{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:34:47Z","timestamp":1759638887884,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642546303"},{"type":"electronic","value":"9783642546310"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-642-54631-0_11","type":"book-chapter","created":{"date-parts":[[2014,2,20]],"date-time":"2014-02-20T05:04:17Z","timestamp":1392872657000},"page":"185-202","source":"Crossref","is-referenced-by-count":16,"title":["Rounding and Chaining LLL: Finding Faster Small Roots of Univariate Polynomial Congruences"],"prefix":"10.1007","author":[{"given":"Jingguo","family":"Bi","sequence":"first","affiliation":[]},{"given":"Jean-S\u00e9bastien","family":"Coron","sequence":"additional","affiliation":[]},{"given":"Jean-Charles","family":"Faug\u00e8re","sequence":"additional","affiliation":[]},{"given":"Phong Q.","family":"Nguyen","sequence":"additional","affiliation":[]},{"given":"Gu\u00e9na\u00ebl","family":"Renault","sequence":"additional","affiliation":[]},{"given":"Rina","family":"Zeitoun","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"4","key":"11_CR1","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1109\/18.850673","volume":"46","author":"D. Boneh","year":"2000","unstructured":"Boneh, D., Durfee, G.: Cryptanalysis of RSA with private key d less than N0.292. IEEE Transactions on Information Theory\u00a046(4), 1339 (2000)","journal-title":"IEEE Transactions on Information Theory"},{"key":"11_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1007\/3-540-58691-1_54","volume-title":"Algorithmic Number Theory","author":"J. Buchmann","year":"1994","unstructured":"Buchmann, J.: Reducing lattice bases by means of approximations. In: Huang, M.-D.A., Adleman, L.M. (eds.) ANTS 1994. LNCS, vol.\u00a0877, pp. 160\u2013168. Springer, Heidelberg (1994)"},{"key":"11_CR3","unstructured":"Cad\u00e9, D., Pujol, X., Stehl\u00e9, D.: FPLLL library, version 3.0 (September 2008), \n                    \n                      http:\/\/perso.ens-lyon.fr\/damien.stehle"},{"key":"11_CR4","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-02945-9","volume-title":"A course in computational algebraic number theory","author":"H. Cohen","year":"1993","unstructured":"Cohen, H.: A course in computational algebraic number theory. Graduate Texts in Mathematics, vol.\u00a0138. Springer, Berlin (1993)"},{"key":"11_CR5","unstructured":"Cohn, H., Heninger, N.: Approximate common divisors via lattices. IACR Cryptology ePrint Archive\u00a02011:437 (2011)"},{"key":"11_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1007\/3-540-68339-9_16","volume-title":"Advances in Cryptology - EUROCRYPT \u201996","author":"D. Coppersmith","year":"1996","unstructured":"Coppersmith, D.: Finding a small root of a bivariate integer equation; factoring with high bits known. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol.\u00a01070, pp. 178\u2013189. Springer, Heidelberg (1996)"},{"key":"11_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/3-540-68339-9_14","volume-title":"Advances in Cryptology - EUROCRYPT \u201996","author":"D. Coppersmith","year":"1996","unstructured":"Coppersmith, D.: Finding a small root of a univariate modular equation. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol.\u00a01070, pp. 155\u2013165. Springer, Heidelberg (1996)"},{"issue":"4","key":"11_CR8","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1007\/s001459900030","volume":"10","author":"D. Coppersmith","year":"1997","unstructured":"Coppersmith, D.: Small solutions to polynomial equations, and low exponent RSA vulnerabilities. J. Cryptology\u00a010(4), 233\u2013260 (1997); Journal version [7,6]","journal-title":"J. Cryptology"},{"key":"11_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/978-3-540-74143-5_21","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"J.-S. Coron","year":"2007","unstructured":"Coron, J.-S.: Finding small roots of bivariate integer polynomial equations: A direct approach. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol.\u00a04622, pp. 379\u2013394. Springer, Heidelberg (2007)"},{"key":"11_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1007\/3-540-49162-7_16","volume-title":"Public Key Cryptography","author":"C. Coup\u00e9","year":"1999","unstructured":"Coup\u00e9, C., Nguy\u00ean, P.Q., Stern, J.: The effectiveness of lattice attacks against low-exponent RSA. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol.\u00a01560, pp. 204\u2013218. Springer, Heidelberg (1999)"},{"issue":"1","key":"11_CR11","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/0304-3975(94)90071-X","volume":"123","author":"H. Daud\u00e9","year":"1994","unstructured":"Daud\u00e9, H., Vall\u00e9e, B.: An upper bound on the average number of iterations of the lll algorithm. Theor. Comput. Sci.\u00a0123(1), 95\u2013115 (1994)","journal-title":"Theor. Comput. Sci."},{"key":"11_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/BFb0024458","volume-title":"Cryptography and Coding","author":"N. Howgrave-Graham","year":"1997","unstructured":"Howgrave-Graham, N.: Finding small roots of univariate modular equations revisited. In: Darnell, M.J. (ed.) Cryptography and Coding 1997. LNCS, vol.\u00a01355, pp. 131\u2013142. Springer, Heidelberg (1997)"},{"key":"11_CR13","first-page":"513","volume":"261","author":"A.K. Lenstra","year":"1982","unstructured":"Lenstra, A.K., Lenstra Jr., H.W., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Mathematische Ann.\u00a0261, 513\u2013534 (1982)","journal-title":"Mathematische Ann."},{"key":"11_CR14","doi-asserted-by":"crossref","unstructured":"May, A.: Using LLL-reduction for solving RSA and factorization problems: A survey. In: [19] (2010)","DOI":"10.1007\/978-3-642-02295-1_10"},{"issue":"5","key":"11_CR15","doi-asserted-by":"publisher","first-page":"1224","DOI":"10.1109\/TCOMM.2011.022811.090576","volume":"59","author":"H. Najafi","year":"2011","unstructured":"Najafi, H., Jafari, M., Damen, M.-O.: On adaptive lattice reduction over correlated fading channels. IEEE Transactions on Communications\u00a059(5), 1224\u20131227 (2011)","journal-title":"IEEE Transactions on Communications"},{"key":"11_CR16","doi-asserted-by":"crossref","unstructured":"Nguyen, P.Q.: Public-key cryptanalysis. In: Luengo, I. (ed.) Recent Trends in Cryptography. Contemporary Mathematics, vol.\u00a0477. AMS\u2013RSME (2009)","DOI":"10.1090\/conm\/477\/09304"},{"key":"11_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/11792086_18","volume-title":"Algorithmic Number Theory","author":"P.Q. Nguy\u00ean","year":"2006","unstructured":"Nguy\u00ean, P.Q., Stehl\u00e9, D.: LLL on the average. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol.\u00a04076, pp. 238\u2013256. Springer, Heidelberg (2006)"},{"issue":"3","key":"11_CR18","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1137\/070705702","volume":"39","author":"P.Q. Nguyen","year":"2009","unstructured":"Nguyen, P.Q., Stehl\u00e9, D.: An LLL algorithm with quadratic complexity. SIAM J. of Computing\u00a039(3), 874\u2013903 (2009)","journal-title":"SIAM J. of Computing"},{"key":"11_CR19","doi-asserted-by":"crossref","unstructured":"Nguyen, P.Q., Vall\u00e9e, B. (eds.): The LLL Algorithm: Survey and Applications. Information Security and Cryptography. Springer (2010)","DOI":"10.1007\/978-3-642-02295-1"},{"key":"11_CR20","doi-asserted-by":"crossref","unstructured":"Novocin, A., Stehl\u00e9, D., Villard, G.: An LLL-reduction algorithm with quasi-linear time complexity: extended abstract. In: Proc. STOC 2011, pp. 403\u2013412. ACM (2011)","DOI":"10.1145\/1993636.1993691"},{"key":"11_CR21","unstructured":"Shoup, V.: Number Theory C++ Library (NTL) version 5.4.1, \n                    \n                      http:\/\/www.shoup.net\/ntl\/"},{"issue":"4","key":"11_CR22","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s00145-002-0133-9","volume":"15","author":"V. Shoup","year":"2002","unstructured":"Shoup, V.: OAEP reconsidered. J. Cryptology\u00a015(4), 223\u2013249 (2002)","journal-title":"J. Cryptology"}],"container-title":["Lecture Notes in Computer Science","Public-Key Cryptography \u2013 PKC 2014"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-54631-0_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T04:45:08Z","timestamp":1558845908000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-54631-0_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783642546303","9783642546310"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-54631-0_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}