{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:20:57Z","timestamp":1764980457669,"version":"3.46.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2014,7,26]],"date-time":"2014-07-26T00:00:00Z","timestamp":1406332800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004410","name":"Scientific and Technological Research Council of Turkey","doi-asserted-by":"crossref","award":["National Postdoctoral Research Scholarship no. 2219"],"award-info":[{"award-number":["National Postdoctoral Research Scholarship no. 2219"]}],"id":[{"id":"10.13039\/501100004410","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    T. Harayama and D. K. Friesen\n[J. Math. Cryptol. 1 (2007), 79\u2013104]\nproposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski\u2013Ostrom (DO) polynomials in this framework over the finite field \ud835\udd3d\n                    <jats:sub>2<\/jats:sub>\n                    . We extend the linearized binomial attack to multivariate quadratic cryptosystems over \ud835\udd3d\n                    <jats:sub>\n                      <jats:italic>p<\/jats:italic>\n                    <\/jats:sub>\n                    for any prime\n                    <jats:italic>p<\/jats:italic>\n                    and redefine the weak DO polynomials for general case.\nWe identify infinite classes of weak DO polynomials for these systems by considering highly degenerate quadratic forms over algebraic function fields and Artin\u2013Schreier type curves to achieve our results. This gives a general answer to the conjecture stated by Harayama and Friesen and also a partial enumeration of weak DO polynomials over finite fields.\n                  <\/jats:p>","DOI":"10.1515\/jmc-2013-0019","type":"journal-article","created":{"date-parts":[[2014,8,4]],"date-time":"2014-08-04T16:34:20Z","timestamp":1407170060000},"page":"11-22","source":"Crossref","is-referenced-by-count":0,"title":["Classes of weak Dembowski\u2013Ostrom polynomials for multivariate quadratic cryptosystems"],"prefix":"10.1515","volume":"9","author":[{"given":"Bilal","family":"Alam","sequence":"first","affiliation":[{"name":"Institute of Applied Mathematics, Middle East Technical University, Dumlup\u0131nar Blv. No:1, 06800 Ankara, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ferruh","family":"\u00d6zbudak","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Institute of Applied Mathematics, Middle East Technical University, Dumlup\u0131nar Blv. No:1, 06800 Ankara, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"O\u011fuz","family":"Yayla","sequence":"additional","affiliation":[{"name":"Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Altenberger Str. 69, 4040 Linz, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,7,26]]},"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2013-0019\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2013-0019\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:16:50Z","timestamp":1764980210000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2013-0019\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,7,26]]},"published-print":{"date-parts":[[2015,3,1]]}},"alternative-id":["10.1515\/jmc-2013-0019"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2013-0019","relation":{},"ISSN":["1862-2984","1862-2976"],"issn-type":[{"type":"electronic","value":"1862-2984"},{"type":"print","value":"1862-2976"}],"subject":[],"published":{"date-parts":[[2014,7,26]]}}}