{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T18:23:26Z","timestamp":1742927006372,"version":"3.40.3"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031459320"},{"type":"electronic","value":"9783031459337"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-45933-7_7","type":"book-chapter","created":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T09:02:37Z","timestamp":1700470957000},"page":"115-126","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implementation of\u00a0the\u00a0Elliptic Curve Method"],"prefix":"10.1007","author":[{"given":"Xiuxiu","family":"Li","sequence":"first","affiliation":[]},{"given":"Wei","family":"Yu","sequence":"additional","affiliation":[]},{"given":"Kunpeng","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,11,21]]},"reference":[{"key":"7_CR1","doi-asserted-by":"publisher","unstructured":"Barbulescu, R., Bos, J.W., Bouvier, C., Kleinjung, T., Montgomery, P.: Finding ECM-friendly curves through a study of Galois properties. In: ANTS X: Proceedings of the Tenth Algorithmic Number Theory Symposium. Open Book Series, vol. 1, pp. 63\u201386 (2013). https:\/\/doi.org\/10.2140\/obs.2013.1.63","DOI":"10.2140\/obs.2013.1.63"},{"key":"7_CR2","doi-asserted-by":"publisher","first-page":"1139","DOI":"10.1090\/S0025-5718-2012-02633-0","volume":"82","author":"DJ Bernstein","year":"2013","unstructured":"Bernstein, D.J., Birkner, P., Lange, T., Peters, C.: ECM using Edwards curves. Math. Comput. 82, 1139\u20131179 (2013)","journal-title":"Math. Comput."},{"key":"7_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/978-3-319-22174-8_15","volume-title":"Progress in Cryptology \u2013 LATINCRYPT 2015","author":"DJ Bernstein","year":"2015","unstructured":"Bernstein, D.J., Chuengsatiansup, C., Kohel, D., Lange, T.: Twisted hessian curves. In: Lauter, K., Rodr\u00edguez-Henr\u00edquez, F. (eds.) LATINCRYPT 2015. LNCS, vol. 9230, pp. 269\u2013294. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-22174-8_15"},{"key":"7_CR4","unstructured":"Bernstein, D.J., Chuengsatiansup, C., Lange, T.: Double-base scalar multiplication revisited. Cryptology ePrint Archive, Report 2017\/037 (2017). https:\/\/eprint.iacr.org\/2017\/037"},{"key":"7_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/978-3-642-34961-4_29","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2012","author":"JW Bos","year":"2012","unstructured":"Bos, J.W., Kleinjung, T.: ECM at work. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 467\u2013484. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-34961-4_29"},{"key":"7_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/978-3-030-56880-1_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2020","author":"F Boudot","year":"2020","unstructured":"Boudot, F., Gaudry, P., Guillevic, A., Heninger, N., Thom\u00e9, E., Zimmermann, P.: Comparing the difficulty of factorization and discrete logarithm: a 240-digit experiment. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 62\u201391. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-56880-1_3"},{"key":"7_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"483","DOI":"10.1007\/978-3-030-45388-6_17","volume-title":"Public-Key Cryptography \u2013 PKC 2020","author":"C Bouvier","year":"2020","unstructured":"Bouvier, C., Imbert, L.: Faster cofactorization with ECM using\u00a0mixed representations. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 483\u2013504. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45388-6_17"},{"key":"7_CR8","first-page":"149","volume":"8","author":"RP Brent","year":"1986","unstructured":"Brent, R.P.: Some integer factorization algorithms using elliptic curves. Austral. Comput. Sci. Comm. 8, 149\u2013163 (1986)","journal-title":"Austral. Comput. Sci. Comm."},{"key":"7_CR9","unstructured":"The CADO-NFS Development Team: CADO-NFS, An Implementation of the Number Field Sieve Algorithm (2017). http:\/\/cado-nfs.gforge.inria.fr\/. Release 2.3.0"},{"issue":"3","key":"7_CR10","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1007\/s13389-017-0157-6","volume":"8","author":"C Costello","year":"2017","unstructured":"Costello, C., Smith, B.: Montgomery curves and their arithmetic: the case of large characteristic fields. J. Cryptogr. Eng. 8(3), 227\u2013240 (2017)","journal-title":"J. Cryptogr. Eng."},{"key":"7_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/11593447_4","volume-title":"Advances in Cryptology - ASIACRYPT 2005","author":"V Dimitrov","year":"2005","unstructured":"Dimitrov, V., Imbert, L., Mishra, P.K.: Efficient and secure elliptic curve point multiplication using double-base chains. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 59\u201378. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11593447_4"},{"key":"7_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 \u2014 EUROCRYPT\u2019 92","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. 658, pp. 183\u2013193. Springer, Heidelberg (1993). https:\/\/doi.org\/10.1007\/3-540-47555-9_16"},{"key":"7_CR13","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1090\/S0273-0979-07-01153-6","volume":"44","author":"HM Edwards","year":"2007","unstructured":"Edwards, H.M.: A normal form for elliptic curves. Bull. Am. Math. Soc. 44, 393\u2013422 (2007)","journal-title":"Bull. Am. Math. Soc."},{"key":"7_CR14","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. 5350, pp. 326\u2013343. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-89255-7_20"},{"key":"7_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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., et al.: Factorization of a 768-bit RSA modulus. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 333\u2013350. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-14623-7_18"},{"issue":"3","key":"7_CR16","doi-asserted-by":"publisher","first-page":"649","DOI":"10.2307\/1971363","volume":"126","author":"HW Lenstra","year":"1987","unstructured":"Lenstra, H.W.: Factoring integers with elliptic curves. Ann. Math. 126(3), 649\u2013673 (1987)","journal-title":"Ann. Math."},{"issue":"8","key":"7_CR17","doi-asserted-by":"publisher","first-page":"2204","DOI":"10.1109\/TC.2014.2360539","volume":"64","author":"N Meloni","year":"2015","unstructured":"Meloni, N., Hasan, M.: Efficient double bases for scalar multiplication. IEEE Trans. Comput. 64(8), 2204\u20132212 (2015)","journal-title":"IEEE Trans. Comput."},{"key":"7_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1007\/978-3-642-04138-9_22","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2009","author":"N M\u00e9loni","year":"2009","unstructured":"M\u00e9loni, N., Hasan, M.A.: Elliptic curve scalar multiplication combining Yao\u2019s algorithm and double bases. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 304\u2013316. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-04138-9_22"},{"issue":"177","key":"7_CR19","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1090\/S0025-5718-1987-0866113-7","volume":"48","author":"PL Montgomery","year":"1987","unstructured":"Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Math. Comput. 48(177), 243\u2013264 (1987)","journal-title":"Math. Comput."},{"key":"7_CR20","unstructured":"Montgomery, P.L.: Evaluating recurrences of form Xm + n = f(Xm, Xn, Xm $$-$$ n) via Lucas chains. (1983). Unpublished"},{"key":"7_CR21","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1017\/S0305004100049252","volume":"76","author":"JM Pollard","year":"1974","unstructured":"Pollard, J.M.: Theorems on factorization and primality testing. Proc. Camb. Philos. Soc. 76, 521\u2013528 (1974)","journal-title":"Proc. Camb. Philos. Soc."},{"key":"7_CR22","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. 209, pp. 169\u2013182. Springer, Heidelberg (1985). https:\/\/doi.org\/10.1007\/3-540-39757-4_17"},{"key":"7_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1007\/978-3-030-45727-3_18","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"W Yu","year":"2020","unstructured":"Yu, W., Musa, S.A., Li, B.: Double-base chains for scalar multiplications on elliptic curves. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12107, pp. 538\u2013565. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45727-3_18"},{"key":"7_CR24","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. 4076, pp. 525\u2013542. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11792086_37"},{"key":"7_CR25","unstructured":"Zimmermann, P., et al.: GMP-ECM (elliptic curve method for integer factorization) (2012). https:\/\/gforge.inria.fr\/projects\/ecm\/"}],"container-title":["Lecture Notes in Computer Science","Science of Cyber Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-45933-7_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T09:03:38Z","timestamp":1700471018000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-45933-7_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031459320","9783031459337"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-45933-7_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"21 November 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"SciSec","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Science of Cyber Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Melbourne, VIC","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Australia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 July 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 July 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"5","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"scisec2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/scisec.org\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"60","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"21","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"6","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"35% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}