/10.1007\/978-3-319-70694-8_14","DOI":"10.1007\/978-3-319-70694-8_14"},{"issue":"1","key":"8_CR17","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). https:\/\/doi.org\/10.1007\/S00145-019-09319-X","journal-title":"J. Cryptol."},{"key":"8_CR18","doi-asserted-by":"publisher","unstructured":"Clear, M., McGoldrick, C.: Multi-identity and multi-key leveled FHE from learning with errors. In: CRYPTO 2015. LNCS, vol.\u00a09216, pp. 630\u2013656. Springer (2015). https:\/\/doi.org\/10.1007\/978-3-662-48000-7_31","DOI":"10.1007\/978-3-662-48000-7_31"},{"key":"8_CR19","doi-asserted-by":"publisher","unstructured":"Cong, K., et al.: Labeled PSI from homomorphic encryption with reduced computation and communication. In: CCS 21, pp. 1135\u20131150. ACM (2021). https:\/\/doi.org\/10.1145\/3460120.3484760","DOI":"10.1145\/3460120.3484760"},{"key":"8_CR20","doi-asserted-by":"publisher","unstructured":"Dahl, M., et al.: Noah\u2019s ark: Efficient threshold-FHE using noise flooding. In: Proceedings of the 11th Workshop on Encrypted Computing & Applied Homomorphic Cryptography, Copenhagen, Denmark, 26 November 2023, pp. 35\u201346. ACM (2023). https:\/\/doi.org\/10.1145\/3605759.3625259","DOI":"10.1145\/3605759.3625259"},{"key":"8_CR21","doi-asserted-by":"publisher","unstructured":"Dalvi, A., et al.: Securing neural networks using homomorphic encryption. In: 2021 International Conference on Intelligent Technologies (CONIT), pp.\u00a01\u20137 (2021). https:\/\/doi.org\/10.1109\/CONIT51480.2021.9498376","DOI":"10.1109\/CONIT51480.2021.9498376"},{"key":"8_CR22","doi-asserted-by":"publisher","unstructured":"Fisch, B., Lazzaretti, A., Liu, Z., Papamanthou, C.: Thorpir: Single server PIR via homomorphic thorp shuffles. In: CCS 2024, pp. 1448\u20131462. ACM (2024). https:\/\/doi.org\/10.1145\/3658644.3690326","DOI":"10.1145\/3658644.3690326"},{"key":"8_CR23","doi-asserted-by":"publisher","unstructured":"Friedman, O., et al.: Tiresias: Large scale, UC-secure threshold Paillier. In: ASIACRYPT 2024. vol. 15486, pp. 141\u2013173. Springer (2024). https:\/\/doi.org\/10.1007\/978-981-96-0891-1_5","DOI":"10.1007\/978-981-96-0891-1_5"},{"key":"8_CR24","doi-asserted-by":"publisher","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC 2009, pp. 169\u2013178 (2009). https:\/\/doi.org\/10.1145\/1536414.1536440","DOI":"10.1145\/1536414.1536440"},{"key":"8_CR25","doi-asserted-by":"publisher","unstructured":"Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: CRYPTO 2013, vol.\u00a08042, pp. 75\u201392. Springer (2013). https:\/\/doi.org\/10.1007\/978-3-642-40041-4_5","DOI":"10.1007\/978-3-642-40041-4_5"},{"key":"8_CR26","unstructured":"Goldwasser, S., Kalai, Y.T., Peikert, C., Vaikuntanathan, V.: Robustness of the learning with errors assumption. In: Innovations in Computer Science - ICS 2010, Tsinghua University, Beijing, China, January 5-7, 2010. Proceedings, pp. 230\u2013240. Tsinghua University Press (2010). http:\/\/conference.iiis.tsinghua.edu.cn\/ICS2010\/content\/papers\/19.html"},{"key":"8_CR27","unstructured":"Hwang, I.: TFHE-go (2023). https:\/\/github.com\/sp301415\/tfhe-go"},{"key":"8_CR28","unstructured":"Juvekar, C., Vaikuntanathan, V., Chandrakasan, A.P.: GAZELLE: a low latency framework for secure neural network inference. In: USENIX Security 2018, pp. 1651\u20131669. USENIX Association (2018). https:\/\/www.usenix.org\/conference\/usenixsecurity18\/presentation\/juvekar"},{"key":"8_CR29","doi-asserted-by":"publisher","unstructured":"Kim, T., Kwak, H., Lee, D., Seo, J., Song, Y.: Asymptotically faster multi-key homomorphic encryption from homomorphic gadget decomposition. In: CCS 2023, pp. 726\u2013740. ACM (2023). https:\/\/doi.org\/10.1145\/3576915.3623176","DOI":"10.1145\/3576915.3623176"},{"key":"8_CR30","doi-asserted-by":"publisher","unstructured":"Kraitsberg, M., Lindell, Y., Osheter, V., Smart, N.P., Alaoui, Y.T.: Adding distributed decryption and key generation to a ring-LWE based CCA encryption scheme. In: ACISP 2019, vol. 11547, pp. 192\u2013210. Springer (2019). https:\/\/doi.org\/10.1007\/978-3-030-21548-4_11","DOI":"10.1007\/978-3-030-21548-4_11"},{"key":"8_CR31","doi-asserted-by":"publisher","unstructured":"Kwak, H., Min, S., Song, Y.: Towards practical multi-key TFHE: parallelizable, key-compatible, quasi-linear complexity. In: PKC 2024. Lecture Notes in Computer Science, vol. 14604, pp. 354\u2013385. Springer (2024). https:\/\/doi.org\/10.1007\/978-3-031-57728-4_12","DOI":"10.1007\/978-3-031-57728-4_12"},{"key":"8_CR32","doi-asserted-by":"publisher","unstructured":"Lee, C., Min, S., Seo, J., Song, Y.: Faster TFHE bootstrapping with block binary keys. In: ASIA CCS 2023, pp. 2\u201313. ACM (2023). https:\/\/doi.org\/10.1145\/3579856.3595804","DOI":"10.1145\/3579856.3595804"},{"key":"8_CR33","doi-asserted-by":"publisher","first-page":"30039","DOI":"10.1109\/ACCESS.2022.3159694","volume":"10","author":"JW Lee","year":"2022","unstructured":"Lee, J.W., et al.: Privacy-preserving machine learning with fully homomorphic encryption for deep neural network. IEEE Access 10, 30039\u201330054 (2022). https:\/\/doi.org\/10.1109\/ACCESS.2022.3159694","journal-title":"IEEE Access"},{"key":"8_CR34","doi-asserted-by":"publisher","unstructured":"Lee, J., Lee, E., Kim, Y., No, J.: Rotation key reduction for client-server systems of deep neural network on fully homomorphic encryption. In: ASIACRYPT 2023, vol. 14443, pp. 36\u201368. Springer (2023). https:\/\/doi.org\/10.1007\/978-981-99-8736-8_2","DOI":"10.1007\/978-981-99-8736-8_2"},{"key":"8_CR35","unstructured":"Lee, K., Yeo, Y.: Sophomr: Improved oblivious message retrieval from simd-aware homomorphic compression. IACR Cryptol. ePrint Arch, p.\u00a01814 (2024). https:\/\/eprint.iacr.org\/2024\/1814"},{"key":"8_CR36","doi-asserted-by":"publisher","unstructured":"Liu, Z., Tromer, E.: Oblivious message retrieval. In: CRYPTO 2022. Lecture Notes in Computer Science, vol. 13507, pp. 753\u2013783. Springer (2022). https:\/\/doi.org\/10.1007\/978-3-031-15802-5_26","DOI":"10.1007\/978-3-031-15802-5_26"},{"key":"8_CR37","doi-asserted-by":"publisher","unstructured":"Liu, Z., Tromer, E., Wang, Y.: Group oblivious message retrieval. In: IEEE Symposium on Security and Privacy, SP 2024, San Francisco, CA, USA, May 19-23, 2024, pp. 4367\u20134385. IEEE (2024). https:\/\/doi.org\/10.1109\/SP54263.2024.00115","DOI":"10.1109\/SP54263.2024.00115"},{"key":"8_CR38","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 2012, pp. 1219\u20131234. ACM (2012)","DOI":"10.1145\/2213977.2214086"},{"key":"8_CR39","doi-asserted-by":"publisher","unstructured":"Lu, W., Huang, Z., Hong, C., Ma, Y., Qu, H.: PEGASUS: bridging polynomial and non-polynomial evaluations in homomorphic encryption. In: SP 2021, pp. 1057\u20131073. IEEE (2021). https:\/\/doi.org\/10.1109\/SP40001.2021.00043","DOI":"10.1109\/SP40001.2021.00043"},{"key":"8_CR40","doi-asserted-by":"publisher","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: EUROCRYPT 2010, pp. 1\u201323. Springer (2010). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_1","DOI":"10.1007\/978-3-642-13190-5_1"},{"key":"8_CR41","doi-asserted-by":"publisher","unstructured":"Menon, S.J., Wu, D.J.: SPIRAL: fast, high-rate single-server PIR via FHE composition. In: 43rd IEEE Symposium on Security and Privacy, SP 2022, San Francisco, CA, USA, May 22-26, 2022, pp. 930\u2013947. IEEE (2022). https:\/\/doi.org\/10.1109\/SP46214.2022.9833700","DOI":"10.1109\/SP46214.2022.9833700"},{"key":"8_CR42","doi-asserted-by":"publisher","unstructured":"Micciancio, D., Suhl, A.: Simulation-secure threshold PKE from LWE with polynomial modulus. IACR Commun. Cryptol. 1(4), 2 (2024). https:\/\/doi.org\/10.62056\/A0ZOGY4E-","DOI":"10.62056\/A0ZOGY4E-"},{"issue":"2","key":"8_CR43","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1007\/S00145-023-09452-8","volume":"36","author":"C Mouchet","year":"2023","unstructured":"Mouchet, C., Bertrand, E., Hubaux, J.: An efficient threshold access-structure for RLWE-based multiparty homomorphic encryption. J. Cryptol. 36(2), 10 (2023). https:\/\/doi.org\/10.1007\/S00145-023-09452-8","journal-title":"J. Cryptol."},{"issue":"4","key":"8_CR44","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). https:\/\/doi.org\/10.2478\/POPETS-2021-0071","journal-title":"Proc. Priv. Enhancing Technol."},{"key":"8_CR45","doi-asserted-by":"publisher","unstructured":"Mukherjee, P., Wichs, D.: Two round multiparty computation via multi-key FHE. In: EUROCRYPT 2016. LNCS, vol.\u00a09666, pp. 735\u2013763. Springer (2016). https:\/\/doi.org\/10.1007\/978-3-662-49896-5_26","DOI":"10.1007\/978-3-662-49896-5_26"},{"key":"8_CR46","doi-asserted-by":"publisher","unstructured":"Okada, H., Takagi, T.: Low communication threshold FHE from standard (module-)LWE. In: ASIACRYPT 2025. Lecture Notes in Computer Science, vol. 16251, pp. 165\u2013198. Springer (2025). https:\/\/doi.org\/10.1007\/978-981-95-5122-4_6","DOI":"10.1007\/978-981-95-5122-4_6"},{"key":"8_CR47","doi-asserted-by":"publisher","first-page":"135915","DOI":"10.1109\/ACCESS.2021.3117029","volume":"9","author":"J Park","year":"2021","unstructured":"Park, J.: Homomorphic encryption for multiple users with less communications. IEEE Access 9, 135915\u2013135926 (2021). https:\/\/doi.org\/10.1109\/ACCESS.2021.3117029","journal-title":"IEEE Access"},{"key":"8_CR48","doi-asserted-by":"publisher","unstructured":"Park, J., Leeuwen, B.V., Zajonc, O.: FINALLY: A multi-key FHE scheme based on NTRU and LWE. IACR Commun. Cryptol. 1(3), 15 (2024). https:\/\/doi.org\/10.62056\/AEBN-4C2H","DOI":"10.62056\/AEBN-4C2H"},{"key":"8_CR49","doi-asserted-by":"publisher","unstructured":"Passel\u00e8gue, A., Stehl\u00e9, D.: Low communication threshold fully homomorphic encryption. In: Advances in Cryptology - ASIACRYPT 2024. Lecture Notes in Computer Science, vol. 15484, pp. 297\u2013329. Springer (2024). https:\/\/doi.org\/10.1007\/978-981-96-0875-1_10","DOI":"10.1007\/978-981-96-0875-1_10"},{"key":"8_CR50","doi-asserted-by":"publisher","unstructured":"Peikert, C., Shiehian, S.: Multi-key FHE from LWE, revisited. In: TCC 2016-B. LNCS, vol.\u00a09986, pp. 217\u2013238 (2016). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_9","DOI":"10.1007\/978-3-662-53644-5_9"},{"issue":"6","key":"8_CR51","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1568318.1568324","volume":"56","author":"O Regev","year":"2009","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56(6), 1\u201340 (2009). https:\/\/doi.org\/10.1145\/1568318.1568324","journal-title":"J. ACM (JACM)"},{"key":"8_CR52","doi-asserted-by":"publisher","unstructured":"Sugizaki, Y., et al.: Threshold fully homomorphic encryption over the torus. In: Computer Security - ESORICS 2023. Lecture Notes in Computer Science, vol. 14344, pp. 45\u201365. Springer (2023). https:\/\/doi.org\/10.1007\/978-3-031-50594-2_3","DOI":"10.1007\/978-3-031-50594-2_3"},{"key":"8_CR53","unstructured":"Wang, R., et al.: FHEW-like leveled homomorphic evaluation: refined workflow and polished building blocks. Cryptology ePrint Archive, Paper 2024\/1318 (2024). https:\/\/eprint.iacr.org\/2024\/1318"},{"key":"8_CR54","doi-asserted-by":"publisher","unstructured":"Xiang, B., Zhang, J., Wang, K., Deng, Y., Feng, D.: NTRU-based bootstrapping for MK-FHEs without using overstretched parameters. In: ASIACRYPT 2024. Lecture Notes in Computer Science, vol. 15484, pp. 241\u2013270. Springer (2024). https:\/\/doi.org\/10.1007\/978-981-96-0875-1_8","DOI":"10.1007\/978-981-96-0875-1_8"},{"key":"8_CR55","doi-asserted-by":"publisher","DOI":"10.1016\/J.TCS.2023.114026","volume":"968","author":"K Xu","year":"2023","unstructured":"Xu, K., Tan, B.H.M., Wang, L., Aung, K.M.M., Wang, H.: Multi-key fully homomorphic encryption from NTRU and (R)LWE with faster bootstrapping. Theor. Comput. Sci. 968, 114026 (2023). https:\/\/doi.org\/10.1016\/J.TCS.2023.114026","journal-title":"Theor. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2026"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-25327-9_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T16:33:01Z","timestamp":1778085181000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-25327-9_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032253262","9783032253279"],"references-count":55,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-25327-9_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"7 May 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EUROCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Conference on the Theory and Applications of Cryptographic Techniques","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Rome","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Italy","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 May 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 May 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"45","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2026","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt.iacr.org\/2026\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}