{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T05:05:27Z","timestamp":1764997527649,"version":"3.44.0"},"publisher-location":"New York, NY, USA","reference-count":19,"publisher":"ACM","license":[{"start":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T00:00:00Z","timestamp":1690156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Research Foundation - Flanders (FWO)","award":["12ZZC23N"],"award-info":[{"award-number":["12ZZC23N"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,7,24]]},"DOI":"10.1145\/3597066.3597068","type":"proceedings-article","created":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T18:15:27Z","timestamp":1688580927000},"page":"335-344","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiplication polynomials for elliptic curves over finite local rings"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2271-6822","authenticated-orcid":false,"given":"Riccardo","family":"Invernizzi","sequence":"first","affiliation":[{"name":"KU Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3402-4863","authenticated-orcid":false,"given":"Daniele","family":"Taufer","sequence":"additional","affiliation":[{"name":"KU Leuven, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,7,24]]},"reference":[{"key":"e_1_3_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2010.06.015"},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jnth.1995.1088"},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1063\/1.4822863"},{"volume-title":"Handbook of Mathematical Induction","author":"Gunderson S","key":"e_1_3_2_1_5_1","unstructured":"David\u00a0S Gunderson and Kenneth\u00a0H Rosen. 2010. Handbook of Mathematical Induction. CRC Press LLC, Boca Raton, Florida US."},{"key":"e_1_3_2_1_6_1","unstructured":"Riccardo Invernizzi and Daniele Taufer. 2023. Elliptic Curves over Local Rings. KU Leuven. https:\/\/github.com\/r98inver\/ec-local-rings\/"},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s102070100002"},{"key":"e_1_3_2_1_8_1","volume-title":"Modular elliptic curves and Fermat\u2019s Last Theorem. Mathematics of computation 48, 177","author":"Koblitz Neal","year":"1987","unstructured":"Neal Koblitz. 1987. Modular elliptic curves and Fermat\u2019s Last Theorem. Mathematics of computation 48, 177 (1987), 203\u2013209."},{"key":"e_1_3_2_1_9_1","volume-title":"Proceedings of the International Congress of Mathematicians","author":"Lenstra W.","year":"1986","unstructured":"Hendrik\u00a0W. Lenstra. 1986. Elliptic curves and number-theoretic algorithms. Proceedings of the International Congress of Mathematicians (1986), 99\u2013120."},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/359460.359473"},{"key":"e_1_3_2_1_11_1","volume-title":"Proceedings 218","author":"Miller S.","year":"1985","unstructured":"Victor\u00a0S. Miller. 1985. Use of elliptic curves in cryptography. Advances in Cryptology \u2014 CRYPTO \u201985 Proceedings 218 (1985), 417\u2013426."},{"key":"e_1_3_2_1_12_1","volume-title":"The group structure of elliptic curves over Z\/NZ. arXiv preprint arXiv:2010.15543","author":"Sala Massimiliano","year":"2020","unstructured":"Massimiliano Sala and Daniele Taufer. 2020. The group structure of elliptic curves over Z\/NZ. arXiv preprint arXiv:2010.15543 (2020)."},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2023.107417"},{"key":"e_1_3_2_1_14_1","first-page":"177","article-title":"A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring","volume":"12","author":"Sala Massimiliano","year":"2023","unstructured":"Massimiliano Sala and Daniele Taufer. 2023. A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring. International Journal of Group Theory 12, 3 (2023), 177\u2013196.","journal-title":"International Journal of Group Theory"},{"key":"e_1_3_2_1_15_1","first-page":"81","article-title":"Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves","volume":"47","author":"Satoh Takakazu","year":"1998","unstructured":"Takakazu Satoh and Kiyomichi Araki. 1998. Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves. Commentarii Mathematici Universitatis Sancti Pauli 47, 1 (1998), 81\u201392.","journal-title":"Commentarii Mathematici Universitatis Sancti Pauli"},{"key":"e_1_3_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/477\/09305"},{"volume-title":"The arithmetic of elliptic curves. Vol.\u00a0106","author":"Silverman H.","key":"e_1_3_2_1_17_1","unstructured":"Joseph\u00a0H. Silverman. 2009. The arithmetic of elliptic curves. Vol.\u00a0106. Springer."},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s001459900052"},{"key":"e_1_3_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.2307\/2118559"}],"event":{"name":"ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023","acronym":"ISSAC 2023","location":"Troms\u00f8 Norway"},"container-title":["Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3597066.3597068","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3597066.3597068","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T09:36:51Z","timestamp":1755855411000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3597066.3597068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,24]]},"references-count":19,"alternative-id":["10.1145\/3597066.3597068","10.1145\/3597066"],"URL":"https:\/\/doi.org\/10.1145\/3597066.3597068","relation":{},"subject":[],"published":{"date-parts":[[2023,7,24]]},"assertion":[{"value":"2023-07-24","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}