{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T04:59:05Z","timestamp":1764997145922,"version":"3.40.3"},"publisher-location":"Cham","reference-count":46,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319702773"},{"type":"electronic","value":"9783319702780"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-70278-0_4","type":"book-chapter","created":{"date-parts":[[2017,11,18]],"date-time":"2017-11-18T02:03:19Z","timestamp":1510970599000},"page":"53-74","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Privacy-Preserving Computations of Predictive Medical Models with Minimax Approximation and Non-Adjacent Form"],"prefix":"10.1007","author":[{"given":"Jung Hee","family":"Cheon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinhyuck","family":"Jeong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joohee","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keewoo","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,11,19]]},"reference":[{"key":"4_CR1","volume-title":"Theory of Approximation","author":"NI Achieser","year":"2013","unstructured":"Achieser, N.I.: Theory of Approximation. Courier Corporation, Chelmsford (2013)"},{"unstructured":"Albrecht, M.R.: On dual lattice attacks against small-secret LWE and parameter choices in HElib and SEAL. Cryptology ePrint Archive, Report 2017\/047 (2017). http:\/\/eprint.iacr.org\/2017\/047","key":"4_CR2"},{"issue":"3","key":"4_CR3","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1515\/jmc-2015-0016","volume":"9","author":"MR Albrecht","year":"2015","unstructured":"Albrecht, M.R., Player, R., Scott, S.: On the concrete hardness of learning with errors. J. Math. Cryptol. 9(3), 169\u2013203 (2015)","journal-title":"J. Math. Cryptol."},{"issue":"3","key":"4_CR4","first-page":"124","volume":"7","author":"A Abadi","year":"2014","unstructured":"Abadi, A., Yavari, P., Dehghani-Arani, M., Alavi-Majd, H., Ghasemi, E., Amanpour, F., Bajdik, C.: Cox models survival analysis based on breast cancer treatments. Iran. J. Cancer Prev. 7(3), 124 (2014)","journal-title":"Iran. J. Cancer Prev."},{"doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pp. 309\u2013325. ACM (2012)","key":"4_CR5","DOI":"10.1145\/2090236.2090262"},{"key":"4_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/978-3-642-45239-0_4","volume-title":"Cryptography and Coding","author":"JW Bos","year":"2013","unstructured":"Bos, J.W., Lauter, K., Loftus, J., Naehrig, M.: Improved security for a ring-based fully homomorphic encryption scheme. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 45\u201364. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-45239-0_4"},{"key":"4_CR7","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.jbi.2014.04.003","volume":"50","author":"JW Bos","year":"2014","unstructured":"Bos, J.W., Lauter, K., Naehrig, M.: Private predictive analysis on encrypted medical data. J. Biomed. Inform. 50, 234\u2013243 (2014)","journal-title":"J. Biomed. Inform."},{"key":"4_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1007\/978-3-642-32009-5_50","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"Z Brakerski","year":"2012","unstructured":"Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868\u2013886. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_50"},{"issue":"6","key":"4_CR9","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/S1072-7515(00)00758-4","volume":"191","author":"S Biondo","year":"2000","unstructured":"Biondo, S., Ramos, E., Deiros, M., Ragu\u00e9, J.M., De Oca, J., Moreno, P., Farran, L., Jaurrieta, E.: Prognostic factors for mortality in left colonic peritonitis: a new scoring system. J. Am. Coll. Surg. 191(6), 635\u2013642 (2000)","journal-title":"J. Am. Coll. Surg."},{"issue":"3","key":"4_CR10","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1161\/01.CIR.0000153341.46271.40","volume":"111","author":"SM Boekholdt","year":"2005","unstructured":"Boekholdt, S.M., Sacks, F.M., Jukema, J.W., Shepherd, J., Freeman, D.J., McMahon, A.D., Cambien, F., Nicaud, V., De Grooth, G.J., Talmud, P.J., et al.: Cholesteryl ester transfer protein TaqIB variant, high-density lipoprotein cholesterol levels, cardiovascular risk, and efficacy of pravastatin treatment individual patient meta-analysis of 13 677 subjects. Circulation 111(3), 278\u2013287 (2005)","journal-title":"Circulation"},{"issue":"4","key":"4_CR11","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1097\/00005373-198704000-00005","volume":"27","author":"CR Boyd","year":"1987","unstructured":"Boyd, C.R., Tolson, M.A., Copes, W.S.: Evaluating trauma care: the TRISS method. J. Trauma Acute Care Surg. 27(4), 370\u2013378 (1987)","journal-title":"J. Trauma Acute Care Surg."},{"doi-asserted-by":"crossref","unstructured":"Blankstein, R., Ward, R.P., Arnsdorf, M., Jones, B., Lou, Y.-B., Pine, M.: Female gender is an independent predictor of operative mortality after coronary artery bypass graft surgery contemporary analysis of 31 midwestern hospitals. Circulation 112(9 suppl), I\u2013323 (2005)","key":"4_CR12","DOI":"10.1161\/CIRCULATIONAHA.104.525139"},{"key":"4_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/978-3-642-38348-9_20","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"JH Cheon","year":"2013","unstructured":"Cheon, J.H., Coron, J.-S., Kim, J., Lee, M.S., Lepoint, T., Tibouchi, M., Yun, A.: Batch fully homomorphic encryption over the integers. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 315\u2013335. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-38348-9_20"},{"key":"4_CR14","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.ins.2015.03.019","volume":"310","author":"JH Cheon","year":"2015","unstructured":"Cheon, J.H., Kim, J., Lee, M.S., Yun, A.: CRT-based fully homomorphic encryption over the integers. Inf. Sci. 310, 149\u2013162 (2015)","journal-title":"Inf. Sci."},{"unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: Cryptanalysis of two candidate fixes of multilinear maps over the integers. IACR Cryptology ePrint Archive 2014, p. 975 (2014)","key":"4_CR15"},{"key":"4_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/978-3-642-22792-9_28","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"J-S Coron","year":"2011","unstructured":"Coron, J.-S., Mandal, A., Naccache, D., Tibouchi, M.: Fully homomorphic encryption over the integers with shorter public keys. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 487\u2013504. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22792-9_28"},{"key":"4_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1007\/978-3-642-29011-4_27","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"J-S Coron","year":"2012","unstructured":"Coron, J.-S., Naccache, D., Tibouchi, M.: Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 446\u2013464. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-29011-4_27"},{"key":"4_CR18","volume-title":"Analysis of Survival Data","author":"DR Cox","year":"1984","unstructured":"Cox, D.R., Oakes, D.: Analysis of Survival Data, vol. 21. CRC Press, Boca Raton (1984)"},{"issue":"2","key":"4_CR19","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1111\/j.2517-6161.1958.tb00292.x","volume":"20","author":"DR Cox","year":"1958","unstructured":"Cox, D.R.: The regression analysis of binary sequences. J. R. Stat. Soc. Ser. B (Methodol.) 20(2), 215\u2013242 (1958). JSTOR. www.jstor.org\/stable\/2983890","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"issue":"2","key":"4_CR20","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","volume":"34","author":"DR Cox","year":"1972","unstructured":"Cox, D.R.: Regression models and life-tables. J. R. Stat. Soc. Ser. B 34(2), 187\u2013220 (1972)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"4_CR21","series-title":"Springer Series in Statistics (Perspectives in Statistics)","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1007\/978-1-4612-4380-9_37","volume-title":"Breakthroughs in Statistics","author":"DR Cox","year":"1992","unstructured":"Cox, D.R.: Regression models and life-tables. In: Kotz, S., Johnson, N.L. (eds.) Breakthroughs in Statistics. SSS, pp. 527\u2013541. Springer, New York (1992). https:\/\/doi.org\/10.1007\/978-1-4612-4380-9_37"},{"unstructured":"Costache, A., Smart, N.P., Vivek, S., Waller, A.: Fixed point arithmetic in SHE schemes. Technical report, Cryptology ePrint Archive, Report 2016\/250 (2016). http:\/\/eprint.iacr.org\/2016\/250","key":"4_CR22"},{"unstructured":"Dowlin, N., Gilad-Bachrach, R., Laine, K., Lauter, K., Naehrig, M., Wernsing, J.: Manual for using homomorphic encryption for bioinformatics. Microsoft Research (2015). http:\/\/research.microsoft.com\/pubs\/258435\/ManualHEv2.pdf","key":"4_CR23"},{"issue":"1","key":"4_CR24","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.gheart.2013.01.001","volume":"8","author":"RB D\u2019Agostino","year":"2013","unstructured":"D\u2019Agostino, R.B., Pencina, M.J., Massaro, J.M., Coady, S.: Cardiovascular disease risk assessment: insights from Framingham. Glob. Heart 8(1), 11\u201323 (2013)","journal-title":"Glob. Heart"},{"issue":"6","key":"4_CR25","doi-asserted-by":"crossref","first-page":"743","DOI":"10.1161\/CIRCULATIONAHA.107.699579","volume":"117","author":"RB D\u2019Agostino","year":"2008","unstructured":"D\u2019Agostino, R.B., Vasan, R.S., Pencina, M.J., Wolf, P.A., Cobain, M., Massaro, J.M., Kannel, W.B.: General cardiovascular risk profile for use in primary care the Framingham heart study. Circulation 117(6), 743\u2013753 (2008)","journal-title":"Circulation"},{"unstructured":"http:\/\/www.framinghamheartstudy.org\/risk-functions\/cardiovascular-disease\/10-year-risk.php","key":"4_CR26"},{"issue":"3","key":"4_CR27","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1145\/321281.321282","volume":"12","author":"W Fraser","year":"1965","unstructured":"Fraser, W.: A survey of methods of computing minimax and near-minimax polynomial approximations for functions of a single independent variable. J. ACM (JACM) 12(3), 295\u2013314 (1965)","journal-title":"J. ACM (JACM)"},{"unstructured":"Gentry, C.: A fully homomorphic encryption scheme. PhD thesis, Stanford University (2009). https:\/\/crypto.stanford.edu\/craig\/","key":"4_CR28"},{"doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing-STOC 2009, pp. 169\u2013169. ACM Press (2009)","key":"4_CR29","DOI":"10.1145\/1536414.1536440"},{"unstructured":"Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. Cryptology ePrint Archive, Report 2012\/099 (2009). https:\/\/eprint.iacr.org\/2012\/099","key":"4_CR30"},{"key":"4_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1007\/978-3-642-32009-5_49","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"C Gentry","year":"2012","unstructured":"Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 850\u2013867. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_49"},{"unstructured":"Halevi, S., Shoup, V.: Design and implementation of a homomorphic-encryption library. IBM Research, Manuscript (2013)","key":"4_CR32"},{"key":"4_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1007\/978-3-662-44371-2_31","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"S Halevi","year":"2014","unstructured":"Halevi, S., Shoup, V.: Algorithms in HElib. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 554\u2013571. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-44371-2_31"},{"key":"4_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1007\/978-3-662-46800-5_25","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2015","author":"S Halevi","year":"2015","unstructured":"Halevi, S., Shoup, V.: Bootstrapping for HElib. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 641\u2013670. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-46800-5_25"},{"issue":"37","key":"4_CR35","first-page":"147","volume":"48","author":"M Kologlu","year":"2000","unstructured":"Kologlu, M., Elker, D., Altun, H., Sayek, I.: Validation of MPI and PIA II in two different groups of patients with secondary peritonitis. Hepatogastroenterology 48(37), 147\u2013151 (2000)","journal-title":"Hepatogastroenterology"},{"unstructured":"http:\/\/www.claudiaflowers.net\/rsch8140\/logistic_regression_example.htm","key":"4_CR36"},{"issue":"17","key":"4_CR37","doi-asserted-by":"crossref","first-page":"2992","DOI":"10.1016\/j.spl.2008.05.005","volume":"78","author":"L Mattner","year":"2008","unstructured":"Mattner, L., Roos, B.: Maximal probabilities of convolution powers of discrete uniform distributions. Stat. Probab. Lett. 78(17), 2992\u20132996 (2008)","journal-title":"Stat. Probab. Lett."},{"issue":"6","key":"4_CR38","first-page":"174","volume":"6","author":"EP Novodvorskii","year":"1951","unstructured":"Novodvorskii, E.P., Pinsker, I.S.: The process of equating maxima. Uspekhi Matematicheskikh Nauk 6(6), 174\u2013181 (1951)","journal-title":"Uspekhi Matematicheskikh Nauk"},{"key":"4_CR39","first-page":"337","volume":"199","author":"EY Remez","year":"1934","unstructured":"Remez, E.Y.: Sur le calcul effectif des polynomes d\u2019approximation de tschebyscheff. CR Acad. Sci. Paris 199, 337\u2013340 (1934)","journal-title":"CR Acad. Sci. Paris"},{"key":"4_CR40","volume-title":"Chebyshev Polynomials","author":"T-J Rivlin","year":"1990","unstructured":"Rivlin, T.-J.: Chebyshev Polynomials. Wiley, New York (1990)"},{"issue":"1","key":"4_CR41","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s10623-012-9720-4","volume":"71","author":"NP Smart","year":"2014","unstructured":"Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations. Des. Codes Crypt. 71(1), 57\u201381 (2014)","journal-title":"Des. Codes Crypt."},{"issue":"7","key":"4_CR42","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/0021-9681(67)90082-3","volume":"20","author":"J Truett","year":"1967","unstructured":"Truett, J., Cornfield, J., Kannel, W.: A multivariate analysis of the risk of coronary heart disease in Framingham. J. Chronic Dis. 20(7), 511\u2013524 (1967)","journal-title":"J. Chronic Dis."},{"issue":"11","key":"4_CR43","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.2337\/diacare.25.11.1999","volume":"25","author":"BP Tabaei","year":"2002","unstructured":"Tabaei, B.P., Herman, W.H.: A multivariate logistic regression equation to screen for diabetes development and validation. Diab. Care 25(11), 1999\u20132003 (2002)","journal-title":"Diab. Care"},{"doi-asserted-by":"publisher","unstructured":"Tolosie, K., Sharma, M.K.: Application of Cox proportional hazards model in case of tuberculosis patients in selected Addis Ababa health centres, Ethiopia. Tuberc. Res. Treat. 2014, 11 p. (2014). https:\/\/doi.org\/10.1155\/2014\/536976 . Article ID 536976","key":"4_CR44","DOI":"10.1155\/2014\/536976"},{"key":"4_CR45","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/978-3-642-13190-5_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"M Dijk van","year":"2010","unstructured":"van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24\u201343. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_2"},{"issue":"1","key":"4_CR46","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/BF01386215","volume":"2","author":"L Veidinger","year":"1960","unstructured":"Veidinger, L.: On the numerical determination of the best approximations in the Chebyshev sense. Numer. Math. 2(1), 99\u2013105 (1960)","journal-title":"Numer. Math."}],"container-title":["Lecture Notes in Computer Science","Financial Cryptography and Data Security"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-70278-0_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T19:29:39Z","timestamp":1719602979000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-70278-0_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319702773","9783319702780"],"references-count":46,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-70278-0_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}