{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T23:27:22Z","timestamp":1725578842387},"publisher-location":"Berlin, Heidelberg","reference-count":13,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642193781"},{"type":"electronic","value":"9783642193798"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-19379-8_9","type":"book-chapter","created":{"date-parts":[[2011,3,1]],"date-time":"2011-03-01T17:29:44Z","timestamp":1299000584000},"page":"147-155","source":"Crossref","is-referenced-by-count":14,"title":["Cryptanalysis of the RSA Subgroup Assumption from TCC 2005"],"prefix":"10.1007","author":[{"given":"Jean-S\u00e9bastien","family":"Coron","sequence":"first","affiliation":[]},{"given":"Antoine","family":"Joux","sequence":"additional","affiliation":[]},{"given":"Avradip","family":"Mandal","sequence":"additional","affiliation":[]},{"given":"David","family":"Naccache","sequence":"additional","affiliation":[]},{"given":"Mehdi","family":"Tibouchi","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"9_CR1","series-title":"MSRI Publications","first-page":"325","volume-title":"Algorithmic number theory: lattices, number fields, curves and cryptography","author":"D.J. Bernstein","year":"2008","unstructured":"Bernstein, D.J.: Fast multiplication and its applications. In: Algorithmic number theory: lattices, number fields, curves and cryptography. MSRI Publications, vol.\u00a044, pp. 325\u2013384. Cambridge University Press, Cambridge (2008)"},{"key":"9_CR2","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1109\/TAU.1970.1162132","volume":"18","author":"L.I. Bluestein","year":"1970","unstructured":"Bluestein, L.I.: A linear filtering approach to the computation of the discrete Fourier transform. IEEE Trans. Electroacoustics\u00a018, 451\u2013455 (1970)","journal-title":"IEEE Trans. Electroacoustics"},{"key":"9_CR3","unstructured":"Bostan, A.: Algorithmique efficace pour des op\u00e9rations de base en calcul formel, Ph.D. thesis, \u00c9cole polytechnique (2003) (in English)"},{"issue":"4","key":"9_CR4","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1016\/j.jco.2004.09.009","volume":"21","author":"A. Bostan","year":"2005","unstructured":"Bostan, A., Schost, E.: Polynomial evaluation and interpolation on special sets of points. Journal of Complexity\u00a021(4), 420\u2013446 (2005)","journal-title":"Journal of Complexity"},{"key":"9_CR5","doi-asserted-by":"crossref","unstructured":"Coron, J.-S., Joux, A., Mandal, A., Naccache, D., Tibouchi, M.: Cryptanalysis of the RSA subgroup assumption from TCC 2005, Cryptology ePrint Archive, Report 2010\/650 (2005), \n \n http:\/\/eprint.iacr.org\/\n \n \n , Full version of this paper","DOI":"10.1007\/978-3-642-19379-8_9"},{"key":"9_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/978-3-540-73458-1_30","volume-title":"Information Security and Privacy","author":"I.B. Damg\u00e5rd","year":"2007","unstructured":"Damg\u00e5rd, I.B., Geisler, M., Kr\u00f8igaard, M.: Efficient and Secure Comparison for On-Line Auctions. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP 2007. LNCS, vol.\u00a04586, pp. 416\u2013430. Springer, Heidelberg (2007)"},{"key":"9_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/978-3-540-30576-7_4","volume-title":"Theory of Cryptography","author":"J. Groth","year":"2005","unstructured":"Groth, J.: Cryptography in Subgroups of \n $Z_n^*$\n . In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378, pp. 50\u201365. Springer, Heidelberg (2005)"},{"key":"9_CR8","first-page":"415","volume-title":"Applicable Algebra in Engineering, Communication and Computing","author":"G. Hanrot","year":"2004","unstructured":"Hanrot, G., Quercia, M., Zimmermann, P.: The middle product algorithm, I. In: Applicable Algebra in Engineering, Communication and Computing, vol.\u00a014, pp. 415\u2013438. Springer, Heidelberg (2004)"},{"key":"9_CR9","unstructured":"Hart, W.B., Harvey, D., et al.: Fast library for number theory, \n \n http:\/\/www.flintlib.org"},{"key":"9_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/978-3-642-14623-7_18","volume-title":"Advances in Cryptology \u2013 CRYPTO 2010","author":"T. Kleinjung","year":"2010","unstructured":"Kleinjung, T., Aoki, K., Franke, J., Lenstra, A.K., Thom\u00e9, E., Bos, J.W., Gaudry, P., Kruppa, A., Montgomery, P.L., Osvik, D.A., te Riele, H., Timofeev, A., Zimmermann, P.: Factorization of a 768-Bit RSA Modulus. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol.\u00a06223, pp. 333\u2013350. Springer, Heidelberg (2010)"},{"key":"9_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/978-3-540-48000-6_14","volume-title":"Advances in Cryptology - ASIACRYPT\u201999","author":"P. Paillier","year":"1999","unstructured":"Paillier, P., Pointcheval, D.: Efficient Public-Key Cryptosystems Provably Secure Against Active Adversaries. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol.\u00a01716, pp. 165\u2013179. Springer, Heidelberg (1999)"},{"key":"9_CR12","doi-asserted-by":"crossref","first-page":"1249","DOI":"10.1002\/j.1538-7305.1969.tb04268.x","volume":"48","author":"L.R. Rabiner","year":"1969","unstructured":"Rabiner, L.R., Schafer, R.W., Rader, C.M.: The chirp z-transform algorithm and its applications. Bell System Tech. J.\u00a048, 1249\u20131292 (1969)","journal-title":"Bell System Tech. J."},{"key":"9_CR13","unstructured":"Sage Library, \n \n http:\/\/www.sagemath.org\/"}],"container-title":["Lecture Notes in Computer Science","Public Key Cryptography \u2013 PKC 2011"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-19379-8_9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T02:46:48Z","timestamp":1606186008000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-19379-8_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642193781","9783642193798"],"references-count":13,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-19379-8_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}