{"id":27003,"date":"2026-09-27T20:02:20","date_gmt":"2026-09-27T18:02:20","guid":{"rendered":"https:\/\/www.itspy.cz\/thesis\/comparative-evaluation-of-open-source-implementations-ofgrobner-basis-computation-algorithms-for-small-scale-aespolynomial-systems-over-gf2\/"},"modified":"2026-09-27T20:05:01","modified_gmt":"2026-09-27T18:05:01","slug":"comparative-evaluation-of-open-source-implementations-ofgrobner-basis-computation-algorithms-for-small-scale-aespolynomial-systems-over-gf2","status":"publish","type":"thesis","link":"https:\/\/www.itspy.cz\/en\/thesis\/comparative-evaluation-of-open-source-implementations-ofgrobner-basis-computation-algorithms-for-small-scale-aespolynomial-systems-over-gf2\/","title":{"rendered":"Comparative Evaluation of Open-Source Implementations of\nGr\u00f6bner Basis Computation Algorithms for Small-Scale AES\nPolynomial Systems over GF(2)"},"content":{"rendered":"<p>This thesis focuses on the comparative evaluation of<br \/>\nexisting implementations of Gr\u00f6bner basis computation based<br \/>\non the Faug\u00e8re F4 algorithm for polynomial systems over the<br \/>\nfinite field GF(2). Such polynomial systems naturally arise<br \/>\nin the algebraic analysis of cryptographic primitives,<br \/>\nincluding simplified variants of the AES cipher. Rather<br \/>\nthan developing a new Gr\u00f6bner basis algorithm, the thesis<br \/>\naims to study, configure, and experimentally compare<br \/>\navailable implementations, with a particular emphasis on<br \/>\nopen-source tools. The evaluated systems will be applied to<br \/>\npolynomial representations of small-scale AES variants, and<br \/>\ntheir performance will be assessed in terms of computation<br \/>\ntime, memory consumption, and practical usability. The<br \/>\nresults will be analyzed and compared with the established<br \/>\nreference system Magma, providing insights into the<br \/>\nstrengths and limitations of current open-source Gr\u00f6bner<br \/>\nbasis solvers for cryptographic applications.<\/p>\n","protected":false},"featured_media":26769,"template":"","meta":{"_acf_changed":false,"_links_to":"","_links_to_target":""},"university":[45,429],"thesis-year":[466],"class_list":["post-27003","thesis","type-thesis","status-publish","has-post-thumbnail","hentry","thesis-year-466"],"acf":{"autor":"Pavel Hol\u00fd","portret":"","vedouci":"Mgr. Martin Jure\u010dek, Ph.D."},"_links":{"self":[{"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/thesis\/27003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/thesis"}],"about":[{"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/types\/thesis"}],"version-history":[{"count":1,"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/thesis\/27003\/revisions"}],"predecessor-version":[{"id":27058,"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/thesis\/27003\/revisions\/27058"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/media\/26769"}],"wp:attachment":[{"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/media?parent=27003"}],"wp:term":[{"taxonomy":"university","embeddable":true,"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/university?post=27003"},{"taxonomy":"thesis-year","embeddable":true,"href":"https:\/\/www.itspy.cz\/en\/wp-json\/wp\/v2\/thesis-year?post=27003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}