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href=\"http:\/\/www.inforsec.org\/wp\/wp-content\/uploads\/2016\/03\/\u56fe\u72471.png\" rel=\"attachment wp-att-716\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-716 aligncenter\" src=\"http:\/\/www.inforsec.org\/wp\/wp-content\/uploads\/2016\/03\/\u56fe\u72471.png\" alt=\"\u56fe\u72471\" width=\"347\" height=\"127\" srcset=\"http:\/\/202.112.238.40\/wp\/wp-content\/uploads\/2016\/03\/\u56fe\u72471.png 347w, http:\/\/202.112.238.40\/wp\/wp-content\/uploads\/2016\/03\/\u56fe\u72471-300x110.png 300w, http:\/\/202.112.238.40\/wp\/wp-content\/uploads\/2016\/03\/\u56fe\u72471-250x91.png 250w, http:\/\/202.112.238.40\/wp\/wp-content\/uploads\/2016\/03\/\u56fe\u72471-150x55.png 150w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/a><\/p>\n<p>\u8be5\u95ee\u9898\u8981\u6c42\u5728\u5df2\u77e5\u7ed9\u5b9a\u7684\u7cfb\u6570a<sub>11<\/sub>,\u2026,a<sub>qn<\/sub>\u548c\u7ed3\u679cy<sub>1<\/sub>,\u2026,y<sub>q<\/sub>\u7684\u6761\u4ef6\u4e0b\uff0c\u6c42\u89e3\u672a\u77e5\u6570x<sub>1<\/sub>,\u2026,x<sub>n<\/sub>(\u5982\u679cx<sub>1<\/sub>,\u2026,x<sub>n<\/sub>\u6c42\u89e3\u51fa\u6765\uff0ce<sub>1<\/sub>,\u2026,e<sub>q<\/sub>\u4e5f\u7acb\u5373\u53ef\u4ee5\u5f97\u5230)\u3002\u4ee5\u4e0a\u95ee\u9898\u5c31\u662f\u8457\u540d\u7684LearningParitywithNoise(LPN)\u95ee\u9898\u3002\u5f53q\u8fdc\u5927\u4e8en\uff0c\u5e76\u4e14u\u662f\u5c0f\u4e8e1\/2\u7684\u5e38\u6570\u7684\u60c5\u51b5\u4e0b\uff0c\u672a\u77e5\u6570x1,\u2026,xn\u662f\u51e0\u4e4e\u53ef\u4ee5\u552f\u4e00\u786e\u5b9a\u7684\u3002\u8be5\u95ee\u9898\u88ab\u8bc1\u660e\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u662fNP\u5b8c\u5168\u7684\uff0c\u5373\u4f7f\u5728\u5e73\u5747\u60c5\u51b5\u4e0b\uff0c\u4eba\u4eec\u81f3\u4eca\u6ca1\u6709\u627e\u5230\u89e3\u51b3\u8be5\u95ee\u9898\u7684\u6709\u6548\u7b97\u6cd5\uff0c\u76ee\u524d\u6e10\u8fdb\u610f\u4e49\u4e0a\u6700\u597d\u7684BKW\u7b97\u6cd5\u9700\u8981\u4e9a\u6307\u6570\u7684\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u66f4\u91cd\u8981\u7684\u662f\uff0c\u91cf\u5b50\u7b97\u6cd5\u89e3\u51b3\u8be5\u95ee\u9898\u4e5f\u4e0d\u5177\u6709\u4efb\u4f55\u4f18\u52bf\u3002\u6211\u56fd\u5b66\u8005\u5728\u5229\u7528LPN\u8bbe\u8ba1\u540e\u91cf\u5b50\u5bf9\u79f0\u5bc6\u7801\u7b97\u6cd5[2]\u548c\u9488\u5bf9LPN\u5728\u5177\u4f53\u53c2\u6570\u8bbe\u5b9a\u4e0b\u7684\u5bc6\u7801\u5206\u6790[3,4]\u4e0a\u53d6\u5f97\u4e86\u8f83\u4e3a\u9886\u5148\u7684\u6210\u679c\uff0c\u6211\u4eec\u4e5f\u6709\u4e00\u9879\u8fdb\u884c\u4e2d\u7684\u5de5\u4f5c\u662f\u57fa\u4e8e\u6807\u51c6LPN\u95ee\u9898\u7684\u56f0\u96be\u6027\u8bbe\u8ba1\u516c\u94a5\u5bc6\u7801\u7b97\u6cd5\u548c\u4e0d\u7ecf\u610f\u4f20\u8f93\u534f\u8bae\u3002OdedRegev\u8fdb\u4e00\u6b65\u5c06\u4ee5\u4e0a\u7684LPN\u95ee\u9898\u63a8\u5e7f\u5230\u66f4\u5927\u7684\u7d20\u6570\u57df\u4e0a\uff0c\u5373\u4ee5\u4e0a\u65b9\u7a0b\u7ec4\u4e2d\u6240\u6709\u7684\u7cfb\u6570\u548c\u672a\u77e5\u6570\u90fd\u662fGF(p)\u4e0a\u7684\u5143\u7d20\uff0c\u4e14\u76f8\u5173\u7684\u52a0\u6cd5\u548c\u4e58\u6cd5\u90fd\u5728GF(p)\u4e0a\u8fd0\u7b97\uff0c\u5176\u4e2dp\u662f\u4e00\u4e2a\u8f83\u5927\u7684\u7d20\u6570\uff0ce<sub>1<\/sub>,\u2026,e<sub>q<\/sub>\u90fd\u72ec\u7acb\u5730\u670d\u4eceGF(p)\u4e0a\u7684\u79bb\u6563\u9ad8\u65af\u5206\u5e03\u3002\u4ee5\u4e0a\u63a8\u5e7f\u540e\u7684\u95ee\u9898\u5c31\u662f\u8457\u540d\u7684LearningwithErrors(LWE)\u95ee\u9898\u3002\u76ee\u524d\u5df2\u77e5LWE\u5728\u4e00\u5b9a\u7684\u53c2\u6570\u8bbe\u5b9a\u4e0b\u53ef\u4ee5\u5f52\u7ea6\u5230GapSVP\uff0cSIVP\u7b49\u683c\u4e0a\u7684\u56f0\u96be\u95ee\u9898\uff08\u5373\u6c42\u89e3LWE\u95ee\u9898\u5e76\u4e0d\u6bd4\u6c42\u89e3\u683c\u4e0a\u56f0\u96be\u95ee\u9898\u5bb9\u6613\uff09\uff0c\u56e0\u6b64\u4e5f\u662f\u540e\u91cf\u5b50\u5b89\u5168\u7684\u3002\u867d\u7136LWE\u76f8\u5bf9\u4e8eLPN\u5728\u6548\u7387\u4e0a\u6709\u4e00\u5b9a\u964d\u4f4e\uff0c\u4f46\u5176\u5177\u6709\u66f4\u5e7f\u6cdb\u7684\u5bc6\u7801\u5e94\u7528\uff0c\u9664\u4e86\u516c\u94a5\u52a0\u5bc6\uff0cLWE\u8fd8\u53ef\u4ee5\u7528\u6765\u8bbe\u8ba1\u6297\u78b0\u649e\u54c8\u5e0c\u51fd\u6570\u3001\u5168\u540c\u6001\u52a0\u5bc6\u7b49\u3002\u6211\u56fd\u5b66\u8005\u5728\u8fd9\u65b9\u9762\u4e5f\u6709\u4e00\u4e9b\u5de5\u4f5c\uff0c\u5982\u5f20\u6c5f\u7b49\u4eba\u57fa\u4e8eRing-LWE\u8bbe\u8ba1\u7684\u53ef\u7528\u4e8eTLS\u534f\u8bae\u7684\u540e\u91cf\u5b50\u5b89\u5168\u7684\u9ad8\u6548\u5bc6\u94a5\u4ea4\u6362\u534f\u8bae[5]\u3002<\/p>\n<p>\u7efc\u4e0a\uff0c\u73b0\u4ee3\u5bc6\u7801\u5b66\u5e76\u4e0d\u7b49\u540c\u4e8e\u57fa\u4e8eRSA\u3001\u79bb\u6563\u5bf9\u6570\u7b49\u5c11\u6570\u51e0\u4e2a\u6570\u8bba\u56f0\u96be\u95ee\u9898\u7684\u5bc6\u7801\u7cfb\u7edf\uff0c\u91cf\u5b50\u8ba1\u7b97\u673a\u7684\u5230\u6765\u4e5f\u5e76\u4e0d\u662f\u73b0\u4ee3\u5bc6\u7801\u5b66\u7684\u672b\u65e5\uff0c\u5b89\u5168\u4fe1\u606f\u4f20\u8f93\u53ea\u662f\u4f20\u7edf\u5bc6\u7801\u5b66\u8bf8\u591a\u5e94\u7528\u4e2d\u7684\u4e00\u4e2a\uff0c\u56e0\u6b64\u91cf\u5b50\u5bc6\u7801\u4e0d\u53ef\u80fd\u5b8c\u5168\u53d6\u4ee3\u4f20\u7edf\u5bc6\u7801\u3002\u7ecf\u8fc7\u8fd120\u5e74\u7684\u53d1\u5c55\uff0c\u540e\u91cf\u5b50\u5bc6\u7801\u5b66\u7684\u7814\u7a76\u5df2\u7ecf\u53d6\u5f97\u4e86\u4e30\u7855\u7684\u6210\u679c\uff0c\u540c\u65f6\u4e5f\u4e3a\u62b5\u6297\u91cf\u5b50\u8ba1\u7b97\u673a\u653b\u51fb\u50a8\u5907\u4e86\u5927\u91cf\u4e86\u7684\u5bc6\u7801\u6280\u672f\uff0c\u4e00\u4e9b\u6807\u51c6\u5236\u5b9a\u673a\u6784\u5373\u5c06\u751a\u81f3\u5df2\u7ecf\u5728\u5f00\u5c55\u540e\u91cf\u5b50\u5bc6\u7801\u7b97\u6cd5\u7684\u6807\u51c6\u5316\u5de5\u4f5c\uff0c\u76f8\u4fe1\u5728\u4e0d\u4e45\u7684\u5c06\u6765\u91cf\u5b50\u5b89\u5168\u7684\uff08\u4f46\u4ecd\u662f\u5728\u4f20\u7edf\u8ba1\u7b97\u673a\u4e0a\u8fd0\u884c\uff09\u5bc6\u7801\u7cfb\u7edf\u5373\u53ef\u4ee5\u90e8\u7f72\u5230\u6211\u4eec\u65e5\u5e38\u4f7f\u7528\u7684\u7cfb\u7edf\u548c\u7f51\u7edc\u4e2d\uff0c\u66f4\u597d\u5730\u4fdd\u62a4\u6211\u4eec\u7684\u4fe1\u606f\u5b89\u5168\u3002<\/p>\n<p>\u4f5c\u8005\u7b80\u4ecb\uff1a<\/p>\n<p>\u90c1\u6631\uff0c\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u7279\u522b\u7814\u7a76\u5458\uff0c\u535a\u58eb\u751f\u5bfc\u5e08\u3002\u4e3b\u8981\u4ece\u4e8b\u5bc6\u7801\u5b66\u57fa\u7840\u7406\u8bba\u7684\u7814\u7a76\u5de5\u4f5c\uff0c2010\u5e74\u56de\u56fd\u540e\u66fe\u5206\u522b\u5728\u534e\u4e1c\u5e08\u8303\u5927\u5b66\u548c\u6e05\u534e\u5927\u5b66\u4efb\u6559\uff0c\u591a\u9879\u7814\u7a76\u6210\u679c\u53d1\u8868\u5728\u5bc6\u7801\u4e09\u5927\u4f1a(CRYPTO\/EUROCRYPT\/ASIACRYPT)\u548cCCS,TCC,CHES,CT-RSA,ESORICS\u7b49\u5bc6\u7801\u4e0e\u4fe1\u606f\u5b89\u5168\u7684\u4ee3\u8868\u6027\u4f1a\u8bae\u4e0a\u3002\u76ee\u524d\u670d\u52a1\u4e8e\u56fd\u9645\u5bc6\u7801\u5b66\u4f1a\u7406\u4e8b\u4f1a\uff08IACRboard\uff09\u62c5\u4efb\u89c2\u5bdf\u5458\u5e76\u8d1f\u8d23\u5b66\u4f1a\u5b98\u7f51www.iacr.org\u7684\u65e5\u5e38\u7ba1\u7406\u4e8b\u52a1\uff0c2015\u5e74\u83b7\u5f97\u4e2d\u56fd\u5bc6\u7801\u5b66\u4f1a\u4f18\u79c0\u9752\u5e74\u5956\u3002<\/p>\n<p>\u5f20\u6c5f\uff0c\u4fe1\u606f\u5b89\u5168\u535a\u58eb\uff0c\u4e3b\u8981\u5173\u6ce8\u4e8e\u53ef\u8bc1\u660e\u5b89\u5168\u3001\u516c\u94a5\u52a0\u5bc6\u548c\u5bc6\u7801\u534f\u8bae\u7684\u7814\u7a76\uff0c\u73b0\u4e3a\u5bc6\u7801\u79d1\u5b66\u6280\u672f\u56fd\u5bb6\u91cd\u70b9\u5b9e\u9a8c\u5ba4\u52a9\u7406\u7814\u7a76\u5458\uff0c\u5728\u56fd\u9645\u91cd\u8981\u5bc6\u7801\u4f1a\u8bae\u548c\u671f\u520aEUROCRYPT\u3001ASIACRYPT\u3001PKC\u3001DCC\u3001TCS\u7b49\u53d1\u8868\u4e86\u591a\u9879\u7814\u7a76\u6210\u679c\u3002\u4e2a\u4eba\u4e3b\u9875\uff1ajiangzhang.net\u3002<\/p>\n<p>\u53c2\u8003\u6587\u732e<\/p>\n<p>[1]\u5f20\u7115\u56fd\uff0c\u97e9\u6587\u62a5\uff0c\u6765\u5b66\u5609\uff0c\u6797\u4e1c\u5cb1\uff0c\u9a6c\u5efa\u5cf0\uff0c\u674e\u5efa\u534e.\u201c\u7f51\u7edc\u7a7a\u95f4\u5b89\u5168\u7efc\u8ff0\u201d\u4e2d\u56fd\u79d1\u5b66\uff0c\u7b2c46\u5377\uff0c\u7b2c2\u671f\uff1a125-164\uff0c2016.<\/p>\n<p>[2]YuYuandJohnSteinberger.\u201cPseudorandomFunctionsinAlmostConstantDepthfromLow-NoiseLPN\u201d,inAdvancesinCryptology-EUROCRYPT2016.<\/p>\n<p>[3]QianGuo,ThomasJohansson,CarlL?ndah.,\u201cSolvingLPNUsingCoveringCodes\u201d.InAdvancesinCryptology-ASIACRYPT2014.<\/p>\n<p>[4]BinZhang,LinJiao,MingshengWang.\u201cFasterAlgorithmsforSolvingLPN\u201d.InAdvancesinCryptology\u2013EUROCRYPT2016.<\/p>\n<p>[5]JiangZhang,ZhenfengZhang,JintaiDing,MichaelSnook,?zg\u00fcrDagdelen.\u201cAuthenticatedKeyExchangefromIdealLattices\u201d,InAdvancesinCryptology\u2013EUROCRYPT2015.<\/p>\n<p>\u5168\u6587\u4e0b\u8f7d\u94fe\u63a5\uff1a<a href=\"http:\/\/www.inforsec.org\/wp\/wp-content\/uploads\/2016\/03\/\u91cf\u5b50\u8ba1\u7b97VS\u5bc6\u7801\u6280\u672f-v324-Duan.pdf\" rel=\"\">\u91cf\u5b50\u8ba1\u7b97VS\u5bc6\u7801\u6280\u672f-v324-Duan<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4f5c\u8005\uff1a\u90c1\u6631\uff08\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u7279\u522b\u7814\u7a76\u5458\uff0c\u535a\u58eb\u751f\u5bfc\u5e08\uff09\uff0c\u5f20\u6c5f\uff08\u4fe1\u606f\u5b89\u5168\u535a\u58eb\uff09 \u6700\u8fd1\u6709\u4e00\u4e9b\u65b0\u95fb\u5a92\u4f53\u62a5\u9053\u4e86\u91cf\u5b50&#8230; <a class=\"continue-reading-link\" href=\"http:\/\/202.112.238.40\/wp\/?p=708\"> Continue reading <span class=\"meta-nav\">&rarr; <\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-708","post","type-post","status-publish","format-standard","hentry","category-research"],"_links":{"self":[{"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=\/wp\/v2\/posts\/708","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=708"}],"version-history":[{"count":12,"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=\/wp\/v2\/posts\/708\/revisions"}],"predecessor-version":[{"id":723,"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=\/wp\/v2\/posts\/708\/revisions\/723"}],"wp:attachment":[{"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=708"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=708"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/202.112.238.40\/wp\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=708"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}