{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T01:23:15Z","timestamp":1777339395973,"version":"3.51.4"},"publisher-location":"Singapore","reference-count":26,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819690978","type":"print"},{"value":"9789819690985","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\/978-981-96-9098-5_12","type":"book-chapter","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T09:18:00Z","timestamp":1752139080000},"page":"232-251","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["High-Precision Homomorphic Modular Reduction for\u00a0CKKS Bootstrapping"],"prefix":"10.1007","author":[{"given":"Zejiu","family":"Tan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junping","family":"Wan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zoe L.","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingjing","family":"Fan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Man Ho","family":"Au","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siu Ming","family":"Yiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,7]]},"reference":[{"key":"12_CR1","doi-asserted-by":"crossref","unstructured":"Boemer, F., Costache, A., Cammarota, R., Wierzynski, C.: ngraph-he2: a high-throughput framework for neural network inference on encrypted data. In: Proceedings of the 7th ACM Workshop on Encrypted Computing & Applied Homomorphic Cryptography, pp. 45\u201356 (2019)","DOI":"10.1145\/3338469.3358944"},{"key":"12_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1007\/978-3-030-77870-5_21","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2021","author":"J-P Bossuat","year":"2021","unstructured":"Bossuat, J.-P., Mouchet, C., Troncoso-Pastoriza, J., Hubaux, J.-P.: Efficient bootstrapping for approximate homomorphic encryption with non-sparse keys. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12696, pp. 587\u2013617. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-77870-5_21"},{"issue":"3","key":"12_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2633600","volume":"6","author":"Z Brakerski","year":"2014","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (leveled) fully homomorphic encryption without bootstrapping. ACM Trans. Comput. Theory (TOCT) 6(3), 1\u201336 (2014)","journal-title":"ACM Trans. Comput. Theory (TOCT)"},{"key":"12_CR4","unstructured":"Brutzkus, A., Gilad-Bachrach, R., Elisha, O.: Low latency privacy preserving inference. In: International Conference on Machine Learning, pp. 812\u2013821. PMLR (2019)"},{"key":"12_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/978-3-030-17656-3_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"H Chen","year":"2019","unstructured":"Chen, H., Chillotti, I., Song, Y.: Improved bootstrapping for approximate homomorphic encryption. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11477, pp. 34\u201354. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17656-3_2"},{"key":"12_CR6","doi-asserted-by":"crossref","unstructured":"Cheney, E.W.: Introduction to approximation theory (1966)","DOI":"10.2307\/2314671"},{"key":"12_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1007\/978-3-319-78381-9_14","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2018","author":"JH Cheon","year":"2018","unstructured":"Cheon, J.H., Han, K., Kim, A., Kim, M., Song, Y.: Bootstrapping for approximate homomorphic encryption. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 360\u2013384. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-78381-9_14"},{"key":"12_CR8","doi-asserted-by":"crossref","unstructured":"Cheon, J.H., Han, K., Kim, A., Kim, M., Song, Y.: A full RNS variant of approximate homomorphic encryption. In: Selected Areas in Cryptography\u2013SAC 2018: 25th International Conference, Calgary, AB, Canada, August 15\u201317, 2018, Revised Selected Papers 25, pp. 347\u2013368. Springer (2019)","DOI":"10.1007\/978-3-030-10970-7_16"},{"key":"12_CR9","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":"12_CR10","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."},{"issue":"1","key":"12_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2904902","volume":"43","author":"S-I Filip","year":"2016","unstructured":"Filip, S.-I.: A robust and scalable implementation of the parks-mcclellan algorithm for designing fir filters. ACM Trans. Math. Softw. (TOMS) 43(1), 1\u201324 (2016)","journal-title":"ACM Trans. Math. Softw. (TOMS)"},{"key":"12_CR12","unstructured":"Folland, G.B.: Fourier Analysis and its Applications, vol. 4. American Mathematical Soc. (2009)"},{"key":"12_CR13","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, pp. 169\u2013178 (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"12_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1007\/978-3-030-40186-3_16","volume-title":"Topics in Cryptology \u2013 CT-RSA 2020","author":"K Han","year":"2020","unstructured":"Han, K., Ki, D.: Better bootstrapping for approximate homomorphic encryption. In: Jarecki, S. (ed.) CT-RSA 2020. LNCS, vol. 12006, pp. 364\u2013390. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-40186-3_16"},{"key":"12_CR15","doi-asserted-by":"crossref","unstructured":"Harris, J.M.: Combinatorics and Graph Theory. Springer, Cham (2008)","DOI":"10.1007\/978-0-387-79711-3"},{"key":"12_CR16","doi-asserted-by":"crossref","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (2012)","DOI":"10.1017\/CBO9781139020411"},{"key":"12_CR17","doi-asserted-by":"crossref","unstructured":"Jiang, X., Kim, M., Lauter, K., Song, Y.: Secure outsourced matrix computation and application to neural networks. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, pp. 1209\u20131222 (2018)","DOI":"10.1145\/3243734.3243837"},{"key":"12_CR18","unstructured":"Jutla, C.S., Manohar, N.: Modular lagrange interpolation of the mod function for bootstrapping of approximate he. Cryptology ePrint Archive (2020)"},{"key":"12_CR19","doi-asserted-by":"crossref","unstructured":"Jutla, C.S., Manohar, N.: Sine series approximation of the mod function for bootstrapping of approximate he. In: Annual International Conference on the Theory and Applications of Cryptographic Techniques, pp. 491\u2013520. Springer (2022)","DOI":"10.1007\/978-3-031-06944-4_17"},{"key":"12_CR20","unstructured":"Lee, E., et al.: Low-complexity deep convolutional neural networks on fully homomorphic encryption using multiplexed parallel convolutions. In: International Conference on Machine Learning, pp. 12403\u201312422. PMLR (2022)"},{"key":"12_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1007\/978-3-030-77870-5_22","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2021","author":"J-W Lee","year":"2021","unstructured":"Lee, J.-W., Lee, E., Lee, Y., Kim, Y.-S., No, J.-S.: High-precision bootstrapping of\u00a0RNS-CKKS homomorphic encryption using optimal minimax polynomial approximation and inverse sine function. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12696, pp. 618\u2013647. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-77870-5_22"},{"key":"12_CR22","unstructured":"Lee, S., Lee, G., Kim, J.W., Shin, J., Lee, M-K.: Hetal: efficient privacy-preserving transfer learning with homomorphic encryption. In: International Conference on Machine Learning, pp. 19010\u201319035. PMLR (2023)"},{"issue":"2","key":"12_CR23","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1109\/MSP.2005.1406492","volume":"22","author":"JH McClellan","year":"2005","unstructured":"McClellan, J.H., Parks, T.W.: A personal history of the parks-mcclellan algorithm. IEEE Signal Process. Mag. 22(2), 82\u201386 (2005)","journal-title":"IEEE Signal Process. Mag."},{"key":"12_CR24","unstructured":"James\u00a0David Powell, M.: Approximation Theory and Methods. Cambridge University Press, Cambridge (1981)"},{"issue":"6","key":"12_CR25","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)","journal-title":"J. ACM (JACM)"},{"key":"12_CR26","unstructured":"Microsoft SEAL (release 3.6) (2020). https:\/\/github.com\/Microsoft\/SEAL. Microsoft Research, Redmond, WA"}],"container-title":["Lecture Notes in Computer Science","Information Security and Privacy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-96-9098-5_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T09:18:12Z","timestamp":1752139092000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-96-9098-5_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9789819690978","9789819690985"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-981-96-9098-5_12","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":"7 July 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ACISP","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Australasian Conference on Information Security and Privacy","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Wollongong, NSW","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Australia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 July 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 July 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"acisp2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/uow-ic2.github.io\/acisp2025\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}