{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T01:40:05Z","timestamp":1745199605550,"version":"3.40.4"},"publisher-location":"Berlin, Heidelberg","reference-count":41,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642349607"},{"type":"electronic","value":"9783642349614"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-34961-4_29","type":"book-chapter","created":{"date-parts":[[2012,11,16]],"date-time":"2012-11-16T09:22:26Z","timestamp":1353057746000},"page":"467-484","source":"Crossref","is-referenced-by-count":9,"title":["ECM at Work"],"prefix":"10.1007","author":[{"given":"Joppe W.","family":"Bos","sequence":"first","affiliation":[]},{"given":"Thorsten","family":"Kleinjung","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"29_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/978-3-642-14712-8_4","volume-title":"Progress in Cryptology \u2013 LATINCRYPT 2010","author":"D.J. Bernstein","year":"2010","unstructured":"Bernstein, D.J., Birkner, P., Lange, T.: Starfish on Strike. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol.\u00a06212, pp. 61\u201380. Springer, Heidelberg (2010)"},{"key":"29_CR2","unstructured":"Bernstein, D.J., Birkner, P., Lange, T., Peters, C.: EECM: ECM using Edwards curves (2010), Software, http:\/\/eecm.cr.yp.to\/"},{"key":"29_CR3","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J., Birkner, P., Lange, T., Peters, C.: ECM using Edwards curves. Mathematics of Computation (to appear, 2012)","DOI":"10.1090\/S0025-5718-2012-02633-0"},{"key":"29_CR4","unstructured":"Bernstein, D.J., Chen, H.-C., Chen, M.-S., Cheng, C.-M., Hsiao, C.-H., Lange, T., Lin, Z.-C., Yang, B.-Y.: The billion-mulmod-per-second PC. In: Special-purpose Hardware for Attacking Cryptographic Systems, SHARCS 2009, pp. 131\u2013144 (2009)"},{"key":"29_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/978-3-642-01001-9_28","volume-title":"Advances in Cryptology - EUROCRYPT 2009","author":"D.J. Bernstein","year":"2009","unstructured":"Bernstein, D.J., Chen, T.-R., Cheng, C.-M., Lange, T., Yang, B.-Y.: ECM on Graphics Cards. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol.\u00a05479, pp. 483\u2013501. Springer, Heidelberg (2009)"},{"key":"29_CR6","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J., Lange, T.: Analysis and Optimization of Elliptic-Curve Single-Scalar Multiplication. In: Mullen, G.L., Panario, D., Shparlinski, I.E. (eds.) Finite Fields and Applications. Contemporary Mathematics Series, vol. 461, pp. 1\u201319. American Mathematical Society (2008)","DOI":"10.1090\/conm\/461\/08979"},{"key":"29_CR7","doi-asserted-by":"crossref","unstructured":"Bos, J.W., Kleinjung, T.: ECM at work, project page (2012), http:\/\/research.microsoft.com\/ecmatwork\/","DOI":"10.1007\/978-3-642-34961-4_29"},{"key":"29_CR8","doi-asserted-by":"crossref","unstructured":"Bos, J.W., Kleinjung, T., Lenstra, A.K., Montgomery, P.L.: Efficient SIMD arithmetic modulo a Mersenne number. In: IEEE Symposium on Computer Arithmetic, ARITH-20, pp. 213\u2013221. IEEE Computer Society (2011)","DOI":"10.1109\/ARITH.2011.37"},{"key":"29_CR9","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1090\/S0002-9904-1939-07068-7","volume":"45","author":"A. Brauer","year":"1939","unstructured":"Brauer, A.: On addition chains. Bulletin of the American Mathematical Society\u00a045, 736\u2013739 (1939)","journal-title":"Bulletin of the American Mathematical Society"},{"key":"29_CR10","first-page":"149","volume":"8","author":"R.P. Brent","year":"1986","unstructured":"Brent, R.P.: Some integer factorization algorithms using elliptic curves. Australian Computer Science Communications\u00a08, 149\u2013163 (1986)","journal-title":"Australian Computer Science Communications"},{"key":"29_CR11","doi-asserted-by":"crossref","unstructured":"de Meulenaer, G., Gosset, F., de Dormale, G.M., Quisquater, J.-J.: Integer factorization based on elliptic curve method: Towards better exploitation of reconfigurable hardware. In: Field-Programmable Custom Computing Machines, FCCM 2007, pp. 197\u2013206. IEEE Computer Society (2007)","DOI":"10.1109\/FCCM.2007.12"},{"key":"29_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/3-540-47555-9_16","volume-title":"Advances in Cryptology - EUROCRYPT \u201992","author":"B. Dixon","year":"1993","unstructured":"Dixon, B., Lenstra, A.K.: Massively Parallel Elliptic Curve Factoring. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol.\u00a0658, pp. 183\u2013193. Springer, Heidelberg (1993)"},{"key":"29_CR13","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1090\/S0273-0979-07-01153-6","volume":"44","author":"H.M. Edwards","year":"2007","unstructured":"Edwards, H.M.: A normal form for elliptic curves. Bulletin of the American Mathematical Society\u00a044, 393\u2013422 (2007)","journal-title":"Bulletin of the American Mathematical Society"},{"key":"29_CR14","unstructured":"Franke, J., Kleinjung, T.: GNFS for linux. Software (2012)"},{"key":"29_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1007\/978-3-540-24847-7_14","volume-title":"Algorithmic Number Theory","author":"J. Franke","year":"2004","unstructured":"Franke, J., Kleinjung, T., Morain, F., Wirth, T.: Proving the Primality of Very Large Numbers with fastECPP. In: Buell, D.A. (ed.) ANTS 2004. LNCS, vol.\u00a03076, pp. 194\u2013207. Springer, Heidelberg (2004)"},{"key":"29_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/11894063_10","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2006","author":"K. Gaj","year":"2006","unstructured":"Gaj, K., Kwon, S., Baier, P., Kohlbrenner, P., Le, H., Khaleeluddin, M., Bachimanchi, R.: Implementing the Elliptic Curve Method of Factoring in Reconfigurable Hardware. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol.\u00a04249, pp. 119\u2013133. Springer, Heidelberg (2006)"},{"key":"29_CR17","doi-asserted-by":"publisher","first-page":"1498","DOI":"10.1109\/TC.2008.80","volume":"57","author":"T. G\u00fcneysu","year":"2008","unstructured":"G\u00fcneysu, T., Kasper, T., Novotny, M., Paar, C., Rupp, A.: Cryptanalysis with COPACOBANA. IEEE Transactions on Computers\u00a057, 1498\u20131513 (2008)","journal-title":"IEEE Transactions on Computers"},{"key":"29_CR18","doi-asserted-by":"crossref","unstructured":"Guy, R.: Unsolved problems in number theory, 3rd edn., vol.\u00a01. Springer (2004)","DOI":"10.1007\/978-0-387-26677-0_1"},{"key":"29_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/978-3-540-89255-7_20","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"H. Hisil","year":"2008","unstructured":"Hisil, H., Wong, K.K.-H., Carter, G., Dawson, E.: Twisted Edwards Curves Revisited. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol.\u00a05350, pp. 326\u2013343. Springer, Heidelberg (2008)"},{"key":"29_CR20","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":"29_CR21","unstructured":"Kruppa, A.: A software implementation of ECM for NFS. Research Report RR-7041, INRIA (2009), http:\/\/hal.inria.fr\/inria-00419094\/PDF\/RR-7041.pdf"},{"key":"29_CR22","doi-asserted-by":"crossref","unstructured":"Lenstra, A.K., Lenstra Jr., H.W.: Algorithms in number theory. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science (vol. A: Algorithms and Complexity), pp. 673\u2013715. Elsevier and MIT Press (1990)","DOI":"10.1016\/B978-0-444-88071-0.50017-5"},{"key":"29_CR23","doi-asserted-by":"crossref","unstructured":"Lenstra, A.K., Lenstra Jr., H.W.: The Development of the Number Field Sieve. Lecture Notes in Mathematics, vol.\u00a01554. Springer (1993)","DOI":"10.1007\/BFb0091534"},{"issue":"3","key":"29_CR24","doi-asserted-by":"publisher","first-page":"649","DOI":"10.2307\/1971363","volume":"126","author":"H.W. Lenstra Jr.","year":"1987","unstructured":"Lenstra Jr., H.W.: Factoring integers with elliptic curves. Annals of Mathematics\u00a0126(3), 649\u2013673 (1987)","journal-title":"Annals of Mathematics"},{"key":"29_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1007\/978-3-642-05445-7_11","volume-title":"Selected Areas in Cryptography","author":"D. Loebenberger","year":"2009","unstructured":"Loebenberger, D., Putzka, J.: Optimization Strategies for Hardware-Based Cofactorization. In: Jacobson Jr., M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol.\u00a05867, pp. 170\u2013181. Springer, Heidelberg (2009)"},{"issue":"177","key":"29_CR26","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1090\/S0025-5718-1987-0866113-7","volume":"48","author":"P.L. Montgomery","year":"1987","unstructured":"Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation\u00a048(177), 243\u2013264 (1987)","journal-title":"Mathematics of Computation"},{"key":"29_CR27","unstructured":"Montgomery, P.L.: An FFT extension of the elliptic curve method of factorization. PhD thesis, University of California (1992)"},{"key":"29_CR28","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1051\/ita\/1990240605311","volume":"24","author":"F. Morain","year":"1990","unstructured":"Morain, F., Olivos, J.: Speeding up the computations on an elliptic curve using addition-subtraction chains. Informatique Th\u00e9orique et Applications\/Theoretical Informatics and Applications\u00a024, 531\u2013544 (1990)","journal-title":"Informatique Th\u00e9orique et Applications\/Theoretical Informatics and Applications"},{"key":"29_CR29","unstructured":"NVIDIA. NVIDIA\u2019s next generation CUDA compute architecture: Fermi (2009)"},{"key":"29_CR30","unstructured":"NVIDIA. NVIDIA CUDA Programming Guide 3.2 (2010)"},{"issue":"2","key":"29_CR31","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1016\/0377-2217(95)00015-I","volume":"83","author":"D. Pisinger","year":"1995","unstructured":"Pisinger, D.: A minimal algorithm for the multiple-choice knapsack problem. European Journal of Operational Research\u00a083(2), 394\u2013410 (1995)","journal-title":"European Journal of Operational Research"},{"key":"29_CR32","doi-asserted-by":"crossref","unstructured":"Pollard, J.M.: The lattice sieve. In: [23], pp. 43\u201349","DOI":"10.1007\/BFb0091538"},{"key":"29_CR33","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1017\/S0305004100049252","volume":"76","author":"J.M. Pollard","year":"1974","unstructured":"Pollard, J.M.: Theorems on factorization and primality testing. Proceedings of the Cambridge Philosophical Society\u00a076, 521\u2013528 (1974)","journal-title":"Proceedings of the Cambridge Philosophical Society"},{"key":"29_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/3-540-39757-4_17","volume-title":"Advances in Cryptology","author":"C. Pomerance","year":"1985","unstructured":"Pomerance, C.: The Quadratic Sieve Factoring Algorithm. In: Beth, T., Cot, N., Ingemarsson, I. (eds.) EUROCRYPT 1984. LNCS, vol.\u00a0209, pp. 169\u2013182. Springer, Heidelberg (1985)"},{"key":"29_CR35","first-page":"41","volume":"47","author":"A. Scholz","year":"1937","unstructured":"Scholz, A.: Aufgabe 253. Jahresbericht der deutschen Mathematiker-Vereingung\u00a047, 41\u201342 (1937)","journal-title":"Jahresbericht der deutschen Mathematiker-Vereingung"},{"key":"29_CR36","doi-asserted-by":"crossref","unstructured":"Silverman, J.H.: The Arithmetic of Elliptic Curves. Gradute Texts in Mathematics, vol.\u00a0106. Springer (1986)","DOI":"10.1007\/978-1-4757-1920-8"},{"key":"29_CR37","doi-asserted-by":"crossref","unstructured":"\u0160imka, M., Pelzl, J., Kleinjung, T., Franke, J., Priplata, C., Stahlke, C., Drutarovsk\u00fd, M., Fischer, V.: Hardware factorization based on elliptic curve method. In: Field-Programmable Custom Computing Machines, FCCM 2005, pp. 107\u2013116. IEEE Computer Society (2005)","DOI":"10.1109\/FCCM.2005.40"},{"key":"29_CR38","doi-asserted-by":"publisher","first-page":"907","DOI":"10.1215\/S0012-7094-73-04085-4","volume":"40","author":"E.G. Thurber","year":"1973","unstructured":"Thurber, E.G.: On addition chains l(mn)\u2009\u2264\u2009l(n)\u2009\u2212\u2009b and lower bounds for c(r). Duke Mathematical Journal\u00a040, 907\u2013913 (1973)","journal-title":"Duke Mathematical Journal"},{"key":"29_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1007\/11792086_37","volume-title":"Algorithmic Number Theory","author":"P. Zimmermann","year":"2006","unstructured":"Zimmermann, P., Dodson, B.: 20 Years of ECM. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol.\u00a04076, pp. 525\u2013542. Springer, Heidelberg (2006)"},{"key":"29_CR40","doi-asserted-by":"crossref","unstructured":"Zimmermann, R., G\u00fcneysu, T., Paar, C.: High-performance integer factoring with reconfigurable devices. In: Field Programmable Logic and Applications, FPL 2010, pp. 83\u201388. IEEE (2010)","DOI":"10.1109\/FPL.2010.26"},{"key":"29_CR41","unstructured":"Zimmermann, P., et al.: GMP-ECM (elliptic curve method for integer factorization) (2012), Software, https:\/\/gforge.inria.fr\/projects\/ecm\/"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2012"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-34961-4_29.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T01:09:07Z","timestamp":1745197747000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-34961-4_29"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642349607","9783642349614"],"references-count":41,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-34961-4_29","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2012]]}}}