{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T19:41:20Z","timestamp":1770493280813,"version":"3.49.0"},"reference-count":0,"publisher":"Rinton Press","issue":"9&10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QIC"],"published-print":{"date-parts":[[2014,7]]},"abstract":"<jats:p>Improving over an earlier construction by Kaye and Zalka \\cite{KaZa04}, in \\cite{MMCP09b} Maslov et al. describe an implementation of Shor's algorithm, which can solve the discrete logarithm problem on ordinary binary elliptic curves in quadratic depth $\\bigO(n^2)$. In this paper we show that discrete logarithms on such curves can be found with a quantum circuit of depth $\\bigO(\\log^2n)$. As technical tools we introduce quantum circuits for ${\\mathbb F}_{2^n}$-multiplication in depth $\\bigO(\\log n)$ and for ${\\mathbb F}_{2^n}$-inversion in depth $\\bigO(\\log^2 n)$.<\/jats:p>","DOI":"10.26421\/qic14.9-10-11","type":"journal-article","created":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T04:01:06Z","timestamp":1614571266000},"page":"888-900","source":"Crossref","is-referenced-by-count":4,"title":["A quantum circuit to find discrete logarithms on ordinary binary elliptic curves in depth O(log^2n)"],"prefix":"10.26421","volume":"14","author":[{"given":"Martin","family":"Rotteler","sequence":"first","affiliation":[]},{"given":"Rainer","family":"Steinwandt","sequence":"additional","affiliation":[]}],"member":"10955","published-online":{"date-parts":[[2014,7]]},"container-title":["Quantum Information and Computation"],"original-title":[],"deposited":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T04:01:14Z","timestamp":1614571274000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.rintonpress.com\/journals\/doi\/QIC14.9-10-11.html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7]]},"references-count":0,"journal-issue":{"issue":"9&10","published-online":{"date-parts":[[2014,7]]},"published-print":{"date-parts":[[2014,7]]}},"URL":"https:\/\/doi.org\/10.26421\/qic14.9-10-11","relation":{},"ISSN":["1533-7146","1533-7146"],"issn-type":[{"value":"1533-7146","type":"print"},{"value":"1533-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7]]}}}