{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:54:27Z","timestamp":1776768867314,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":15,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540602217","type":"print"},{"value":"9783540447504","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1995]]},"DOI":"10.1007\/3-540-44750-4_30","type":"book-chapter","created":{"date-parts":[[2007,8,16]],"date-time":"2007-08-16T08:39:53Z","timestamp":1187253593000},"page":"372-385","source":"Crossref","is-referenced-by-count":15,"title":["NFS with Four Large Primes: An Explosive Experiment"],"prefix":"10.1007","author":[{"given":"Bruce","family":"Dodson","sequence":"first","affiliation":[]},{"given":"Arjen K.","family":"Lenstra","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2001,7,13]]},"reference":[{"key":"30_CR1","unstructured":"D. Atkins, M. Graff, A.K. Lenstra, and P.C. Leyland, THE MAGIC WORDS ARE SQUEAMISH OSSIFRAGE, Asiacrypt\u201994, to appear."},{"key":"30_CR2","unstructured":"J. Buchmann, J. Loho, and J. Zayer, Triple-large-prime variation, manuscript, 1993."},{"key":"30_CR3","first-page":"159","volume":"773","author":"J. Buchmann","year":"1994","unstructured":"J. Buchmann, J. Loho, and J. Zayer, An implementation of the general number field sieve, Advances in Cryptology, Crypto\u201993, Lecture Notes in Comput. Sci. 773 (1994), 159\u2013165.","journal-title":"Sci."},{"key":"30_CR4","unstructured":"S. Contini and A. K. Lenstra, Implementations of blocked Lanczos and Wiedemann algorithms, in preparation."},{"key":"30_CR5","doi-asserted-by":"crossref","unstructured":"T. Denny, B. Dodson, A. K. Lenstra, and M. S. Manasse, On the factorization of RSA-120, Advances in Cryptology, Crypto\u201993, Lecture Notes in Comput. Sci. 773 (1994), 166\u2013174.","DOI":"10.1007\/3-540-48329-2_15"},{"key":"30_CR6","doi-asserted-by":"crossref","unstructured":"R. Golliver, A. K. Lenstra, and K. McCurley, Lattice sieving and trial division, ANTS\u201994, Lecture Notes in Comput. Sci. 877 (1994), 18\u201327.","DOI":"10.1007\/3-540-58691-1_38"},{"key":"30_CR7","doi-asserted-by":"crossref","unstructured":"B. A. LaMacchia and A. M. Odlyzko, Solving Large Sparse Linear Systems over Finite Fields, Advances in Cryptology, Crypto\u201990, Lecture Notes in Comput. Sci. 537 (1991), 109\u2013133.","DOI":"10.1007\/3-540-38424-3_8"},{"key":"30_CR8","series-title":"Lecture Notes in Math.","volume-title":"The development of the number field sieve","year":"1993","unstructured":"A. K. Lenstra and H. W. Lenstra, Jr. (eds), The development of the number field sieve, Lecture Notes in Math. 1554, Springer-Verlag, Berlin, 1993."},{"key":"30_CR9","doi-asserted-by":"publisher","first-page":"785","DOI":"10.2307\/2153299","volume":"63","author":"A. K. Lenstra","year":"1994","unstructured":"A. K. Lenstra and M. S. Manasse, Factoring with two large primes, Math. Comp 63 (1994), 785\u2013798.","journal-title":"Math. Comp"},{"key":"30_CR10","doi-asserted-by":"crossref","unstructured":"P. L. Montgomery, Square roots of products of algebraic numbers, Proceedings of Symposia in Applied Mathematics, Mathematics of Computation 1943\u20131993, Vancouver, 1993, Walter Gautschi, ed.","DOI":"10.1090\/psapm\/048\/1314892"},{"key":"30_CR11","doi-asserted-by":"crossref","unstructured":"P. L. Montgomery, A block Lanczos algorithm for finding dependencies over GF(2), Advances in Cryptology, Eurocrypt\u201995, Lecture Notes in Comput. Sci. 921 (1995), 106\u2013120.","DOI":"10.1007\/3-540-49264-X_9"},{"key":"30_CR12","doi-asserted-by":"crossref","unstructured":"A. M. Odlyzko, Discrete Logarithms in Finite Fields and their Cryptographic Significance, Advances in Cryptology, Eurocrypt\u201984, Lecture Notes in Comput. Sci. 209, 224\u2013314.","DOI":"10.1007\/3-540-39757-4_20"},{"key":"30_CR13","doi-asserted-by":"crossref","unstructured":"C. Pomerance, The quadratic sieve factoring algorithm, Advances in Cryptology, Eurocrypt\u201984, Springer, Lecture Notes in Comput. Sci. 209, 169\u2013182.","DOI":"10.1007\/3-540-39757-4_17"},{"key":"30_CR14","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1080\/10586458.1992.10504250","volume":"1","author":"C. Pomerance","year":"1992","unstructured":"C. Pomerance and J. W. Smith, Reduction of huge, sparse matrices over finite fields via created catastrophes, Experiment. Math. 1 (1992) 89\u201394.","journal-title":"Experiment. Math."},{"key":"30_CR15","doi-asserted-by":"publisher","first-page":"329","DOI":"10.2307\/2007894","volume":"48","author":"B. Silverman","year":"1987","unstructured":"B. Silverman, The multiple polynomial quadratic sieve, Math. Comp. 48 (1987), 329\u2013339.","journal-title":"Math. Comp."}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2014 CRYPT0\u2019 95"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-44750-4_30","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T04:18:36Z","timestamp":1556770716000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-44750-4_30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995]]},"ISBN":["9783540602217","9783540447504"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/3-540-44750-4_30","relation":{},"ISSN":["0302-9743"],"issn-type":[{"value":"0302-9743","type":"print"}],"subject":[],"published":{"date-parts":[[1995]]}}}