{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,7]],"date-time":"2024-07-07T00:14:42Z","timestamp":1720311282997},"reference-count":10,"publisher":"The Japan Society for Industrial and Applied Mathematics","issue":"0","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JSIAM Letters"],"published-print":{"date-parts":[[2022]]},"DOI":"10.14495\/jsiaml.14.135","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T22:10:31Z","timestamp":1671660631000},"page":"135-138","source":"Crossref","is-referenced-by-count":1,"title":["Polynomial selection of <i>F<\/i><sub>4<\/sub> for solving the MQ problem"],"prefix":"10.14495","volume":"14","author":[{"given":"Takuma","family":"Ito","sequence":"first","affiliation":[{"name":"National Institute of Information and Communications Technology"}]},{"given":"Yuta","family":"Hoshi","sequence":"additional","affiliation":[{"name":"Canon IT Solutions Inc."}]},{"given":"Naoyuki","family":"Shinohara","sequence":"additional","affiliation":[{"name":"National Institute of Information and Communications Technology"}]},{"given":"Shigenori","family":"Uchiyama","sequence":"additional","affiliation":[{"name":"Graduate School of Science, Tokyo Metropolitan University"}]}],"member":"5623","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[1] J. C. Faug\u00e8re, A new efficient algorithm for computing Gr\u00f6bner bases (F<\/i>4<\/sub>), J. Pure Appl. Algebra, 139<\/b> (1999), 61\u201388.","DOI":"10.1016\/S0022-4049(99)00005-5"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] R. H. Makarim and M. Stevens, M4GB: An efficient Gr\u00f6bner-basis algorithm, in: Proc. of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, pp.293\u2013300, Association for Computing Machinery, 2017.","DOI":"10.1145\/3087604.3087638"},{"key":"3","doi-asserted-by":"crossref","unstructured":"[3] P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Review, 41<\/b> (1999), 303\u2013332.","DOI":"10.1137\/S0036144598347011"},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] B. Buchberger, A criterion for detecting unnecessary reductions in the construction of Gr\u00f6bner bases, in: Proc. of the International Symposium on Symbolic and Algebraic Computation, pp.3\u201321, Springer, Berlin, Heidelberg, 1979.","DOI":"10.1007\/3-540-09519-5_52"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] L. Bettale, J. C. Faug\u00e8re and L. Perret, Hybrid approach for solving multivariate systems over finite fields, J. Math. Cryptol., 3<\/b> (2009), 177\u2013197.","DOI":"10.1515\/JMC.2009.009"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[6] J. Ding and D. Schmidt, Rainbow, a new multivariable polynomial signature scheme, in: Proc. of Applied Cryptography and Network Security 2005, pp.164\u2013175, Springer, Berlin, Heidelberg, 2005.","DOI":"10.1007\/11496137_12"},{"key":"7","unstructured":"[7] A. Casanova, J. C. Faug\u00e8re, G. Macario-Rat, J. Patarin, L. Perret and J. Ryckeghem, GeMSS: A Great Multivariate Short Signature, Version second round, https:\/\/www-polsys.lip6.fr\/Links\/NIST\/GeMSS.html (accessed 25 Mar. 2022)."},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] T. Becker and V. Weispfenning, Gr\u00f6bner Bases, a Computationnal Approach to Commutative Algebra. Graduate Texts in Mathematics, Springer, New York, 1993.","DOI":"10.1007\/978-1-4612-0913-3"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] T. Ito, N. Shinohara and S. Uchiyama, An efficient F<\/i>4<\/sub>-style based algorithm to solve MQ problems, in: Proc. of 14th International Workshop on Security 2019, pp.37\u201352, Information Processing Society of Japan, 2019.","DOI":"10.1007\/978-3-030-26834-3_3"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] T. Ito, A. Nitta, Y. Hoshi, N. Shinohara and S. Uchiyama, Polynomial selection for computing Gr\u00f6bner bases, JSIAM Lett., 13<\/b> (2021), 72\u201375.","DOI":"10.14495\/jsiaml.13.72"}],"container-title":["JSIAM Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/jsiaml\/14\/0\/14_135\/_pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T05:19:57Z","timestamp":1720243197000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/jsiaml\/14\/0\/14_135\/_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"references-count":10,"journal-issue":{"issue":"0","published-print":{"date-parts":[[2022]]}},"URL":"https:\/\/doi.org\/10.14495\/jsiaml.14.135","relation":{},"ISSN":["1883-0609","1883-0617"],"issn-type":[{"value":"1883-0609","type":"print"},{"value":"1883-0617","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]}}}