{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T11:30:18Z","timestamp":1774611018399,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":25,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642420009","type":"print"},{"value":"9783642420016","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-42001-6_6","type":"book-chapter","created":{"date-parts":[[2013,11,20]],"date-time":"2013-11-20T23:25:02Z","timestamp":1384989902000},"page":"73-93","source":"Crossref","is-referenced-by-count":4,"title":["Factoring Integers by CVP Algorithms"],"prefix":"10.1007","author":[{"given":"Claus Peter","family":"Schnorr","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"6_CR1","unstructured":"Adleman, L.A.: Factoring and lattice reduction. Manuscript (1995)"},{"issue":"1","key":"6_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02579403","volume":"6","author":"L. Babai","year":"1986","unstructured":"Babai, L.: On Lov\u00e1sz lattice reduction and the nearest lattice point problem. Combinatorica\u00a06 (1), 1\u201313 (1986)","journal-title":"Combinatorica"},{"key":"6_CR3","doi-asserted-by":"crossref","unstructured":"Buchmann, J., Ludwig, C.: Practical lattice basis sampling reduction. eprint.iacr.org, TR 072 (2005)","DOI":"10.1007\/11792086_17"},{"key":"6_CR4","unstructured":"Charlet, M.: Faktorisierung ganzer Zahlen mit dem NEW ENUM-Gitteralgorithmus. Diplomarbeit, Frankfurt (2013)"},{"key":"6_CR5","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1090\/S0025-5718-1985-0777278-8","volume":"44","author":"U. Fincke","year":"1985","unstructured":"Fincke, U., Pohst, M.: Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math. of Comput.\u00a044, 463\u2013471 (1985)","journal-title":"Math. of Comput."},{"key":"6_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/978-3-540-78967-3_3","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2008","author":"N. Gama","year":"2008","unstructured":"Gama, N., Nguyen, P.Q.: Predicting lattice reduction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol.\u00a04965, pp. 31\u201351. Springer, Heidelberg (2008)"},{"key":"6_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/978-3-642-13190-5_13","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"N. Gama","year":"2010","unstructured":"Gama, N., Nguyen, P.Q., Regev, O.: Lattice enumeration using extreme pruning. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol.\u00a06110, pp. 257\u2013278. Springer, Heidelberg (2010)"},{"key":"6_CR8","first-page":"267","volume":"44","author":"A. Granville","year":"2008","unstructured":"Granville, A.: Smooth numbers: computational number theory and beyond. Algorithmic Number Theory\u00a044, 267\u2013323 (2008)","journal-title":"Algorithmic Number Theory"},{"key":"6_CR9","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1112\/S0025579300012481","volume":"31","author":"A. Hildebrand","year":"1984","unstructured":"Hildebrand, A.: Integers free of large prime factors and the Riemann hypothesis. Mathematika\u00a031, 258\u2013271 (1984)","journal-title":"Mathematika"},{"key":"6_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/978-3-642-01957-9_27","volume-title":"Applied Cryptography and Network Security","author":"P.S. Hirschhorn","year":"2009","unstructured":"Hirschhorn, P.S., Hoffstein, J., Howgrave-Graham, N., Whyte, W.: Choosing NTRUEncrypt parameters in light of combined lattice reduction and MITM approaches. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol.\u00a05536, pp. 437\u2013455. Springer, Heidelberg (2009)"},{"key":"6_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/978-3-540-74143-5_9","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"N. Howgrave-Graham","year":"2007","unstructured":"Howgrave-Graham, N.: A hybrid lattice\u2013reduction and meet-in-the-middle attiack against NTRU. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol.\u00a04622, pp. 150\u2013169. Springer, Heidelberg (2007)"},{"key":"6_CR12","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1287\/moor.12.3.415","volume":"12","author":"R. Kannan","year":"1987","unstructured":"Kannan, R.: Minkowski\u2019s convex body theorem and integer programming. Math. Oper. Res.\u00a012, 415\u2013440 (1987)","journal-title":"Math. Oper. Res."},{"key":"6_CR13","unstructured":"Lange, B.: Neue Schranken f\u00fcr SVP-Approximation und SVP-Algorithmen. Dissertation, Frankfurt (2013)"},{"key":"6_CR14","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"H.W. Lenstra Jr.","year":"1982","unstructured":"Lenstra Jr., H.W., Lenstra, A.K., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Mathematische Annalen\u00a0261, 515\u2013534 (1982)","journal-title":"Mathematische Annalen"},{"key":"6_CR15","doi-asserted-by":"crossref","unstructured":"lOV\u00e1sz, L.: An Algorithmic Theory of Numbers, Graphs and Convexity. SIAM (1986)","DOI":"10.1137\/1.9781611970203"},{"key":"6_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0897-7","volume-title":"Complexity of Lattice Problems: A Cryptographic Perspective","author":"D. Micciancio","year":"2002","unstructured":"Micciancio, D., Goldwasser, S.: Complexity of Lattice Problems: A Cryptographic Perspective. Kluwer Academic Publishers, Boston (2002)"},{"key":"6_CR17","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Voulgaris, P.: Faster exponential time algorithms for the shortest vector problem. ECCC Report No. 65 (2009)","DOI":"10.1137\/1.9781611973075.119"},{"key":"6_CR18","doi-asserted-by":"crossref","unstructured":"Nguyen, P.Q.: Hermite\u2019s Constant and Lattice Algorithms. In: Nguyen, P.Q., Vall\u00e9e, B. (eds.) The LLL Algorithm. Springer (January 2010)","DOI":"10.1007\/978-3-642-02295-1_2"},{"key":"6_CR19","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/0304-3975(87)90064-8","volume":"53","author":"C.P. Schnorr","year":"1987","unstructured":"Schnorr, C.P.: A hierarchy of polynomial time lattice basis reduction algorithms. Theoret. Comput. Sci.\u00a053, 201\u2013224 (1987)","journal-title":"Theoret. Comput. Sci."},{"key":"6_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/3-540-46416-6_24","volume-title":"Advances in Cryptology - EUROCRYPT \u201991","author":"C.-P. Schnorr","year":"1991","unstructured":"Schnorr, C.-P.: Factoring integers and computing discrete logarithms via Diophantine approximation. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol.\u00a0547, pp. 281\u2013293. Springer, Heidelberg (1991)"},{"key":"6_CR21","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/BF01581144","volume":"66","author":"C.P. Schnorr","year":"1994","unstructured":"Schnorr, C.P., Euchner, M.: Lattce basis reduction: Improved practical algorithms and solving subset sum problems. Mathematical Programming\u00a066, 181\u2013199 (1994), \n                    \n                      http:\/\/www.mi.informatik.uni-frankfurt.de\/","journal-title":"Mathematical Programming"},{"key":"6_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-49264-X_1","volume-title":"Advances in Cryptology - EUROCRYPT \u201995","author":"C.-P. Schnorr","year":"1995","unstructured":"Schnorr, C.-P., H\u00f6rner, H.H.: Attacking the Chor\u2013Rivest cryptosystem by improved lattice reduction. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol.\u00a0921, pp. 1\u201312. Springer, Heidelberg (1995)"},{"key":"6_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/3-540-36494-3_14","volume-title":"STACS 2003","author":"C.P. Schnorr","year":"2003","unstructured":"Schnorr, C.P.: Lattice reduction by sampling and birthday methods. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol.\u00a02607, pp. 145\u2013156. Springer, Heidelberg (2003), \n                    \n                      www.mi.informatik.uni-frankfurt.de"},{"key":"6_CR24","unstructured":"Schnorr, C.P.: Progress on LLL and lattice reduction. In: Phong, P.Q., Vall\u00e9e, B. (eds.) Proceedings LLL+25, Caen, France, June 29-July 1. The LLL Algorithm (2007), \n                    \n                      www.mi.informatik.uni-frankfurt.de\/"},{"key":"6_CR25","unstructured":"Schnorr, C.P.: Average Time Fast SVP and CVP Algorithms for Low Density Lattices and the Factorisation of Integers (2010), \n                    \n                      www.mi.informatik.uni-frankfurt.de"}],"container-title":["Lecture Notes in Computer Science","\u2018"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-42001-6_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T08:36:28Z","timestamp":1558686988000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-42001-6_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642420009","9783642420016"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-42001-6_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}