{"id":327629,"date":"2016-11-27T23:11:43","date_gmt":"2016-11-28T07:11:43","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=327629"},"modified":"2018-10-16T21:31:24","modified_gmt":"2018-10-17T04:31:24","slug":"deja-q-tighter-broader-reductions-q-type-assumptions","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/deja-q-tighter-broader-reductions-q-type-assumptions\/","title":{"rendered":"D\u00c3\u00a9j\u00c3\u00a0 Q All Over Again: Tighter and Broader Reductions of q-Type Assumptions"},"content":{"rendered":"<p>In this paper, we demonstrate that various cryptographic constructions\u2014including ones for broadcast, attribute-based, and hierarchical identity-based encryption\u2014can rely for security on only the static subgroup hiding assumption when instantiated in composite-order bilinear groups, as opposed to the dynamic <em class=\"EmphasisTypeItalic \">q<\/em>-type assumptions on which their security previously was based. This specific goal is accomplished by more generally extending the recent D\u00e9j\u00e0 Q framework (Chase and Meiklejohn, Eurocrypt 2014) in two main directions. First, by teasing out common properties of existing reductions, we expand the <em class=\"EmphasisTypeItalic \">q<\/em>-type assumptions that can be covered by the framework; i.e., we demonstrate broader classes of assumptions that can be reduced to subgroup hiding. Second, while the original framework applied only to asymmetric composite-order bilinear groups, we provide a reduction to subgroup hiding that works in symmetric (as well as asymmetric) composite-order groups. As a bonus, our new reduction achieves a tightness of <span id=\"IEq1\" class=\"InlineEquation\"><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" style=\"border: 0px;font-style: normal;font-variant: inherit;font-weight: normal;font-size: 13px;line-height: normal;font-family: inherit;margin: 0px;padding: 0px;vertical-align: baseline;text-indent: 0px;text-align: left;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mi\">log<\/span><span id=\"MathJax-Span-4\" class=\"mo\"><\/span><span id=\"MathJax-Span-5\" class=\"mo\">(<\/span><span id=\"MathJax-Span-6\" class=\"mi\">q<\/span><span id=\"MathJax-Span-7\" class=\"mo\">)<\/span><\/span><\/span><span class=\"MJX_Assistive_MathML\">log\u2061(q)<\/span><\/span><\/span> rather than <em class=\"EmphasisTypeItalic \">q<\/em>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this paper, we demonstrate that various cryptographic constructions\u2014including ones for broadcast, attribute-based, and hierarchical identity-based encryption\u2014can rely for security on only the static subgroup hiding assumption when instantiated in composite-order bilinear groups, as opposed to the dynamic q-type assumptions on which their security previously was based. This specific goal is accomplished by more generally [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Springer Berlin Heidelberg","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"Asiacrypt 2016","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Asiacrypt 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