{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T08:12:31Z","timestamp":1785831151539,"version":"3.56.0"},"publisher-location":"Cham","reference-count":74,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031780226","type":"print"},{"value":"9783031780233","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,12,3]],"date-time":"2024-12-03T00:00:00Z","timestamp":1733184000000},"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\/978-3-031-78023-3_5","type":"book-chapter","created":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T10:51:24Z","timestamp":1733136684000},"page":"130-163","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["More Efficient Functional Bootstrapping for\u00a0General Functions in\u00a0Polynomial Modulus"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-4629-2905","authenticated-orcid":false,"given":"Han","family":"Xia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4298-3925","authenticated-orcid":false,"given":"Feng-Hao","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3102-604X","authenticated-orcid":false,"given":"Han","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,12,3]]},"reference":[{"key":"5_CR1","doi-asserted-by":"publisher","unstructured":"Abla, P., Liu, F.H., Wang, H., Wang, Z.: Ring-based identity based encryption - asymptotically shorter MPK and tighter security. In: Nissim, K., Waters, B. (eds.) TCC\u00a02021, Part\u00a0III. LNCS, vol. 13044, pp. 157\u2013187. Springer, Cham (Nov 2021). https:\/\/doi.org\/10.1007\/978-3-030-90456-2_6","DOI":"10.1007\/978-3-030-90456-2_6"},{"key":"5_CR2","volume-title":"ASIACRYPT 2022, Part II, LNCS","year":"2022","unstructured":"Agrawal, S., Lin, D. (eds.): ASIACRYPT 2022, Part II, LNCS, vol. 13792. Springer, Cham (Dec (2022)"},{"key":"5_CR3","doi-asserted-by":"publisher","unstructured":"Al\u00a0Badawi, A., et al.: OpenFHE: Open-source fully homomorphic encryption library. In: Proceedings of the 10th Workshop on Encrypted Computing & Applied Homomorphic Cryptography, pp. 53\u201363. WAHC\u201922, Association for Computing Machinery, New York, NY, USA (2022). https:\/\/doi.org\/10.1145\/3560827.3563379","DOI":"10.1145\/3560827.3563379"},{"key":"5_CR4","doi-asserted-by":"publisher","unstructured":"Alperin-Sheriff, J., Peikert, C.: Practical bootstrapping in quasilinear time. In: Canetti and Garay [17], pp. 1\u201320. https:\/\/doi.org\/10.1007\/978-3-642-40041-4_1","DOI":"10.1007\/978-3-642-40041-4_1"},{"key":"5_CR5","doi-asserted-by":"publisher","unstructured":"Alperin-Sheriff, J., Peikert, C.: Faster bootstrapping with polynomial error. In: Garay and Gennaro [32], pp. 297\u2013314. https:\/\/doi.org\/10.1007\/978-3-662-44371-2_17","DOI":"10.1007\/978-3-662-44371-2_17"},{"key":"5_CR6","doi-asserted-by":"publisher","unstructured":"Barrington, D.A.M.: Bounded-width polynomial-size branching programs recognize exactly those languages in $$\\text{NC}^1$$. In: 18th ACM STOC, pp.\u00a01\u20135. ACM Press (May 1986). https:\/\/doi.org\/10.1145\/12130.12131","DOI":"10.1145\/12130.12131"},{"issue":"3","key":"5_CR7","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/s00145-023-09463-5","volume":"36","author":"L Bergerat","year":"2023","unstructured":"Bergerat, L., et al.: Parameter optimization and larger precision for (T)FHE. J. Cryptol. 36(3), 28 (2023). https:\/\/doi.org\/10.1007\/s00145-023-09463-5","journal-title":"J. Cryptol."},{"key":"5_CR8","doi-asserted-by":"publisher","unstructured":"Biasse, J.F., Ruiz, L.: FHEW with efficient multibit bootstrapping. In: Lauter, K.E., Rodr\u00edguez-Henr\u00edquez, F. (eds.) LATINCRYPT\u00a02015. LNCS, vol.\u00a09230, pp. 119\u2013135. Springer, Cham (Aug 2015). https:\/\/doi.org\/10.1007\/978-3-319-22174-8_7","DOI":"10.1007\/978-3-319-22174-8_7"},{"key":"5_CR9","doi-asserted-by":"publisher","unstructured":"Bonte, C., Iliashenko, I., Park, J., Pereira, H.V.L., Smart, N.P.: FINAL: Faster FHE instantiated with NTRU and LWE. In: Agrawal and Lin [2], pp. 188\u2013215. https:\/\/doi.org\/10.1007\/978-3-031-22966-4_7","DOI":"10.1007\/978-3-031-22966-4_7"},{"key":"5_CR10","doi-asserted-by":"publisher","unstructured":"Boura, C., Gama, N., Georgieva, M., Jetchev, D.: Simulating homomorphic evaluation of deep learning predictions. In: International Symposium on Cyber Security Cryptography and Machine Learning, pp. 212\u2013230. Springer (2019). https:\/\/doi.org\/10.1007\/978-3-030-20951-3_20","DOI":"10.1007\/978-3-030-20951-3_20"},{"key":"5_CR11","doi-asserted-by":"publisher","unstructured":"Bourse, F., Sanders, O., Traor\u00e9, J.: Improved secure integer comparison via homomorphic encryption. In: Jarecki, S. (ed.) CT-RSA\u00a02020. LNCS, vol. 12006, pp. 391\u2013416. Springer, Cham (Feb 2020). https:\/\/doi.org\/10.1007\/978-3-030-40186-3_17","DOI":"10.1007\/978-3-030-40186-3_17"},{"key":"5_CR12","doi-asserted-by":"publisher","unstructured":"Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini and Canetti [64], pp. 868\u2013886. https:\/\/doi.org\/10.1007\/978-3-642-32009-5_50","DOI":"10.1007\/978-3-642-32009-5_50"},{"key":"5_CR13","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Goldwasser, S. (ed.) ITCS 2012, pp. 309\u2013325. ACM (Jan 2012). https:\/\/doi.org\/10.1145\/2090236.2090262","DOI":"10.1145\/2090236.2090262"},{"key":"5_CR14","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehl\u00e9, D.: Classical hardness of learning with errors. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 575\u2013584. ACM Press (Jun 2013). https:\/\/doi.org\/10.1145\/2488608.2488680","DOI":"10.1145\/2488608.2488680"},{"key":"5_CR15","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Ostrovsky, R. (ed.) 52nd FOCS, pp. 97\u2013106. IEEE Computer Society Press (Oct 2011). https:\/\/doi.org\/10.1109\/FOCS.2011.12","DOI":"10.1109\/FOCS.2011.12"},{"key":"5_CR16","doi-asserted-by":"publisher","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Lattice-based FHE as secure as PKE. In: Naor, M. (ed.) ITCS 2014, pp. 1\u201312. ACM (Jan 2014). https:\/\/doi.org\/10.1145\/2554797.2554799","DOI":"10.1145\/2554797.2554799"},{"key":"5_CR17","volume-title":"CRYPTO 2013, Part I, LNCS","year":"2013","unstructured":"Canetti, R., Garay, J.A. (eds.): CRYPTO 2013, Part I, LNCS, vol. 8042. Springer, Berlin, Heidelberg (Aug (2013)"},{"key":"5_CR18","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/978-3-662-49890-3_6","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016: 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria, May 8-12, 2016, Proceedings, Part I","author":"W Castryck","year":"2016","unstructured":"Castryck, W., Iliashenko, I., Vercauteren, F.: Provably weak instances of ring-lwe revisited. In: Fischlin, M., Coron, J.-S. (eds.) Advances in Cryptology \u2013 EUROCRYPT 2016: 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria, May 8-12, 2016, Proceedings, Part I, pp. 147\u2013167. Springer Berlin Heidelberg, Berlin, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49890-3_6"},{"key":"5_CR19","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1007\/978-3-030-78372-3_18","volume-title":"Applied Cryptography and Network Security: 19th International Conference, ACNS 2021, Kamakura, Japan, June 21\u201324, 2021, Proceedings, Part I","author":"H Chen","year":"2021","unstructured":"Chen, H., Dai, W., Kim, M., Song, Y.: Efficient homomorphic conversion between (Ring) LWE Ciphertexts. In: Sako, K., Tippenhauer, N.O. (eds.) Applied Cryptography and Network Security: 19th International Conference, ACNS 2021, Kamakura, Japan, June 21\u201324, 2021, Proceedings, Part I, pp. 460\u2013479. Springer International Publishing, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-78372-3_18"},{"key":"5_CR20","doi-asserted-by":"publisher","unstructured":"Chen, H., Laine, K., Player, R.: Simple encrypted arithmetic library - SEAL v2.1. In: Brenner, M., Rohloff, K., Bonneau, J., Miller, A., Ryan, P.Y.A., Teague, V., Bracciali, A., Sala, M., Pintore, F., Jakobsson, M. (eds.) FC 2017 Workshops. LNCS, vol. 10323, pp. 3\u201318. Springer, Cham (Apr 2017). https:\/\/doi.org\/10.1007\/978-3-319-70278-0_1","DOI":"10.1007\/978-3-319-70278-0_1"},{"key":"5_CR21","doi-asserted-by":"publisher","unstructured":"Cheon, J.H., Kim, A., Kim, M., Song, Y.S.: Homomorphic encryption for arithmetic of approximate numbers. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT\u00a02017, Part\u00a0I. LNCS, vol. 10624, pp. 409\u2013437. Springer, Cham (Dec 2017). https:\/\/doi.org\/10.1007\/978-3-319-70694-8_15","DOI":"10.1007\/978-3-319-70694-8_15"},{"key":"5_CR22","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-662-53887-6_1","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2016: 22nd International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, Vietnam, December 4-8, 2016, Proceedings, Part I","author":"I Chillotti","year":"2016","unstructured":"Chillotti, I., Gama, N., Georgieva, M., Izabach\u00e8ne, M.: Faster Fully Homomorphic Encryption: Bootstrapping in Less Than 0.1 seconds. In: Cheon, J.H., Takagi, T. (eds.) Advances in Cryptology \u2013 ASIACRYPT 2016: 22nd International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, Vietnam, December 4-8, 2016, Proceedings, Part I, pp. 3\u201333. Springer Berlin Heidelberg, Berlin, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53887-6_1"},{"issue":"1","key":"5_CR23","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/s00145-019-09319-x","volume":"33","author":"I Chillotti","year":"2019","unstructured":"Chillotti, I., Gama, N., Georgieva, M., Izabach\u00e8ne, M.: TFHE: fast fully homomorphic encryption over the torus. J. Cryptol. 33(1), 34\u201391 (2019). https:\/\/doi.org\/10.1007\/s00145-019-09319-x","journal-title":"J. Cryptol."},{"key":"5_CR24","unstructured":"Chillotti, I., Gama, N., Georgieva, M., Izabach\u00e8ne, M.: TFHE: Fast fully homomorphic encryption library. GitHub (2023). https:\/\/github.com\/tfhe\/tfhe"},{"key":"5_CR25","doi-asserted-by":"publisher","unstructured":"Chillotti, I., Joye, M., Paillier, P.: Programmable bootstrapping enables efficient homomorphic inference of deep neural networks. In: Cyber Security Cryptography and Machine Learning: 5th International Symposium, CSCML 2021, Be\u2019er Sheva, Israel, July 8\u20139, 2021, Proceedings 5, pp. 1\u201319. Springer (2021). https:\/\/doi.org\/10.1007\/978-3-030-78086-9_1","DOI":"10.1007\/978-3-030-78086-9_1"},{"key":"5_CR26","doi-asserted-by":"publisher","unstructured":"Chillotti, I., Ligier, D., Orfila, J.B., Tap, S.: Improved programmable bootstrapping with larger precision and efficient arithmetic circuits for TFHE. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT\u00a02021, Part\u00a0III. LNCS, vol. 13092, pp. 670\u2013699. Springer, Cham (Dec 2021). https:\/\/doi.org\/10.1007\/978-3-030-92078-4_23","DOI":"10.1007\/978-3-030-92078-4_23"},{"key":"5_CR27","unstructured":"Clet, P.E., Zuber, M., Boudguiga, A., Sirdey, R., Gouy-Pailler, C.: Putting up the swiss army knife of homomorphic calculations by means of TFHE functional bootstrapping. Cryptology ePrint Archive, Report 2022\/149 (2022). https:\/\/eprint.iacr.org\/2022\/149"},{"key":"5_CR28","doi-asserted-by":"publisher","unstructured":"Cong, K., Das, D., Park, J., Pereira, H.V.L.: SortingHat: Efficient private decision tree evaluation via homomorphic encryption and transciphering. In: Yin, H., Stavrou, A., Cremers, C., Shi, E. (eds.) ACM CCS 2022, pp. 563\u2013577. ACM Press (Nov 2022). https:\/\/doi.org\/10.1145\/3548606.3560702","DOI":"10.1145\/3548606.3560702"},{"key":"5_CR29","unstructured":"Crockett, E., Peikert, C.: Challenges for ring-LWE. Cryptology ePrint Archive, Report 2016\/782 (2016). https:\/\/eprint.iacr.org\/2016\/782"},{"key":"5_CR30","doi-asserted-by":"publisher","unstructured":"Ducas, L., Micciancio, D.: FHEW: bootstrapping homomorphic encryption in less than a second. In: Oswald and Fischlin [58], pp. 617\u2013640. https:\/\/doi.org\/10.1007\/978-3-662-46800-5_24","DOI":"10.1007\/978-3-662-46800-5_24"},{"key":"5_CR31","unstructured":"Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. Cryptology ePrint Archive, Report 2012\/144 (2012). https:\/\/eprint.iacr.org\/2012\/144"},{"key":"5_CR32","volume-title":"CRYPTO 2014, Part I, LNCS","year":"2014","unstructured":"Garay, J.A., Gennaro, R. (eds.): CRYPTO 2014, Part I, LNCS, vol. 8616. Springer, Berlin, Heidelberg (Aug (2014)"},{"key":"5_CR33","doi-asserted-by":"publisher","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher [54], pp. 169\u2013178. https:\/\/doi.org\/10.1145\/1536414.1536440","DOI":"10.1145\/1536414.1536440"},{"key":"5_CR34","doi-asserted-by":"publisher","unstructured":"Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini and Canetti [64], pp. 850\u2013867. https:\/\/doi.org\/10.1007\/978-3-642-32009-5_49","DOI":"10.1007\/978-3-642-32009-5_49"},{"key":"5_CR35","doi-asserted-by":"publisher","unstructured":"Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti and Garay [17], pp. 75\u201392. https:\/\/doi.org\/10.1007\/978-3-642-40041-4_5","DOI":"10.1007\/978-3-642-40041-4_5"},{"key":"5_CR36","doi-asserted-by":"publisher","unstructured":"Guimar\u00e3es, A., Borin, E., Aranha, D.F.: Revisiting the functional bootstrap in TFHE. IACR TCHES 2021(2), 229\u2013253 (2021). https:\/\/doi.org\/10.46586\/tches.v2021.i2.229-253, https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/8793","DOI":"10.46586\/tches.v2021.i2.229-253"},{"key":"5_CR37","doi-asserted-by":"publisher","unstructured":"Halevi, S., Shoup, V.: Algorithms in HElib. In: Garay and Gennaro [32], pp. 554\u2013571. https:\/\/doi.org\/10.1007\/978-3-662-44371-2_31","DOI":"10.1007\/978-3-662-44371-2_31"},{"key":"5_CR38","doi-asserted-by":"publisher","unstructured":"Halevi, S., Shoup, V.: Bootstrapping for HElib. In: Oswald and Fischlin [58], pp. 641\u2013670. https:\/\/doi.org\/10.1007\/978-3-662-46800-5_25","DOI":"10.1007\/978-3-662-46800-5_25"},{"key":"5_CR39","unstructured":"Halevi, S., Shoup, V.: Design and implementation of HElib: a homomorphic encryption library. Cryptology ePrint Archive, Report 2020\/1481 (2020). https:\/\/eprint.iacr.org\/2020\/1481"},{"key":"5_CR40","volume-title":"EUROCRYPT 2023, Part III, LNCS","year":"2023","unstructured":"Hazay, C., Stam, M. (eds.): EUROCRYPT 2023, Part III, LNCS, vol. 14006. Springer, Cham (Apr (2023)"},{"key":"5_CR41","doi-asserted-by":"publisher","unstructured":"Joye, M., Walter, M.: Liberating TFHE: programmable bootstrapping with general quotient polynomials. In: Proceedings of the 10th Workshop on Encrypted Computing & Applied Homomorphic Cryptography, pp. 1\u201311 (2022). https:\/\/doi.org\/10.1145\/3560827.3563376","DOI":"10.1145\/3560827.3563376"},{"key":"5_CR42","doi-asserted-by":"publisher","unstructured":"Kluczniak, K., Schild, L.: FDFB: Full domain functional bootstrapping towards practical fully homomorphic encryption. IACR TCHES 2023(1), 501\u2013537 (2023). https:\/\/doi.org\/10.46586\/tches.v2023.i1.501-537","DOI":"10.46586\/tches.v2023.i1.501-537"},{"key":"5_CR43","doi-asserted-by":"publisher","unstructured":"Lee, Y., et al.: Efficient FHEW bootstrapping with small evaluation keys, and applications to threshold homomorphic encryption. In: Hazay and Stam [40], pp. 227\u2013256. https:\/\/doi.org\/10.1007\/978-3-031-30620-4_8","DOI":"10.1007\/978-3-031-30620-4_8"},{"key":"5_CR44","doi-asserted-by":"publisher","unstructured":"Liu, F.H., Wang, H.: Batch bootstrapping I: a new framework for SIMD bootstrapping in polynomial modulus. In: Hazay and Stam [40], pp. 321\u2013352. https:\/\/doi.org\/10.1007\/978-3-031-30620-4_11","DOI":"10.1007\/978-3-031-30620-4_11"},{"key":"5_CR45","doi-asserted-by":"publisher","unstructured":"Liu, F.H., Wang, H.: Batch bootstrapping II: bootstrapping in polynomial modulus only requires $$\\tilde{O}(1)$$ FHE multiplications in amortization. In: Hazay and Stam [40], pp. 353\u2013384. https:\/\/doi.org\/10.1007\/978-3-031-30620-4_12","DOI":"10.1007\/978-3-031-30620-4_12"},{"key":"5_CR46","volume-title":"Computer Security. ESORICS 2023 International Workshops: CPS4CIP, ADIoT, SecAssure, WASP, TAURIN, PriST-AI, and SECAI, The Hague, The Netherlands, September 25\u201329, 2023, Revised Selected Papers, Part II","year":"2024","unstructured":"Katsikas, S., Abie, H., Ranise, S., Verderame, L., Cambiaso, E., Ugarelli, R., Pra\u00e7a, I., Li, W., Meng, W., Furnell, S., Katt, B., Pirbhulal, S., Shukla, A., Ianni, M., Dalla Preda, M., Choo, K.-K.R., Pupo Correia, M., Abhishta, A., Sileno, G., Alishahi, M., Kalutarage, H., Yanai, N. (eds.): Computer Security. ESORICS 2023 International Workshops: CPS4CIP, ADIoT, SecAssure, WASP, TAURIN, PriST-AI, and SECAI, The Hague, The Netherlands, September 25\u201329, 2023, Revised Selected Papers, Part II. Springer Nature Switzerland, Cham (2024)"},{"key":"5_CR47","doi-asserted-by":"publisher","unstructured":"Liu, Z., Micciancio, D., Polyakov, Y.: Large-precision homomorphic sign evaluation using FHEW\/TFHE bootstrapping. In: Agrawal and Lin [2], pp. 130\u2013160. https:\/\/doi.org\/10.1007\/978-3-031-22966-4_5","DOI":"10.1007\/978-3-031-22966-4_5"},{"key":"5_CR48","doi-asserted-by":"publisher","unstructured":"Liu, Z., Wang, Y.: Amortized functional bootstrapping in less than 7 ms, with \u00d5(1) polynomial multiplications. In: Guo, J., Steinfeld, R. (eds.) ASIACRYPT\u00a02023, Part\u00a0VI. LNCS, vol. 14443, pp. 101\u2013132. Springer, Singapore (Dec 2023). https:\/\/doi.org\/10.1007\/978-981-99-8736-8_4","DOI":"10.1007\/978-981-99-8736-8_4"},{"key":"5_CR49","doi-asserted-by":"publisher","unstructured":"Lu, W.J., Huang, Z., Hong, C., Ma, Y., Qu, H.: PEGASUS: Bridging polynomial and non-polynomial evaluations in homomorphic encryption. In: 2021 IEEE Symposium on Security and Privacy. pp. 1057\u20131073. IEEE Computer Society Press (May 2021). https:\/\/doi.org\/10.1109\/SP40001.2021.00043","DOI":"10.1109\/SP40001.2021.00043"},{"key":"5_CR50","doi-asserted-by":"publisher","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT\u00a02010. LNCS, vol.\u00a06110, pp. 1\u201323. Springer, Berlin, Heidelberg (May\u00a0\/\u00a0Jun 2010). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_1","DOI":"10.1007\/978-3-642-13190-5_1"},{"key":"5_CR51","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/978-3-642-38348-9_3","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings","author":"V Lyubashevsky","year":"2013","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: A toolkit for ring-LWE cryptography. In: Johansson, T., Nguyen, P.Q. (eds.) Advances in Cryptology \u2013 EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings, pp. 35\u201354. Springer Berlin Heidelberg, Berlin, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-38348-9_3"},{"key":"5_CR52","doi-asserted-by":"publisher","unstructured":"Ma, S., Huang, T., Wang, A., Zhou, Q., Wang, X.: Fast and accurate: efficient full-domain functional bootstrap and digit decomposition for homomorphic computation. IACR TCHES 2024(1), 592\u2013616 (2024). https:\/\/doi.org\/10.46586\/tches.v2024.i1.592-616","DOI":"10.46586\/tches.v2024.i1.592-616"},{"key":"5_CR53","doi-asserted-by":"publisher","unstructured":"Micciancio, D., Polyakov, Y.: Bootstrapping in FHEW-like cryptosystems. In: WAHC \u201921: Proceedings of the 9th on Workshop on Encrypted Computing & Applied Homomorphic Cryptography, Virtual Event, Korea, 15 November 2021, pp. 17\u201328. WAHC@ACM (2021). https:\/\/doi.org\/10.1145\/3474366.3486924","DOI":"10.1145\/3474366.3486924"},{"key":"5_CR54","unstructured":"Mitzenmacher, M. (ed.): 41st ACM STOC. ACM Press (May\u00a0\/\u00a0Jun 2009)"},{"key":"5_CR55","unstructured":"from MO (https:\/\/mathoverflow.net\/users\/11919\/gh-from mo), G.: Upper bound for product of exponents of prime factorization. MathOverflow. https:\/\/mathoverflow.net\/q\/256452"},{"key":"5_CR56","unstructured":"Open Source: HElib. GitHub. https:\/\/github.com\/shaih\/HElib"},{"key":"5_CR57","unstructured":"Open Source: Palisade lattice cryptography library. GitLab. https:\/\/gitlab.com\/palisade"},{"key":"5_CR58","volume-title":"EUROCRYPT 2015, Part I, LNCS","year":"2015","unstructured":"Oswald, E., Fischlin, M. (eds.): EUROCRYPT 2015, Part I, LNCS, vol. 9056. Springer, Berlin, Heidelberg (Apr (2015)"},{"key":"5_CR59","doi-asserted-by":"publisher","unstructured":"Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Mitzenmacher [54], pp. 333\u2013342. https:\/\/doi.org\/10.1145\/1536414.1536461","DOI":"10.1145\/1536414.1536461"},{"key":"5_CR60","doi-asserted-by":"publisher","unstructured":"Peikert, C.: How (not) to instantiate ring-LWE. In: Zikas, V., De Prisco, R. (eds.) SCN 16. LNCS, vol.\u00a09841, pp. 411\u2013430. Springer, Cham (Aug\u00a0\/\u00a0Sep 2016). https:\/\/doi.org\/10.1007\/978-3-319-44618-9_22","DOI":"10.1007\/978-3-319-44618-9_22"},{"key":"5_CR61","doi-asserted-by":"publisher","unstructured":"Peikert, C., Pepin, Z.: Algebraically structured LWE, revisited. In: Hofheinz, D., Rosen, A. (eds.) TCC\u00a02019, Part\u00a0I. LNCS, vol. 11891, pp. 1\u201323. Springer, Cham (Dec 2019). https:\/\/doi.org\/10.1007\/978-3-030-36030-6_1","DOI":"10.1007\/978-3-030-36030-6_1"},{"key":"5_CR62","doi-asserted-by":"publisher","unstructured":"Peikert, C., Regev, O., Stephens-Davidowitz, N.: Pseudorandomness of ring-LWE for any ring and modulus. In: Hatami, H., McKenzie, P., King, V. (eds.) 49th ACM STOC, pp. 461\u2013473. ACM Press (Jun 2017). https:\/\/doi.org\/10.1145\/3055399.3055489","DOI":"10.1145\/3055399.3055489"},{"key":"5_CR63","doi-asserted-by":"publisher","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, pp. 84\u201393. ACM Press (May 2005). https:\/\/doi.org\/10.1145\/1060590.1060603","DOI":"10.1145\/1060590.1060603"},{"key":"5_CR64","volume-title":"CRYPTO 2012, LNCS","year":"2012","unstructured":"Safavi-Naini, R., Canetti, R. (eds.): CRYPTO 2012, LNCS, vol. 7417. Springer, Berlin, Heidelberg (Aug (2012)"},{"issue":"1","key":"5_CR65","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s10623-012-9720-4","volume":"71","author":"NP Smart","year":"2012","unstructured":"Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes Crypt. 71(1), 57\u201381 (2012). https:\/\/doi.org\/10.1007\/s10623-012-9720-4","journal-title":"Des. Codes Crypt."},{"key":"5_CR66","doi-asserted-by":"publisher","unstructured":"Stehl\u00e9, D., Steinfeld, R., Tanaka, K., Xagawa, K.: Efficient public key encryption based on ideal lattices. In: Matsui, M. (ed.) ASIACRYPT\u00a02009. LNCS, vol.\u00a05912, pp. 617\u2013635. Springer, Berlin, Heidelberg (Dec 2009). https:\/\/doi.org\/10.1007\/978-3-642-10366-7_36","DOI":"10.1007\/978-3-642-10366-7_36"},{"key":"5_CR67","doi-asserted-by":"crossref","unstructured":"Tenenbaum, G.: Introduction to analytic and probabilistic number theory, vol.\u00a0163. American Mathematical Soc. (2015)","DOI":"10.1090\/gsm\/163"},{"key":"5_CR68","unstructured":"The Sage Developers: Sagemath, the Sage Mathematics Software System (Version 10.2) (2023). https:\/\/www.sagemath.org"},{"key":"5_CR69","unstructured":"Vinogradov, I.M.: Chapter VI: Primitive roots and indices. In: Elements of number theory. pp. 105\u2013121. Dover Publications (2003). https:\/\/books.google.com\/books?id=xlIfdGPM9t4C&pg=PA105"},{"key":"5_CR70","doi-asserted-by":"publisher","unstructured":"Wang, R., et al.: Circuit bootstrapping: Faster and smaller. In: Joye, M., Leander, G. (eds.) EUROCRYPT\u00a02024, Part\u00a0II. LNCS, vol. 14652, pp. 342\u2013372. Springer, Cham (May 2024). https:\/\/doi.org\/10.1007\/978-3-031-58723-8_12","DOI":"10.1007\/978-3-031-58723-8_12"},{"key":"5_CR71","doi-asserted-by":"publisher","unstructured":"Xiang, B., Zhang, J., Deng, Y., Dai, Y., Feng, D.: Fast blind rotation for bootstrapping FHEs. In: Handschuh, H., Lysyanskaya, A. (eds.) CRYPTO\u00a02023, Part\u00a0IV. LNCS, vol. 14084, pp. 3\u201336. Springer, Cham (Aug 2023). https:\/\/doi.org\/10.1007\/978-3-031-38551-3_1","DOI":"10.1007\/978-3-031-38551-3_1"},{"key":"5_CR72","unstructured":"Yang, Z., Xie, X., Shen, H., Chen, S., Zhou, J.: TOTA: Fully homomorphic encryption with smaller parameters and stronger security. Cryptology ePrint Archive, Report 2021\/1347 (2021). https:\/\/eprint.iacr.org\/2021\/1347"},{"key":"5_CR73","unstructured":"Zama: TFHE-rs: A Pure Rust Implementation of the TFHE Scheme for Boolean and Integer Arithmetics Over Encrypted Data (2022). https:\/\/github.com\/zama-ai\/tfhe-rs"},{"key":"5_CR74","unstructured":"Zheng, X., Li, H., Wang, D.: A new framework for fast homomorphic matrix multiplication. Cryptology ePrint Archive, Paper 2023\/1649 (2023). https:\/\/eprint.iacr.org\/2023\/1649"}],"container-title":["Lecture Notes in Computer Science","Theory of Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-78023-3_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,2]],"date-time":"2024-12-02T11:04:11Z","timestamp":1733137451000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-78023-3_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,3]]},"ISBN":["9783031780226","9783031780233"],"references-count":74,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-78023-3_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,3]]},"assertion":[{"value":"3 December 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TCC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Theory of Cryptography Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Milan","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":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 December 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6 December 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"tcc2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/tcc.iacr.org\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}