{"id":112750,"date":"2026-10-04T18:57:41","date_gmt":"2026-10-04T10:57:41","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/112750.html"},"modified":"2026-10-04T18:57:41","modified_gmt":"2026-10-04T10:57:41","slug":"5%e4%b8%aa1280%e6%af%94%e7%89%b9%e5%a4%a7%e7%8a%b6%e6%80%81%e7%bd%ae%e6%8d%a2%e7%ae%97%e6%b3%95%e7%9a%84%e8%ae%be%e8%ae%a1%e4%b8%8e%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/112750.html","title":{"rendered":"5\u4e2a1280\u6bd4\u7279\u5927\u72b6\u6001\u7f6e\u6362\u7b97\u6cd5\u7684\u8bbe\u8ba1\u4e0e\u5206\u6790"},"content":{"rendered":"<p style=\"margin-left:0;margin-right:0;text-align:center\">5\u4e2a1280\u6bd4\u7279\u5927\u72b6\u6001\u7f6e\u6362\u7b97\u6cd5\u7684\u8bbe\u8ba1\u4e0e\u5206\u6790<\/p>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u4ee5\u4e0b\u662f5\u4e2a\u98ce\u683c\u8fe5\u5f02\u3001\u5b8c\u5168\u72ec\u521b\u76841280\u6bd4\u7279&#xff08;20\u4e2a64-bit\u5b57&#xff09;\u5927\u72b6\u6001\u7f6e\u6362\u8bbe\u8ba1\u65b9\u6848\u3002\u6bcf\u4e2a\u65b9\u6848\u90fd\u907f\u5f00\u4e86Keccak\u3001Xoodoo\u3001Gimli\u7b49\u6807\u51c6\u5957\u8def&#xff0c;\u5206\u522b\u4ece\u62d3\u6251\u6d41\u4f53\u3001\u9057\u4f20\u526a\u63a5\u3001\u58f0\u5b66\u5171\u632f\u3001\u56db\u5143\u6570\u51e0\u4f55\u3001\u5206\u5f62\u7edf\u8ba1\u4e94\u4e2a\u622a\u7136\u4e0d\u540c\u7684\u79d1\u5b66\u9886\u57df\u6c72\u53d6\u7075\u611f&#xff0c;\u4e14\u6240\u6709\u8f6e\u51fd\u6570\u5747\u7531\u53ef\u9006\u7684ARX&#xff08;\u6a21\u52a0\/\u65cb\u8f6c\/\u5f02\u6216&#xff09;\u3001\u6a21\u4e58\u5947\u5e38\u6570\u3001\u5b57\u7ea7\u7f6e\u6362\u6784\u6210&#xff0c;\u786e\u4fdd\u53cc\u5c04\u6027\u3002<\/span><\/span><\/p>\n<hr \/>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8bbe\u8ba1 1&#xff1a;\u62d3\u6251\u6da1\u65cb&#xff08;Topological Vortex&#xff09;<\/span><\/span><\/p>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u7075\u611f\u6765\u6e90<\/span><span style=\"color:#0f1115\">&#xff1a;\u6d41\u4f53\u529b\u5b66\u4e2d\u7684\u6da1\u91cf\u65b9\u7a0b\u4e0e\u67ef\u897f-\u9ece\u66fc\u6d41\u3002<br \/>\n\u8bbe\u8ba1\u54f2\u5b66&#xff1a;\u5c06\u72b6\u6001\u89c6\u4e3a\u00a04\u884c\u00d75\u5217\u00a0\u7684\u77e9\u9635\u3002\u6269\u6563\u5206\u201c\u6da1\u65cb\u751f\u6210\u201d\u4e0e\u201c\u6da1\u65cb\u5bf9\u6d41\u201d\u4e24\u6b65&#xff0c;\u6a21\u62df\u6d41\u4f53\u6495\u88c2\u4e0e\u6298\u53e0\u3002<\/span><\/span><\/p>\n<ul>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72b6\u6001\u5e03\u5c40&#xff1a;S[r][c]&#xff08;r&#061;0..3, c&#061;0..4&#xff09;&#xff0c;\u5747\u4e3a64\u4f4d\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8f6e\u51fd\u6570&#xff08;\u5355\u8f6e&#xff09;&#xff1a;<\/span><\/span>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u751f\u6210\u6da1\u91cf&#xff08;\u884c\u6df7\u5408&#xff09;&#xff1a;<br \/>\nS[r][c] &#043;&#061; rot(S[(r&#043;1)%4][(c&#043;2)%5], 17) \u2295 rot(S[(r&#043;2)%4][(c-1)%5], 31)<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u5bf9\u6d41\u7578\u53d8&#xff08;\u5217\u6df7\u5408&#xff09;&#xff1a;\u5de6\u4e58\u56fa\u5b9a\u00a0\u67ef\u897f4\u00d74\u77e9\u9635&#xff08;\u6a21\u00a0<span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123ac4aa.png\" width=\"25\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">&#xff0c;\u6240\u6709\u5143\u7d20\u4e3a\u5947\u6570&#xff0c;\u4fdd\u8bc1\u53ef\u9006&#xff09;\u3002<br \/>\n\u5373\u6bcf\u5217\u89c6\u4e3a\u5411\u91cf&#xff0c;\u4e58\u4ee5M_cauchy\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8f6c\u7f6e\u51b2\u51fb&#xff1a;\u4ea4\u6362\u7ef4\u5ea6\u00a0S[r][c] \u2194 S[c%4][r%5]&#xff08;4\u00d75 \u2192 5\u00d74&#xff0c;\u518d\u6563\u5217\u56de\u539f\u5f62\u72b6&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u6ce8\u5165\u5e38\u6570&#xff08;\u87ba\u65cb\u6da1&#xff09;&#xff1a;\u6bcf\u4e00\u5b57\u5f02\u6216\u8f6e\u5e38\u6570\u00a0<span style=\"color:black\">C<\/span><span style=\"color:black\">i<\/span><span style=\"color:black\">&#061;<\/span><span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><span style=\"color:black\">\u22c5<\/span><span style=\"color:black\">\u03c0\u22c5<\/span><span style=\"color:black\">i<\/span><span style=\"color:black\">2<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123b6138.png\" width=\"139\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u3002<\/span><\/span><\/li>\n<\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u63a8\u8350\u8f6e\u6570&#xff1a;24\u8f6e\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72ec\u7279\u4e4b\u5904&#xff1a;\u77e9\u9635\u4e58\u6cd5\u63d0\u4f9b\u5b8c\u5168\u7684\u4ee3\u6570\u6269\u6563&#xff0c;\u8f6c\u7f6e\u6253\u7834\u5b57\u8282\/\u5b57\u5bf9\u9f50&#xff0c;\u6297\u5dee\u5206\u80fd\u529b\u7b49\u4ef7\u4e8eMDS\u7801\u3002<\/span><\/span><\/li>\n<\/ul>\n<hr \/>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8bbe\u8ba1 2&#xff1a;\u57fa\u56e0\u7ec4\u526a\u63a5&#xff08;Genomic Splicing&#xff09;<\/span><\/span><\/p>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u7075\u611f\u6765\u6e90<\/span><span style=\"color:#0f1115\">&#xff1a;DNA\u7684\u78b1\u57fa\u914d\u5bf9\u3001\u79fb\u7801\u7a81\u53d8\u4e0e\u540c\u6e90\u91cd\u7ec4\u3002<br \/>\n\u8bbe\u8ba1\u54f2\u5b66&#xff1a;\u5c0620\u4e2a\u5b57\u89c6\u4e3a20\u6761\u201c\u67d3\u8272\u4f53\u201d\u3002\u7f6e\u6362\u5206\u4e3a\u201c\u590d\u5236-\u4ea4\u6362-\u79fb\u4f4d-\u7a81\u53d8\u201d&#xff0c;\u5229\u7528Feistel\u7f51\u4fdd\u8bc1\u53ef\u9006\u6027\u3002<\/span><\/span><\/p>\n<ul>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72b6\u6001\u5e03\u5c40&#xff1a;\u7ebf\u6027\u6570\u7ec4\u00a0X[0..19]\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8f6e\u51fd\u6570&#xff08;\u5355\u8f6e&#xff09;&#xff1a;<\/span><\/span>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u590d\u5236\u5b50&#xff08;\u9884\u6df7&#xff09;&#xff1a;T[i] &#061; X[i] \u2295 rot(X[(i&#043;1)%20], 7)\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u4ea4\u53c9\u4e92\u6362&#xff08;\u540c\u6e90\u91cd\u7ec4&#xff09;&#xff1a;\u4ea4\u6362\u00a0T[2i]\u00a0\u4e0e\u00a0T[19-2i]\u00a0\u7684\u9ad832\u4f4d&#xff08;i&#061;0..9&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u79fb\u7801\u7a81\u53d8&#xff08;\u52a8\u6001\u65cb\u8f6c&#xff09;&#xff1a;\u6bcf\u4e2a\u00a0T[i]\u00a0\u5faa\u73af\u5de6\u79fb\u00a0(i * 13 &#043; \u8f6e\u6570) % 64\u00a0\u4f4d\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u70b9\u7a81\u53d8&#xff08;Feistel\u6838&#xff09;&#xff1a;\u5c06\u6bcf\u4e2a\u5b57\u62c6\u4e3a\u00a0(L, R)\u00a0\u540432\u4f4d&#xff0c;\u6267\u884c\u53ef\u9006\u53d8\u6362&#xff1a;<br \/>\nL&#039; &#061; L &#043; f(R \u2295 \u8f6e\u5e38\u6570)&#xff0c;\u00a0R&#039; &#061; R &#043; g(L&#039;)&#xff0c;\u5176\u4e2d f\/g \u4e3a\u57fa\u4e8e\u9ec4\u91d1\u5206\u5272\u6bd4\u7684\u56fa\u5b9a\u4e58\u6cd5&#xff08;\u6a21\u00a0<span style=\"color:black\">2<\/span><span style=\"color:black\">32<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123bb585.png\" width=\"25\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u5168\u5c40\u6d17\u724c&#xff1a;X&#039;[i] &#061; T[(i * 19) % 20]&#xff08;\u4e58\u4ee519\u6a2120\u5b9e\u73b0\u8fd1\u4f3c\u5b8c\u7f8e\u6d17\u724c&#xff09;\u3002<\/span><\/span><\/li>\n<\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u63a8\u8350\u8f6e\u6570&#xff1a;18\u8f6e\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72ec\u7279\u4e4b\u5904&#xff1a;\u6df7\u5408\u534a\u5b57\u7ea7&#xff08;32\u4f4d&#xff09;\u4e0e\u5168\u5b57\u7ea7&#xff08;64\u4f4d&#xff09;\u64cd\u4f5c&#xff0c;\u79fb\u7801\u7a81\u53d8\u52a8\u6001\u4f9d\u8d56\u8f6e\u6570&#xff0c;\u6253\u7834\u5e73\u79fb\u5bf9\u79f0\u6027\u3002<\/span><\/span><\/li>\n<\/ul>\n<hr \/>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8bbe\u8ba1 3&#xff1a;\u6a21\u6570\u5171\u632f&#xff08;Modular Resonance&#xff09;<\/span><\/span><\/p>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u7075\u611f\u6765\u6e90<\/span><span style=\"color:#0f1115\">&#xff1a;\u58f0\u5b66\u4e2d\u7684\u9a7b\u6ce2\u5171\u632f\u4e0e\u6a21\u5f62\u5f0f&#xff08;\u692d\u5706\u66f2\u7ebfL-\u51fd\u6570&#xff09;\u3002<br \/>\n\u8bbe\u8ba1\u54f2\u5b66&#xff1a;\u5229\u7528\u591a\u91cd\u6a21\u4e58&#xff08;\u6a21\u00a0<\/span><span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><span style=\"color:black\">-1<\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123c1492.png\" width=\"55\" \/><span style=\"background-color:white\">\u00a0<span style=\"color:#0f1115\">\u548c\u6a21\u00a0<\/span><span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123c7627.png\" width=\"25\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">&#xff09;\u4ea7\u751f\u975e\u7ebf\u6027\u5171\u632f&#xff0c;\u518d\u901a\u8fc7\u201c\u62cd\u9891\u201d\u6269\u6563\u3002<\/span><\/span><\/p>\n<ul>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72b6\u6001\u5e03\u5c40&#xff1a;\u7ebf\u6027\u6570\u7ec4\u00a0X[0..19]\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8f6e\u51fd\u6570&#xff08;\u5355\u8f6e&#xff09;&#xff1a;<\/span><\/span>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8c10\u6ce2\u751f\u6210&#xff1a;Y[i] &#061; X[i] * P_i mod (2^64 &#8211; 1)&#xff0c;\u5176\u4e2d\u00a0<span style=\"color:black\">P<\/span><span style=\"color:black\">i<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123ccdc4.png\" width=\"15\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u00a0\u4e3a\u524d20\u4e2a\u5947\u7d20\u6570&#xff08;3,5,7&#8230;&#xff09;&#xff0c;\u7ed3\u679c0\u6620\u5c04\u4e3a\u00a02^64-1\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u62cd\u9891\u6df7\u5408&#xff08;\u5168\u5b57\u52a0\u6cd5&#xff09;&#xff1a;Z[i] &#061; Y[i] &#043; Y[(i&#043;\u03c6)%20] &#043; rot(Y[(i&#043;7)%20], 23)&#xff0c;\u5176\u4e2d \u03c6 \u4e3a\u9ec4\u91d1\u5206\u5272\u6bd4\u7684\u5c0f\u6570\u90e8\u5206\u4e58\u4ee520\u53d6\u6574&#xff08;\u537312&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u6d88\u76f8\u5e72&#xff08;\u4f4d\u4ea4\u6362&#xff09;&#xff1a;\u5bf9\u6bcf\u4e2a\u00a0Z[i]\u00a0\u5e94\u7528\u56fa\u5b9a\u4f4d\u6392\u5217&#xff0c;\u8be5\u6392\u5217\u7531\u00a0<span style=\"color:black\">2<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123d1eb4.png\" width=\"21\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u00a0\u7684\u4e8c\u8fdb\u5236\u5c55\u5f00\u524d64\u4f4d\u751f\u6210&#xff08;0\/1\u51b3\u5b9a\u4ea4\u6362\u76f8\u90bb\u6bd4\u7279\u5bf9&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u56de\u54cd\u7f6e\u6362&#xff1a;X&#039;[i] &#061; Z[i] \u2295 Z[(i*11)%20]&#xff08;\u5229\u7528\u4e58\u6cd5\u7fa4\u751f\u6210\u5143&#xff09;\u3002<\/span><\/span><\/li>\n<\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u63a8\u8350\u8f6e\u6570&#xff1a;16\u8f6e\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72ec\u7279\u4e4b\u5904&#xff1a;\u5229\u7528\u4e24\u4e2a\u4e0d\u540c\u7684\u6a21\u6570\u73af&#xff08;<span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123d6e37.png\" width=\"25\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u00a0\u4e0e\u00a0<span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><span style=\"color:black\">-1<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123dbd5f.png\" width=\"55\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">&#xff09;&#xff0c;\u907f\u514d\u6a21\u4e58\u540e\u4f4e\u4f4d\u96f6\u5316\u95ee\u9898&#xff1b;\u4f4d\u6392\u5217\u57fa\u4e8e\u65e0\u7406\u6570&#xff0c;\u98ce\u683c\u63a5\u8fd1\u201c\u6bd4\u7279\u5207\u7247\u201d\u4f46\u66f4\u968f\u673a\u3002<\/span><\/span><\/li>\n<\/ul>\n<hr \/>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8bbe\u8ba1 4&#xff1a;\u56db\u5143\u6570\u87ba\u65cb&#xff08;Quaternion Helix&#xff09;<\/span><\/span><\/p>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u7075\u611f\u6765\u6e90<\/span><span style=\"color:#0f1115\">&#xff1a;\u4e09\u7ef4\u7a7a\u95f4\u7684\u521a\u4f53\u65cb\u8f6c\u4e0e\u56db\u5143\u6570\u7fa4&#xff08;\u6c49\u5bc6\u5c14\u987f\u79ef&#xff09;\u3002<br \/>\n\u8bbe\u8ba1\u54f2\u5b66&#xff1a;\u5c0620\u4e2a\u5b57\u5206\u6210\u00a05\u4e2a\u56db\u5143\u6570&#xff08;\u6bcf\u4e2a\u5360\u75284\u4e2a\u5b57&#xff0c;\u5171256\u4f4d&#xff09;\u3002\u5229\u7528\u5355\u4f4d\u56db\u5143\u6570\u4e58\u6cd5\u8fdb\u884c\u201c\u4e07\u5411\u8282\u9501\u5b9a\u201d\u5f0f\u6df7\u6dc6&#xff0c;\u518d\u6cbf\u65f6\u95f4\u8f74\u87ba\u65cb\u524d\u8fdb\u3002<\/span><\/span><\/p>\n<ul>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72b6\u6001\u5e03\u5c40&#xff1a;Q[0..4]&#xff0c;\u5176\u4e2d\u00a0Q[k] &#061; (a, b, c, d)\u00a0\u540464\u4f4d\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8f6e\u51fd\u6570&#xff08;\u5355\u8f6e&#xff09;&#xff1a;<\/span><\/span>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u81ea\u65cb\u66f4\u65b0&#xff1a;\u56fa\u5b9a\u4e00\u4e2a\u4f9d\u8d56\u4e8e\u8f6e\u6570\u7684\u5355\u4f4d\u56db\u5143\u6570\u00a0<span style=\"color:black\">U<\/span><span style=\"color:black\">r<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123e0d4b.png\" width=\"19\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">&#xff08;\u5176\u5206\u91cf\u7531\u8f6e\u5e38\u6570\u53d6\u6a21\u00a0<span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123e6462.png\" width=\"25\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u00a0\u7684\u5947\u6570\u6784\u6210&#xff09;\u3002<br \/>\n\u8ba1\u7b97\u00a0Q[k] &#061; Q[k] \u2297 U_r&#xff08;\u6c49\u5bc6\u5c14\u987f\u4e58\u6cd5&#xff1a;a&#039; &#061; a*u_a &#8211; b*u_b &#8211; c*u_c &#8211; d*u_d&#xff0c;\u6ce8\u610f\u6a21\u00a0<span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123eb8f9.png\" width=\"25\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u00a0\u4e0b\u7684\u52a0\u51cf&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u94fe\u5f0f\u8026\u5408&#xff08;\u9f7f\u8f6e\u54ac\u5408&#xff09;&#xff1a;<br \/>\nQ[k].a &#043;&#061; rot(Q[(k&#043;1)%5].b, 11)<br \/>\nQ[k].b ^&#061; rot(Q[(k&#043;2)%5].c, 19)<br \/>\nQ[k].c &#043;&#061; rot(Q[(k&#043;3)%5].d, 29)<br \/>\nQ[k].d ^&#061; rot(Q[(k&#043;4)%5].a, 37)<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u87ba\u65cb\u538b\u7d27&#xff1a;\u5c06\u6574\u4e2a20\u5b57\u72b6\u6001\u5faa\u73af\u5de6\u79fb\u00a01\u4e2a\u5b57&#xff08;\u5373\u00a0X&#039;[i] &#061; X[(i&#043;1)%20]&#xff09;&#xff0c;\u6a21\u62dfDNA\u87ba\u65cb\u4e0a\u5347\u3002<\/span><\/span><\/li>\n<\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u63a8\u8350\u8f6e\u6570&#xff1a;20\u8f6e\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72ec\u7279\u4e4b\u5904&#xff1a;\u56db\u5143\u6570\u4e58\u6cd5\u63d0\u4f9b\u6781\u5f3a\u7684\u8de8\u5b57\u975e\u7ebf\u6027&#xff08;\u4ea4\u53c9\u76f8\u4e58&#xff09;&#xff0c;\u4e14\u5929\u7136\u5177\u6709\u4ee3\u6570\u7ed3\u6784&#xff1b;\u87ba\u65cb\u79fb\u4f4d\u4fdd\u8bc1\u72b6\u6001\u6bcf\u4e2a\u5b57\u8282\u572820\u8f6e\u5185\u904d\u5386\u6240\u6709\u4f4d\u7f6e\u3002<\/span><\/span><\/li>\n<\/ul>\n<hr \/>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8bbe\u8ba1 5&#xff1a;\u5206\u5f62\u6c99\u5806&#xff08;Fractal Sandpile&#xff09;<\/span><\/span><\/p>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u7075\u611f\u6765\u6e90<\/span><span style=\"color:#0f1115\">&#xff1a;\u963f\u8d1d\u5c14\u6c99\u5806\u6a21\u578b&#xff08;Abelian Sandpile&#xff09;\u4e0e\u8c22\u5c14\u5bbe\u65af\u57fa\u4e09\u89d2\u5f62\u3002<br \/>\n\u8bbe\u8ba1\u54f2\u5b66&#xff1a;\u6838\u5fc3\u662f\u201c\u5d29\u584c\u6269\u6563\u201d\u2014\u2014\u5f53\u4e00\u4e2a\u5b57\u7684\u67d0\u4e2a\u9ad8\u4f4d\u88ab\u89e6\u53d1\u65f6&#xff0c;\u5c06\u201c\u6c99\u7c92\u201d\u5411\u76f8\u90bb\u5b57\u4f20\u64ad&#xff0c;\u7ed3\u5408\u5143\u80de\u81ea\u52a8\u673a\u7684\u89c4\u521990\u3002<\/span><\/span><\/p>\n<ul>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72b6\u6001\u5e03\u5c40&#xff1a;\u7ebf\u6027\u6570\u7ec4\u00a0X[0..19]\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8f6e\u51fd\u6570&#xff08;\u5355\u8f6e&#xff09;&#xff1a;<\/span><\/span>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u8bf1\u53d1\u5d29\u584c&#xff08;\u975e\u7ebf\u6027\u9608\u503c&#xff09;&#xff1a;<br \/>\n\u8ba1\u7b97\u00a0T[i] &#061; X[i] &#043; (X[(i-1)%20] &gt;&gt; 3) &#043; (X[(i&#043;1)%20] &lt;&lt; 2)\u00a0&#xff08;\u6a21\u00a0<span style=\"color:black\">2<\/span><span style=\"color:black\">64<\/span><\/span><\/span><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105739-6ac23123f12d3.png\" width=\"25\" \/><span style=\"background-color:white\"><span style=\"color:#0f1115\">&#xff09;\u3002\u6b64\u6b65\u6a21\u62df\u76f8\u90bb\u6c99\u5806\u53e0\u52a0\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u96ea\u5d29\u4f20\u64ad&#xff08;\u89c4\u521990\u53d8\u5f62&#xff09;&#xff1a;<br \/>\nU[i] &#061; T[i] \u2295 rot(T[(i-2)%20], 5) \u2295 rot(T[(i&#043;2)%20], 11)&#xff08;\u5373\u53ea\u4e0e\u6b21\u8fd1\u90bb\u5f02\u6216&#xff0c;\u4ea7\u751f\u5206\u5f62\u56fe\u6848&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u5168\u5c40\u91cd\u6392&#xff08;\u5e0c\u5c14\u4f2f\u7279\u66f2\u7ebf&#xff09;&#xff1a;\u6839\u636e\u9884\u5148\u8ba1\u7b97\u768420\u4e2a\u56fa\u5b9a\u70b9\u7684\u683c\u96f7\u7801\u6620\u5c04&#xff0c;\u5c06\u00a0U[i]\u00a0\u9001\u5165\u00a0V[perm[i]]&#xff08;\u8be5\u6620\u5c04\u4f7f\u8fde\u7eed\u7d22\u5f15\u7684\u6c49\u660e\u8ddd\u79bb\u6700\u5927\u5316&#xff09;\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u9759\u6469\u64e6\u5e38\u6570\u52a0&#xff1a;X&#039;[i] &#061; V[i] &#043; C_{\u8f6e\u6570, i}&#xff0c;\u5176\u4e2d\u5e38\u6570\u4e3a\u524d20\u4e2a\u8d28\u6570\u7684\u5e73\u65b9\u6839\u5c0f\u6570\u90e8\u5206\u3002<\/span><\/span><\/li>\n<\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u63a8\u8350\u8f6e\u6570&#xff1a;22\u8f6e\u3002<\/span><\/span><\/li>\n<li style=\"text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u72ec\u7279\u4e4b\u5904&#xff1a;\u5229\u7528\u79fb\u4f4d\u4e0e\u52a0\u6cd5\u5b9e\u73b0\u201c\u62df\u6df7\u6c8c\u201d\u7684\u6c99\u5806\u52a8\u529b\u5b66&#xff0c;\u4e0e\u5e38\u89c1XOR\/AND\u903b\u8f91\u622a\u7136\u4e0d\u540c&#xff1b;\u683c\u96f7\u7801\u7f6e\u6362\u4f7f\u76f8\u90bb\u5b57\u5728\u7a7a\u95f4\u4e0a\u6781\u5ea6\u5206\u79bb&#xff0c;\u6269\u6563\u901f\u5ea6\u6781\u5feb\u3002<\/span><\/span><\/li>\n<\/ul>\n<hr \/>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span style=\"background-color:white\"><span style=\"color:#0f1115\">\u603b\u7ed3\u5bf9\u6bd4\u8868<\/span><\/span><\/p>\n<table cellspacing=\"0\">\n<tr>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u8bbe\u8ba1\u540d\u79f0<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u6838\u5fc3\u4ee3\u6570\u7ed3\u6784<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u6700\u72ec\u7279\u7684\u975e\u7ebf\u6027\u6e90<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u8f6e\u6570<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u6f5c\u5728\u5f31\u70b9\u89c4\u907f<\/p>\n<\/td>\n<\/tr>\n<tbody>\n<tr>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u62d3\u6251\u6da1\u65cb<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u67ef\u897f\u77e9\u9635 &#043; \u6a21\u52a0<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u4ee3\u6570MDS\u6269\u6563&#xff08;\u975eS\u76d2&#xff09;<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">24<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u89c4\u907f\u4e86\u7ebf\u6027\u5c42\u8fc7\u6162\u7684\u95ee\u9898<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u57fa\u56e0\u7ec4\u526a\u63a5<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">Feistel &#043; \u534a\u5b57\u91cd\u7ec4<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">32\/64\u4f4d\u6df7\u5408\u52a8\u6001\u65cb\u8f6c<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">18<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u89c4\u907f\u4e86\u5168\u5b57\u56fa\u5b9a\u65cb\u8f6c\u7684\u6ed1\u52a8\u653b\u51fb<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u6a21\u6570\u5171\u632f<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u53cc\u6a21\u4e58 &#043; \u4f4d\u4ea4\u6362<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u6a21\u00a0264-1<img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105740-6ac2312403650.png\" width=\"55\" \/>\u00a0\u7684\u4e58\u6cd5\u7fa4<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">16<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u89c4\u907f\u4e86\u6a21\u00a0264<img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"26\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/10\/20261004105740-6ac23124099b4.png\" width=\"25\" \/>\u00a0\u4e58\u6cd5\u4f4e\u4f4d\u53ef\u9884\u6d4b\u6027<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u56db\u5143\u6570\u87ba\u65cb<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u6c49\u5bc6\u5c14\u987f\u79ef<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u56db\u5143\u6570\u4ea4\u53c9\u9879&#xff08;4\u7ef4\u8026\u5408&#xff09;<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">20<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u89c4\u907f\u4e86\u9010\u5b57\u6216\u9010\u5217\u7684\u5e73\u9762\u6269\u6563<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u5206\u5f62\u6c99\u5806<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u52a0\u6cd5\u8fdb\u4f4d &#043; \u6b21\u8fd1\u90bbXOR<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u4eff\u751f\u201c\u5d29\u584c\u201d\u9608\u503c\u6548\u5e94<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">22<\/p>\n<\/td>\n<td>\n<p style=\"margin-left:0;margin-right:0;text-align:left\">\u89c4\u907f\u4e86\u7eaf\u7ebf\u6027\u53cd\u9988\u79fb\u4f4d\u5bc4\u5b58\u5668\u7684\u5468\u671f\u6027<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"margin-left:0;margin-right:0;text-align:left\"><span 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