{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:57:57Z","timestamp":1772283477545,"version":"3.50.1"},"reference-count":22,"publisher":"Wiley","issue":"A","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"content-version":"unspecified","delay-in-days":212,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2014]]},"abstract":"Abstract<\/jats:title>In this paper we study the discrete logarithm problem in medium- and high-characteristic finite fields. We propose a variant of the number field sieve\u00a0(NFS) based on numerous number fields. Our improved algorithm computes discrete logarithms in $\\def \\xmlpi #1{}\\def \\mathsfbi #1{\\boldsymbol {\\mathsf {#1}}}\\let \\le =\\leqslant \\let \\leq =\\leqslant \\let \\ge =\\geqslant \\let \\geq =\\geqslant \\def \\Pr {\\mathit {Pr}}\\def \\Fr {\\mathit {Fr}}\\def \\Rey {\\mathit {Re}}\\mathbb{F}_{p^n}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> for the whole range of applicability of the NFS and lowers the asymptotic complexity from $L_{p^n}({1\/3},({128\/9})^{1\/3})$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> to $L_{p^n}({1\/3},(2^{13}\/3^6)^{1\/3})$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> in the medium-characteristic case, and from $L_{p^n}({1\/3},({64\/9})^{1\/3})$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> to $L_{p^n}({1\/3},((92 + 26 \\sqrt{13})\/27)^{1\/3})$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> in the high-characteristic case.<\/jats:p>","DOI":"10.1112\/s1461157014000369","type":"journal-article","created":{"date-parts":[[2014,8,5]],"date-time":"2014-08-05T10:34:15Z","timestamp":1407234855000},"page":"230-246","source":"Crossref","is-referenced-by-count":19,"title":["The multiple number field sieve for medium- and high-characteristic finite fields"],"prefix":"10.1112","volume":"17","author":[{"given":"Razvan","family":"Barbulescu","sequence":"first","affiliation":[]},{"given":"C\u00e9cile","family":"Pierrot","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2014,8,1]]},"reference":[{"key":"S1461157014000369_r22","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1986.1057137"},{"key":"S1461157014000369_r20","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-99-01137-0"},{"key":"S1461157014000369_r19","first-page":"239","volume-title":"Advances in cryptology \u2013 CRYPTO\u00a0\u201989","author":"Schnorr","year":"1990"},{"key":"S1461157014000369_r15","first-page":"45","volume-title":"Pairing-based cryptography \u2013 Pairing 2013","author":"Joux","year":"2013"},{"key":"S1461157014000369_r13","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-02-01482-5"},{"key":"S1461157014000369_r12","doi-asserted-by":"publisher","DOI":"10.1007\/s00145-004-0312-y"},{"key":"S1461157014000369_r11","first-page":"186","volume-title":"Advances in cryptology \u2013 CRYPTO \u201986","author":"Fiat","year":"1986"},{"key":"S1461157014000369_r10","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-61581-4_45"},{"key":"S1461157014000369_r8","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1976.1055638"},{"key":"S1461157014000369_r7","doi-asserted-by":"publisher","DOI":"10.1007\/11745853_12"},{"key":"S1461157014000369_r6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00198464"},{"key":"S1461157014000369_r5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(83)90002-1"},{"key":"S1461157014000369_r2","unstructured":"2. 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