{"id":350,"date":"2022-06-19T17:58:42","date_gmt":"2022-06-19T09:58:42","guid":{"rendered":"http:\/\/127.0.0.1\/?p=350"},"modified":"2022-06-19T17:58:43","modified_gmt":"2022-06-19T09:58:43","slug":"%e4%bd%bf%e7%94%a8%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e7%a0%b4%e8%a7%a3%e9%9a%8f%e6%9c%ba%e6%95%b0%e7%94%9f%e6%88%90%e5%99%a8-%e7%ac%ac-1-%e9%83%a8%e5%88%86%ef%bc%9axorshift128","status":"publish","type":"post","link":"https:\/\/rngrb.com\/?p=350","title":{"rendered":"\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u7834\u89e3\u968f\u673a\u6570\u751f\u6210\u5668 &#8211; \u7b2c 1 \u90e8\u5206\uff1axorshift128"},"content":{"rendered":"<div class='booster-block booster-read-block'>\r\n                <div class=\"twp-read-time\">\r\n                \t<i class=\"booster-icon twp-clock\"><\/i> <span>Read Time:<\/span>5 Minute, 39 Second                <\/div>\r\n\r\n            <\/div>\n<h2 class=\"wp-block-heading\">\u5927\u7eb2<\/h2>\n\n\n\n<ul class=\"has-medium-font-size wp-block-list\"><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#1.\">\u4e00\u3001\u7b80\u4ecb<\/a><\/li><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#2.\">2. xorshift128 PRNG \u662f\u5982\u4f55\u5de5\u4f5c\u7684\uff1f<\/a><\/li><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#3.\">3. \u795e\u7ecf\u7f51\u7edc\u548c\u5f02\u6216\u95e8<\/a><\/li><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#4.\">4. \u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u5bf9 xorshift128 PRNG \u8fdb\u884c\u5efa\u6a21<\/a><ul><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#4.1\">4.1 \u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u8bbe\u8ba1<\/a><\/li><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#4.2\">4.2 \u6a21\u578b\u7ed3\u679c<\/a><\/li><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#4.3\">4.3 \u6a21\u578b\u6df1\u6f5c<\/a><\/li><\/ul><\/li><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#5.\">5. \u521b\u5efa\u6297\u673a\u5668\u5b66\u4e60\u7248\u672c\u7684 xorshift128<\/a><\/li><li><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#6.\">\u516d\uff0c\u7ed3\u8bba<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1.\">\u4e00\u3001\u7b80\u4ecb<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u8fd9\u7bc7\u535a\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u7834\u89e3\u4f2a\u968f\u673a\u6570\u751f\u6210\u5668 (PRNG) \u7684\u65b9\u6cd5\u3002\u5728\u8fd9\u91cc\u7834\u89e3\uff0c\u6211\u4eec\u7684\u610f\u601d\u662f\u6211\u4eec\u53ef\u4ee5\u5728\u4e0d\u77e5\u9053\u79cd\u5b50\u7684\u60c5\u51b5\u4e0b\u4f7f\u7528\u5148\u524d\u751f\u6210\u7684\u6570\u5b57\u6765\u9884\u6d4b\u968f\u673a\u6570\u7684\u5e8f\u5217\u3002\u6211\u4eec\u9996\u5148\u6253\u7834\u4e86\u4e00\u4e2a\u7b80\u5355\u7684 PRNG\uff0c\u5373 XORShift\uff0c\u9075\u5faa\u53d1\u8868\u5728<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">[1]<\/a>\u4e2d\u7684\u5e16\u5b50\u3002\u6211\u4eec\u4ece\u90a3\u7bc7\u6587\u7ae0\u4e2d\u63d0\u51fa\u7684\u6a21\u578b\u4e2d\u7b80\u5316\u4e86\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u7684\u7ed3\u6784\u3002\u6b64\u5916\uff0c\u6211\u4eec\u5b9e\u73b0\u4e86\u66f4\u9ad8\u7684\u51c6\u786e\u5ea6\u3002\u672c\u535a\u5ba2\u65e8\u5728\u5c55\u793a\u5982\u4f55\u8bad\u7ec3\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u53ef\u4ee5\u5728\u4e0d\u77e5\u9053\u79cd\u5b50\u7684\u60c5\u51b5\u4e0b\u751f\u6210\u968f\u673a\u6570\u65f6\u8fbe\u5230 100% \u7684\u51c6\u786e\u7387\u3002\u6211\u4eec\u8fd8\u6df1\u5165\u7814\u7a76\u4e86\u7ecf\u8fc7\u8bad\u7ec3\u7684\u6a21\u578b\uff0c\u4ee5\u5c55\u793a\u5b83\u662f\u5982\u4f55\u5de5\u4f5c\u7684\uff0c\u5e76\u4ece\u4e2d\u63d0\u53d6\u6709\u7528\u7684\u4fe1\u606f\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u5728\u63d0\u5230\u7684\u535a\u5ba2\u6587\u7ae0<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">[1] \u4e2d\uff0c<\/a>\u4f5c\u8005\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u5728\u6ca1\u6709 PRNG \u79cd\u5b50\u7684\u60c5\u51b5\u4e0b\u4ee5\u9ad8\u7cbe\u5ea6\u590d\u5236\u4e86<em><strong>xorshift128 PRNG \u5e8f\u5217\u3002<\/strong><\/em>\u8bad\u7ec3\u540e\uff0c\u8be5\u6a21\u578b\u53ef\u4ee5\u4f7f\u7528\u4efb\u610f\u8fde\u7eed\u56db\u4e2a\u751f\u6210\u7684\u6570\u5b57\u6765\u590d\u5236\u76f8\u540c\u7684 PRNG \u5e8f\u5217\uff0c\u5e76\u4e14\u6309\u4f4d\u7cbe\u5ea6\u5927\u4e8e 95%\u3002\u8be5\u5b9e\u9a8c\u7684\u5b9e\u65bd\u7ec6\u8282\u548c\u6700\u4f73\u8bad\u7ec3\u6a21\u578b\u53ef\u4ee5\u5728<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[2]\">[2]<\/a>\u4e2d\u627e\u5230\u3002&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u4e4d\u4e00\u770b\uff0c\u8fd9\u4f3c\u4e4e\u6709\u70b9\u8fdd\u53cd\u76f4\u89c9\uff0c\u56e0\u4e3a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u80cc\u540e\u7684\u6574\u4e2a\u60f3\u6cd5\u662f\u4ece\u6570\u636e\u4e2d\u7684\u6a21\u5f0f\u4e2d\u5b66\u4e60\u4ee5\u6267\u884c\u7279\u5b9a\u4efb\u52a1\uff0c\u8303\u56f4\u4ece\u76d1\u7763\u5b66\u4e60\u3001\u65e0\u76d1\u7763\u5b66\u4e60\u5230\u5f3a\u5316\u5b66\u4e60\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u4f2a\u968f\u673a\u6570\u751f\u6210\u5668\u7684\u4e3b\u8981\u601d\u60f3\u662f\u751f\u6210\u968f\u673a\u5e8f\u5217\uff0c\u56e0\u6b64\u8fd9\u4e9b\u5e8f\u5217\u4e0d\u5e94\u8be5\u9075\u5faa\u4efb\u4f55\u6a21\u5f0f\u3002\u56e0\u6b64\uff0c\uff08\u4e00\u5f00\u59cb\uff09\u8bad\u7ec3\u4e00\u4e2a\u4ece\u6570\u636e\u6a21\u5f0f\u4e2d\u5b66\u4e60\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff08\u4ece\u4e0d\u5e94\u8be5\u9075\u5faa\u4efb\u4f55\u6a21\u5f0f\u7684 PRNG \u4e2d\u5b66\u4e60\uff09\u6ca1\u6709\u4efb\u4f55\u610f\u4e49\u3002\u4e0d\u4ec5\u5b66\u4e60\uff0c\u800c\u4e14\u83b7\u5f97 95% \u7684\u4f4d\u7cbe\u5ea6\uff0c\u8fd9\u610f\u5473\u7740\u8be5\u6a21\u578b\u5c06\u751f\u6210 PRNG \u7684\u7cbe\u786e\u8f93\u51fa\uff0c\u5e76\u4e14\u5e73\u5747\u53ea\u4f1a\u51fa\u9519\u4e24\u4f4d\u3002\u6240\u4ee5\uff0c\u8fd9\u600e\u4e48\u53ef\u80fd\uff1f\u4e3a\u4ec0\u4e48\u673a\u5668\u5b66\u4e60\u53ef\u4ee5\u7834\u89e3 PRNG\uff1f\u6211\u4eec\u751a\u81f3\u53ef\u4ee5\u6bd4 95% \u7684\u4f4d\u7cbe\u5ea6\u66f4\u597d\u5417\uff1f\u8fd9\u5c31\u662f\u6211\u4eec\u5c06\u5728\u672c\u6587\u5176\u4f59\u90e8\u5206\u8ba8\u8bba\u7684\u5185\u5bb9\u3002\u8ba9\u6211\u4eec\u9996\u5148\u68c0\u67e5 xorshift128 \u7b97\u6cd5\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\">**<strong><em>\u7f16\u8005\u6ce8\uff1a\u8fd9\u4e0e\u5b89\u5168\u6027\u6709\u4f55\u5173\u7cfb\uff1f\u867d\u7136\u8fd9\u9879\u7814\u7a76\u7740\u773c\u4e8e\u975e\u52a0\u5bc6 PRNG\uff0c\u4f46\u6211\u4eec\u4e00\u822c\u6709\u5174\u8da3\u4e86\u89e3\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684\u65b9\u6cd5\u5982\u4f55\u5728\u5047\u5b9a\u751f\u6210\u968f\u673a\u8f93\u51fa\u7684\u51fd\u6570\u4e2d\u67e5\u627e\u6f5c\u5728\u6a21\u5f0f\uff0c\u8fd9\u662f\u5c1d\u8bd5\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u7684\u5148\u51b3\u6761\u4ef6\u5728\u5bc6\u7801\uff08P\uff09RNG \u4e2d\u627e\u5230\u4ee5\u524d\u672a\u77e5\u7684\u6a21\u5f0f\uff0c\u56e0\u4e3a\u8fd9\u53ef\u80fd\u4f1a\u4f5c\u4e3a\u5bf9\u8fd9\u4e9b\u51fd\u6570\u8fdb\u884c\u5bc6\u7801\u5206\u6790\u7684\u6709\u8da3\u8865\u5145\u65b9\u6cd5\u3002\u5728\u8fd9\u91cc\uff0c\u6211\u4eec\u5c55\u793a\u4e86\u6211\u4eec\u5f00\u59cb\u63a2\u7d22\u8fd9\u4e2a\u7a7a\u95f4\u7684\u5de5\u4f5c\u3002**<\/em><\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2.\">2. xorshift128 PRNG \u662f\u5982\u4f55\u5de5\u4f5c\u7684\uff1f<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u8981\u4e86\u89e3\u673a\u5668\u5b66\u4e60 (ML) \u662f\u5426\u53ef\u4ee5\u7834\u89e3 xorshift128 PRNG\uff0c\u6211\u4eec\u9700\u8981\u4e86\u89e3\u5b83\u7684\u5de5\u4f5c\u539f\u7406\u5e76\u68c0\u67e5\u5b83\u662f\u5426\u9075\u5faa\u4efb\u4f55\u6a21\u5f0f\u3002\u8ba9\u6211\u4eec\u4ece\u6df1\u5165\u7814\u7a76 xorshift128 PRNG \u7b97\u6cd5\u7684\u5b9e\u73b0\u5f00\u59cb\uff0c\u4e86\u89e3\u5b83\u662f\u5982\u4f55\u5de5\u4f5c\u7684\u3002\u8be5\u7b97\u6cd5\u7684\u4ee3\u7801\u5b9e\u73b0\u53ef\u4ee5\u5728 Wikipedia \u4e0a\u627e\u5230\u5e76\u5728<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[2]\">[2]<\/a>\u4e2d\u5171\u4eab\u3002\u8fd9\u662f repo \u4e2d\u7528\u4e8e\u751f\u6210 PRNG \u5e8f\u5217\uff08\u7528\u4e8e\u8bad\u7ec3 ML \u6a21\u578b\uff09\u7684\u51fd\u6570\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code has-medium-font-size\"><code>def xorshift128():\n    '''xorshift\n    https:&#47;&#47;ja.wikipedia.org\/wiki\/Xorshift\n    '''\n\n    x = 123456789\n    y = 362436069\n    z = 521288629\n    w = 88675123\n\n    def _random():\n        nonlocal x, y, z, w\n        t = x ^ ((x &lt;&lt; 11) &amp; 0xFFFFFFFF)  # 32bit\n        x, y, z = y, z, w\n        w = (w ^ (w &gt;&gt; 19)) ^ (t ^ (t &gt;&gt; 8))\n        return w\n\n    return _random<\/code><\/pre>\n\n\n\n<p class=\"has-medium-font-size\">\u4ece\u4ee3\u7801\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\uff0c\u5b9e\u73b0\u5f88\u7b80\u5355\u3002\u5b83\u6709\u56db\u4e2a\u5185\u90e8\u6570\u5b57\uff0c<strong>x\u3001y\u3001z<\/strong>\u548c<strong>w\uff0c<\/strong>\u540c\u65f6\u4ee3\u8868\u79cd\u5b50\u548c PRNG \u7684\u72b6\u6001\u3002\u5f53\u7136\uff0c\u6211\u4eec\u53ef\u4ee5\u66f4\u65b0\u8fd9\u4e2a\u751f\u6210\u5668\u5b9e\u73b0\uff0c\u4e3a\u79cd\u5b50\u63d0\u4f9b\u4e0d\u540c\u7684\u51fd\u6570\u8c03\u7528\uff0c\u800c\u4e0d\u662f\u5bf9\u5176\u8fdb\u884c\u786c\u7f16\u7801\u3002\u6bcf\u6b21\u6211\u4eec\u8c03\u7528\u751f\u6210\u5668\u65f6\uff0c\u5b83\u90fd\u4f1a\u6309\u5982\u4e0b\u65b9\u5f0f\u79fb\u52a8\u5185\u90e8\u53d8\u91cf\uff1a<strong>y \u2192 x<\/strong>\uff0c<strong>z \u2192 y<\/strong>\u548c<strong>w \u2192 z<\/strong>\u3002<strong>w<\/strong>\u7684\u65b0\u503c&nbsp;\u662f\u901a\u8fc7\u5bf9<strong>x<\/strong>\u548c<strong>w<\/strong>&nbsp;\u7684\u65e7\u503c\u5e94\u7528\u4e00\u4e9b\u4f4d\u64cd\u4f5c\uff08\u79fb\u4f4d\u548c\u5f02\u6216\uff09\u6765\u8bc4\u4f30\u7684\u3002\u65b0\u7684<strong>w<\/strong>\u7136\u540e\u4f5c\u4e3a\u968f\u673a\u6570\u751f\u6210\u5668\u7684\u65b0\u968f\u673a\u6570\u8f93\u51fa\u8fd4\u56de\u3002\u8ba9\u6211\u4eec\u8c03\u7528\u51fd\u6570\u8f93\u51fa<strong>o<\/strong>\u3002&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u4f7f\u7528\u6b64\u4ee3\u7801\uff0c\u6211\u4eec\u53ef\u4ee5\u5bfc\u51fa\u8f93\u51fa\u7684\u6bcf\u4e2a\u4f4d\u7684\u903b\u8f91\u8868\u8fbe\u5f0f\uff0c\u8fd9\u5bfc\u81f4\u6211\u4eec\u5f97\u5230\u8f93\u51fa\u7684\u4ee5\u4e0b\u8f93\u51fa\u4f4d\u8868\u793a<strong>o<\/strong>\uff1a<\/p>\n\n\n\n<p>O&nbsp;<sub>0<\/sub>&nbsp;= W&nbsp;<sub>0<\/sub>&nbsp;^ W&nbsp;<sub>19<\/sub>&nbsp;^ X&nbsp;<sub>0<\/sub>&nbsp;^ X&nbsp;<sub>8<\/sub><\/p>\n\n\n\n<p class=\"has-medium-font-size\">O&nbsp;<sub>1<\/sub>&nbsp;= W&nbsp;<sub>1<\/sub>&nbsp;^ W&nbsp;<sub>20<\/sub>&nbsp;^ X&nbsp;<sub>1<\/sub>&nbsp;^ X&nbsp;<sub>9<\/sub><\/p>\n\n\n\n<p>.<\/p>\n\n\n\n<p>.<\/p>\n\n\n\n<p class=\"has-medium-font-size\">O&nbsp;<sub>31<\/sub>&nbsp;= W&nbsp;<sub>31<\/sub>&nbsp;^ X&nbsp;<sub>20<\/sub>&nbsp;&nbsp;^ X&nbsp;<sub>31<\/sub><\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u5176\u4e2d O&nbsp;<sub>i<\/sub>\u662f\u8f93\u51fa\u7684\u7b2c i<sup>\u4f4d<\/sup>\uff0c\u7b26\u53f7<strong>^<\/strong>\u662f\u6309\u4f4d\u5f02\u6216\u3002\u8be5\u7b97\u6cd5\u7684\u793a\u610f\u56fe\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"623\" height=\"801\" src=\"http:\/\/127.0.0.1\/wp-content\/uploads\/2022\/06\/img1-1.webp\" alt=\"\" class=\"wp-image-351\" srcset=\"https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img1-1.webp 623w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img1-1-233x300.webp 233w\" sizes=\"auto, (max-width: 623px) 100vw, 623px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-medium-font-size\">\u6211\u4eec\u53ef\u4ee5\u4ece\u8fd9\u4e2a\u7b97\u6cd5\u4e2d\u6ce8\u610f\u5230\uff0c\u6211\u4eec\u53ea\u9700\u8981<strong>w<\/strong>\u548c<strong>x<\/strong>\u6765\u751f\u6210\u4e0b\u4e00\u4e2a\u968f\u673a\u6570\u8f93\u51fa\u3002\u5f53\u7136\uff0c\u6211\u4eec\u9700\u8981<strong>y<\/strong>\u548c<strong>z<\/strong>\u6765\u751f\u6210\u968f\u673a\u6570\uff0c\u4f46\u662f<strong>o<\/strong>\u7684\u503c\u4ec5\u53d6\u51b3\u4e8e<strong>x<\/strong>\u548c<strong>w<\/strong>\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u6240\u4ee5\u5728\u7406\u89e3\u4e86\u7b97\u6cd5\u4e4b\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u6700\u540e\u56db\u4e2a\u751f\u6210\u7684\u6570\u5b57\u548c\u4e0b\u4e00\u4e2a\u4e4b\u95f4\u7684\u7b80\u5355\u5173\u7cfb\u3002\u56e0\u6b64\uff0c\u5982\u679c\u6211\u4eec\u77e5\u9053\u8fd9\u4e2a PRNG \u751f\u6210\u7684\u6700\u540e\u56db\u4e2a\u6570\u5b57\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u8be5\u7b97\u6cd5\u751f\u6210\u6574\u4e2a\u5e8f\u5217\uff1b\u8fd9\u53ef\u80fd\u662f\u8be5\u7b97\u6cd5\u5728\u5bc6\u7801\u5b66\u4e0a\u4e0d\u5b89\u5168\u7684\u4e3b\u8981\u539f\u56e0\u3002\u5c3d\u7ba1\u7b97\u6cd5\u751f\u6210\u7684\u6570\u5b57\u4f3c\u4e4e\u662f\u968f\u673a\u7684\uff0c\u5b83\u4eec\u4e4b\u95f4\u6ca1\u6709\u660e\u786e\u7684\u5173\u7cfb\uff0c\u4f46\u5177\u6709\u7b97\u6cd5\u77e5\u8bc6\u7684\u653b\u51fb\u8005\u53ef\u4ee5\u4f7f\u7528\u4efb\u610f\u56db\u4e2a\u8fde\u7eed\u751f\u6210\u7684\u6570\u5b57\u6765\u9884\u6d4b xorshift128 \u7684\u6574\u4e2a\u5e8f\u5217\u3002\u7531\u4e8e\u8fd9\u7bc7\u6587\u7ae0\u7684\u76ee\u7684\u662f\u5c55\u793a ML \u6a21\u578b\u5982\u4f55\u5b66\u4e60\u6837\u672c PRNG \u4e2d\u7684\u9690\u85cf\u5173\u7cfb\uff0c\u6211\u4eec\u5047\u8bbe\u6211\u4eec\u53ea\u77e5\u9053\u65b0\u751f\u6210\u7684\u6570\u5b57\u4e0e\u5176\u540e\u56db\u4e2a\u6570\u5b57\u4e4b\u95f4\u5b58\u5728\u67d0\u79cd\u5173\u7cfb\uff0c\u800c\u4e0d\u77e5\u9053\u7b97\u6cd5\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u7a0d\u5fae\u56de\u5230\u4e3b\u8981\u95ee\u9898\uff1a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u80fd\u5426\u5728\u4e0d\u77e5\u9053\u5176\u5b9e\u73b0\u7684\u60c5\u51b5\u4e0b\u4ec5\u4f7f\u7528\u6700\u540e\u56db\u4e2a\u8f93\u5165\u6765\u5b66\u4e60\u751f\u6210 xorshift128 PRNG \u5e8f\u5217\uff1f<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u4e3a\u4e86\u56de\u7b54\u8fd9\u4e2a\u95ee\u9898\uff0c\u8ba9\u6211\u4eec\u9996\u5148\u4ecb\u7ecd\u4e00\u4e0b\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff08\u7b80\u79f0 ANN \u6216 NN\uff09\u4ee5\u53ca\u5b83\u4eec\u5982\u4f55\u5bf9 XOR \u95e8\u8fdb\u884c\u5efa\u6a21\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3.\">3. \u795e\u7ecf\u7f51\u7edc\u548c\u5f02\u6216\u95e8<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u795e\u7ecf\u7f51\u7edc (NN)\uff0c\u53c8\u540d\u591a\u5c42\u611f\u77e5\u5668 (MLP)\uff0c\u662f\u6700\u5e38\u7528\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u4e4b\u4e00\u3002\u5b83\u7531\u79f0\u4e3a\u795e\u7ecf\u5143\u6216\u611f\u77e5\u5668\u7684\u5c0f\u578b\u8ba1\u7b97\u5355\u5143\u7ec4\u6210\uff0c\u5b83\u4eec\u88ab\u7ec4\u7ec7\u6210\u4e00\u7ec4\u672a\u8fde\u63a5\u7684\u795e\u7ecf\u5143\uff0c\u79f0\u4e3a\u5c42\u3002\u8fd9\u4e9b\u5c42\u76f8\u4e92\u8fde\u63a5\u4ee5\u5f62\u6210\u4ece NN \u7684\u8f93\u5165\u5230\u5176\u8f93\u51fa\u7684\u8def\u5f84\u3002\u4e0b\u56fe\u662f2\u5c42NN\u7684\u7b80\u5355\u4f8b\u5b50\uff08\u8f93\u5165\u5c42\u4e0d\u8ba1\uff09\u3002NN \u7684\u6570\u5b66\u516c\u5f0f\u7684\u7ec6\u8282\u8d85\u51fa\u4e86\u672c\u6587\u7684\u8303\u56f4\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"268\" src=\"http:\/\/127.0.0.1\/wp-content\/uploads\/2022\/06\/Screen.webp\" alt=\"\" class=\"wp-image-352\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-medium-font-size\">\u5728\u4ece\u8f93\u5165\u6570\u636e\u8bad\u7ec3 NN \u65f6\uff0c<strong>\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u8fde\u63a5<\/strong>\uff08\u5373<strong>\u6743\u91cd<\/strong>\uff09\u8981\u4e48\u53d8\u5f97\u66f4\u5f3a\uff08\u9ad8\u6b63\u503c\u6216\u4f4e\u8d1f\u503c\uff09\u4ee5\u8868\u793a\u4e24\u4e2a\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u9ad8\u6b63\/\u8d1f\u5f3a\u8fde\u63a5\uff0c\u8981\u4e48\u53d8\u5f97\u66f4\u5f31\uff08\u63a5\u8fd10) \u8868\u793a\u5b8c\u5168\u6ca1\u6709\u8054\u7cfb\u3002\u5728\u8bad\u7ec3\u7ed3\u675f\u65f6\uff0c\u8fd9\u4e9b\u8fde\u63a5\/\u6743\u91cd\u5bf9\u5b58\u50a8\u5728 NN \u6a21\u578b\u4e2d\u7684\u77e5\u8bc6\u8fdb\u884c\u7f16\u7801\u3002&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u7528\u4e8e\u63cf\u8ff0 NN \u5982\u4f55\u5904\u7406\u975e\u7ebf\u6027\u6570\u636e\u7684\u4e00\u4e2a\u793a\u4f8b\u662f NN \u7528\u4e8e\u5bf9\u53cc\u8f93\u5165 XOR \u95e8\u8fdb\u884c\u5efa\u6a21\u3002\u9009\u62e9\u4e8c\u8f93\u5165\u5f02\u6216\u51fd\u6570\u7684\u4e3b\u8981\u539f\u56e0\u662f\uff0c\u867d\u7136\u5b83\u5f88\u7b80\u5355\uff0c\u4f46\u5b83\u7684\u8f93\u51fa\u4e0d\u662f\u7ebf\u6027\u53ef\u5206\u7684<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[3]\">[3]<\/a>\u3002\u56e0\u6b64\uff0c\u4f7f\u7528\u5177\u6709\u4e24\u5c42\u7684 NN \u662f\u8868\u793a\u4e24\u4e2a\u8f93\u5165 XOR \u95e8\u7684\u6700\u4f73\u65b9\u5f0f\u3002\u4e0b\u56fe\uff08\u6765\u81ea<a href=\"https:\/\/blog.abhranil.net\/2015\/03\/03\/training-neural-networks-with-genetic-algorithms\/\">Abhranil \u535a\u5ba2<\/a>&nbsp;<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[3]\">[3]<\/a>\uff09\u663e\u793a\u4e86\u6211\u4eec\u5982\u4f55\u4f7f\u7528\u4e24\u5c42\u795e\u7ecf\u7f51\u7edc\u6765\u6a21\u62df\u53cc\u8f93\u5165 XOR\u3002\u7ebf\u4e0a\u7684\u6570\u5b57\u662f\u6743\u91cd\uff0c\u8282\u70b9\u5185\u7684\u6570\u5b57\u662f\u9608\u503c\uff08\u8d1f\u504f\u5dee\uff09\u5e76\u5047\u8bbe\u4f7f\u7528\u9636\u8dc3\u6fc0\u6d3b\u51fd\u6570\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"384\" src=\"http:\/\/127.0.0.1\/wp-content\/uploads\/2022\/06\/img3-1.webp\" alt=\"\" class=\"wp-image-353\" srcset=\"https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img3-1.webp 630w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img3-1-300x183.webp 300w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-medium-font-size\">\u5982\u679c\u6211\u4eec\u6709\u4e24\u4e2a\u4ee5\u4e0a\u7684 XOR \u8f93\u5165\uff0c\u6211\u4eec\u5c06\u9700\u8981\u589e\u52a0\u9690\u85cf\u5c42\uff08\u4e2d\u95f4\u7684\u5c42\uff09\u4e2d\u7684\u8282\u70b9\u6570\u91cf\uff0c\u4ee5\u4fbf\u80fd\u591f\u8868\u793a XOR \u7684\u5176\u4ed6\u7ec4\u4ef6\u3002&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4.\">4. \u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u5bf9 xorshift128 PRNG \u8fdb\u884c\u5efa\u6a21<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u57fa\u4e8e\u6211\u4eec\u5728\u4e0a\u4e00\u8282\u4e2d\u8ba8\u8bba\u7684\u5185\u5bb9\u4ee5\u53ca\u6211\u4eec\u5bf9 xorshift128 PRNG \u7b97\u6cd5\u5982\u4f55\u5de5\u4f5c\u7684\u7406\u89e3\uff0c\u73b0\u5728 ML \u53ef\u4ee5\u5b66\u4e60 xorshift128 PRNG \u7b97\u6cd5\u9075\u5faa\u7684\u6a21\u5f0f\u662f\u6709\u610f\u4e49\u7684\u3002\u6211\u4eec\u73b0\u5728\u8fd8\u53ef\u4ee5\u51b3\u5b9a\u5982\u4f55\u6784\u5efa\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u6765\u590d\u5236 xorshift128 PRNG \u7b97\u6cd5\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u6211\u4eec\u5c06\u4f7f\u7528\u53ea\u6709\u4e00\u4e2a\u9690\u85cf\u5c42\u7684\u5bc6\u96c6\u795e\u7ecf\u7f51\u7edc\uff0c\u56e0\u4e3a\u8fd9\u5c31\u662f\u6211\u4eec\u8868\u793a\u5728 xorshift128 \u7b97\u6cd5\u4e2d\u5b9e\u73b0\u7684\u4efb\u4f55 XOR \u51fd\u6570\u96c6\u6240\u9700\u7684\u5168\u90e8\u5185\u5bb9\u3002<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">\u4e0e[1]<\/a>\u4e2d\u5efa\u8bae\u7684\u6a21\u578b\u76f8\u53cd\uff0c\u6211\u4eec\u8ba4\u4e3a\u6ca1\u6709\u4efb\u4f55\u7406\u7531\u4f7f\u7528\u50cf LSTM\uff08<em>\u201c\u957f\u77ed\u671f\u8bb0\u5fc6\u201d\uff0c\u4e00\u79cd\u9012\u5f52\u795e\u7ecf\u7f51\u7edc\uff09\u8fd9\u6837\u7684\u590d\u6742\u6a21\u578b<\/em>)\uff0c\u7279\u522b\u662f\u6240\u6709\u8f93\u51fa\u4f4d\u90fd\u76f4\u63a5\u8fde\u63a5\u5230\u5177\u6709 XOR \u51fd\u6570\u7684\u8f93\u5165\u4f4d\u96c6\u5408\uff0c\u6b63\u5982\u6211\u4eec\u4e4b\u524d\u6240\u5c55\u793a\u7684\uff0c\u5e76\u4e14\u4e0d\u9700\u8981\u50cf\u5728 LSTM \u4e2d\u90a3\u6837\u4fdd\u7559\u5185\u90e8\u72b6\u6001\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4.1\">4.1 \u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u8bbe\u8ba1&nbsp;<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u6211\u4eec\u63d0\u51fa\u7684\u6a21\u578b\u5c06\u5728\u8f93\u5165\u5c42\u6709<strong>128 \u4e2a\u8f93\u5165<\/strong>\u6765\u8868\u793a\u6700\u540e\u56db\u4e2a\u751f\u6210\u7684\u6574\u6570\uff0c\u6bcf\u4e2a 32 \u4f4d\uff0c\u5728\u8f93\u51fa\u5c42\u6709<strong>32 \u4e2a\u8f93\u51fa&nbsp;<\/strong>\u6765\u8868\u793a\u4e0b\u4e00\u4e2a 32 \u4f4d\u968f\u673a\u751f\u6210\u7684\u6570\u5b57\u3002\u6211\u4eec\u9700\u8981\u51b3\u5b9a\u7684\u4e3b\u8981\u8d85\u53c2\u6570\u662f\u9690\u85cf\u5c42\u4e2d\u795e\u7ecf\u5143\/\u8282\u70b9\u7684\u6570\u91cf\u3002\u6211\u4eec\u4e0d\u5e0c\u671b\u5c11\u6570\u8282\u70b9\u4e0d\u80fd\u4ee3\u8868\u6240\u6709 XOR \u51fd\u6570\u672f\u8bed\uff0c\u540c\u65f6\u6211\u4eec\u4e0d\u5e0c\u671b\u4f7f\u7528\u5927\u91cf\u4e0d\u4f1a\u4f7f\u7528\u7684\u8282\u70b9\uff0c\u8fd9\u4f1a\u4f7f\u6a21\u578b\u590d\u6742\u5316\u5e76\u589e\u52a0\u8bad\u7ec3\u91cf\u65f6\u95f4\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6839\u636e\u8f93\u5165\u3001\u8f93\u51fa\u7684\u6570\u91cf\u548c XOR \u51fd\u6570\u7684\u590d\u6742\u6027\uff0c\u6211\u4eec\u505a\u51fa\u4e86\u6709\u6839\u636e\u7684\u731c\u6d4b\u5e76\u4f7f\u7528\u4e86<strong>1024<\/strong>\u9690\u85cf\u5c42\u7684\u9690\u85cf\u8282\u70b9\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u7684\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u5982\u4e0b\uff08\u5ffd\u7565\u8f93\u5165\u5c42\uff09\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted has-medium-font-size\">_________________________________________________________________\n\u5c42\uff08\u7c7b\u578b\uff09\u8f93\u51fa\u5f62\u72b6\u53c2\u6570#   \n==================================================== ================\n\u5bc6\u96c6\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c1024\uff09132096    \n_________________________________________________________________\ndense_1\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c32\uff0932800     \n==================================================== ================\n\u603b\u53c2\u6570\uff1a164,896\n\u53ef\u8bad\u7ec3\u53c2\u6570\uff1a164,896\n\u4e0d\u53ef\u8bad\u7ec3\u53c2\u6570\uff1a0\n_________________________________________________________________<\/pre>\n\n\n\n<p class=\"has-medium-font-size\">\u53ef\u4ee5\u770b\u5230\uff0c\u9690\u85cf\u5c42\u7684\u53c2\u6570\uff08\u6743\u91cd\u548c\u504f\u7f6e\uff09\u4e2a\u6570\u4e3a 132,096\uff08128\u00d71024 \u4e2a\u6743\u91cd + 1024 \u4e2a\u504f\u7f6e\uff09\uff0c\u8f93\u51fa\u5c42\u7684\u53c2\u6570\u4e2a\u6570\u4e3a 32,800 \u4e2a\uff081024\u00d732 \u4e2a\u6743\u91cd + 32\u504f\u5dee\uff09\uff0c\u603b\u5171\u9700\u8981\u8bad\u7ec3<strong>164,896 \u4e2a<\/strong>\u53c2\u6570\u3002<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">\u4e0e[1]<\/a>\u4e2d\u4f7f\u7528\u7684\u6a21\u578b\u6bd4\u8f83\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-preformatted has-medium-font-size\">_________________________________________________________________<br>\u56fe\u5c42\uff08\u7c7b\u578b\uff09 \u8f93\u51fa\u5f62\u72b6\u53c2\u6570 #   \n==================================================== ================\nlstm (LSTM)\uff08\u65e0\uff0c1024\uff094329472   \n_________________________________________________________________\n\u5bc6\u96c6\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c512\uff09524800    \n_________________________________________________________________\ndense_1\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c512\uff09262656    \n_________________________________________________________________\ndense_2\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c512\uff09262656    \n_________________________________________________________________\ndense_3\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c512\uff09262656    \n_________________________________________________________________\ndense_4\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c512\uff09262656    \n_________________________________________________________________\ndense_5\uff08\u5bc6\u96c6\uff09\uff08\u65e0\uff0c32\uff0916416     \n==================================================== ================\n\u603b\u53c2\u6570\uff1a5,921,312\n\u53ef\u8bad\u7ec3\u53c2\u6570\uff1a5,921,312\n\u4e0d\u53ef\u8bad\u7ec3\u53c2\u6570\uff1a0\n_________________________________________________________________<\/pre>\n\n\n\n<p class=\"has-medium-font-size\">\u8fd9\u4e2a\u590d\u6742\u7684\u6a21\u578b\u6709\u5927\u7ea6<strong>600 \u4e07\u4e2a<\/strong>\u53c2\u6570\u9700\u8981\u8bad\u7ec3\uff0c\u8fd9\u5c06\u4f7f\u6a21\u578b\u8bad\u7ec3\u66f4\u52a0\u56f0\u96be\uff0c\u5e76\u4e14\u9700\u8981\u66f4\u957f\u7684\u65f6\u95f4\u624d\u80fd\u83b7\u5f97\u597d\u7684\u7ed3\u679c\u3002\u5b83\u4e5f\u5f88\u5bb9\u6613\u88ab\u56f0\u5728\u90a3\u4e2a\u5de8\u5927\u7684 600 \u4e07\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u5c40\u90e8\u6700\u5c0f\u503c\u4e2d\u3002\u6b64\u5916\uff0c\u5b58\u50a8\u6b64\u6a21\u578b\u5e76\u7a0d\u540e\u63d0\u4f9b\u670d\u52a1\u5c06\u4f7f\u7528\u5b58\u50a8\/\u670d\u52a1\u6a21\u578b\u6240\u9700\u7a7a\u95f4\u7684<strong>36 \u500d\u3002<\/strong>\u6b64\u5916\uff0c\u6a21\u578b\u53c2\u6570\u7684\u6570\u91cf\u4f1a\u5f71\u54cd\u8bad\u7ec3\u6a21\u578b\u6240\u9700\u7684\u6570\u636e\u91cf\uff1b\u53c2\u6570\u8d8a\u591a\uff0c\u8bad\u7ec3\u5b83\u9700\u8981\u7684\u8f93\u5165\u6570\u636e\u5c31\u8d8a\u591a\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u8be5\u6a21\u578b\u7684\u53e6\u4e00\u4e2a\u95ee\u9898\u662f\u4f7f\u7528\u7684\u635f\u5931\u51fd\u6570\u3002\u6211\u4eec\u7684\u76ee\u6807\u662f\u83b7\u5f97\u5c3d\u53ef\u80fd\u591a\u7684\u6b63\u786e\u4f4d\uff1b\u56e0\u6b64\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6700\u9002\u5408\u4f7f\u7528\u7684\u635f\u5931\u51fd\u6570\u662f\u201c&nbsp;<strong>binary_crossentropy<\/strong>&nbsp;\u201d\uff0c\u800c\u4e0d\u662f\u201c&nbsp;<strong>mse<\/strong>&nbsp;\u201d\u3002\u5728\u4e0d\u6d89\u53ca\u8fd9\u4e24\u4e2a\u635f\u5931\u51fd\u6570\u7684\u6570\u5b66\u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u8bf4\u6211\u4eec\u4e0d\u5728\u4e4e\u8f93\u51fa\u662f 0.8\u30010.9 \u8fd8\u662f 100\u3002\u6211\u4eec\u53ea\u5173\u5fc3\u8be5\u503c\u662f\u5426\u8d85\u8fc7\u4e86\u67d0\u4e2a\u9608\u503c\u4ee5\u88ab\u89c6\u4e3a\u4e00\u4e2a\u6216\u4e0d\u88ab\u89c6\u4e3a\u96f6\u3002\u8be5\u6a21\u578b\u4e2d\u53c2\u6570\u7684\u53e6\u4e00\u4e2a\u975e\u6700\u4f73\u9009\u62e9\u662f\u8f93\u51fa\u5c42\u7684\u6fc0\u6d3b\u51fd\u6570\u3002\u7531\u4e8e\u8f93\u51fa\u5c42\u5305\u542b 32 \u4e2a\u795e\u7ecf\u5143\uff0c\u6bcf\u4e2a\u795e\u7ecf\u5143\u4ee3\u8868\u4e00\u4e2a\u4f4d\uff0c\u5176\u503c\u5e94\u59cb\u7ec8\u4e3a 0 \u6216 1\uff0c\u56e0\u6b64\u5bf9\u4e8e\u8fd9\u4e9b\u7c7b\u578b\u7684\u8282\u70b9\u6700\u5408\u9002\u7684\u6fc0\u6d3b\u51fd\u6570\u901a\u5e38\u662f<strong>sigmoid<\/strong>\u529f\u80fd\u3002\u76f8\u53cd\uff0c\u8be5\u6a21\u578b\u4f7f\u7528\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\u6765\u8f93\u51fa\u4ece -inf \u5230 inf \u7684\u4efb\u4f55\u503c\u3002\u5f53\u7136\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e9b\u503c\u8bbe\u7f6e\u4e3a\u9608\u503c\u4ee5\u5c06\u5b83\u4eec\u8f6c\u6362\u4e3a 0 \u548c 1\uff0c\u4f46\u8be5\u6a21\u578b\u7684\u8bad\u7ec3\u5c06\u66f4\u5177\u6311\u6218\u6027\u5e76\u4e14\u9700\u8981\u66f4\u591a\u65f6\u95f4\u3002&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u5bf9\u4e8e\u5176\u4f59\u7684\u8d85\u53c2\u6570\uff0c\u6211\u4eec\u4f7f\u7528\u4e86\u4e0e<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">[1]\u4e2d\u7684\u6a21\u578b\u76f8\u540c\u7684\u53c2\u6570<\/a>.&nbsp;\u6b64\u5916\uff0c\u6211\u4eec\u4f7f\u7528\u4e0e\u5176\u4ed6\u6a21\u578b\u76f8\u540c\u7684\u8f93\u5165\u6837\u672c\uff0c\u5176\u4e2d\u5305\u62ec\u4ece\u4e0a\u8ff0 PRNG \u51fd\u6570\u4e2d\u91c7\u6837\u7684\u5927\u7ea6 200 \u4e07\u4e2a\u968f\u673a\u6570\u7528\u4e8e\u8bad\u7ec3\uff0c\u4ee5\u53ca 10,000 \u4e2a\u968f\u673a\u6570\u7528\u4e8e\u6d4b\u8bd5\u3002\u8bad\u7ec3\u548c\u6d4b\u8bd5\u968f\u673a\u6570\u6837\u672c\u5f62\u6210\u4e00\u4e2a\u56db\u65b9\u5e8f\u5217\u7684\u968f\u673a\u6570\u4f5c\u4e3a\u6a21\u578b\u7684\u8f93\u5165\uff0c\u4e0b\u4e00\u4e2a\u968f\u673a\u6570\u4f5c\u4e3a\u6a21\u578b\u7684\u8f93\u51fa\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u6211\u4eec\u8ba4\u4e3a\u6211\u4eec\u4e0d\u9700\u8981\u90a3\u4e48\u591a\u6570\u636e\u6765\u8fbe\u5230\u6211\u4eec\u6240\u8fbe\u5230\u7684\u6027\u80fd\uff1b\u6211\u4eec\u53ea\u662f\u8bd5\u56fe\u4e0e\u5f15\u7528\u7684\u6587\u7ae0\u4fdd\u6301\u4e00\u81f4\u3002\u7a0d\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5b9e\u9a8c\u6765\u786e\u5b9a\u8db3\u4ee5\u751f\u6210\u8bad\u7ec3\u6709\u7d20\u7684\u6a21\u578b\u7684\u6700\u5c0f\u6570\u636e\u91cf\u3002<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">\u4e0b\u8868\u603b\u7ed3\u4e86\u6211\u4eec\u6a21\u578b\u4e0e[1]<\/a>\u4e2d\u63d0\u51fa\u7684\u6a21\u578b\u76f8\u6bd4\u7684\u6a21\u578b\u53c2\u6570\/\u8d85\u53c2\u6570\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th><\/th><th><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">[1]<\/a>\u4e2d\u7684 NN \u6a21\u578b<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\"><\/a><\/th><th>\u6211\u4eec\u7684\u6a21\u578b<\/th><\/tr><tr><th>\u578b\u53f7\u7c7b\u578b<\/th><td><strong>LSTM<\/strong>\u548c<strong>\u5bc6\u96c6<\/strong>\u7f51\u7edc<\/td><td><strong>\u5bc6\u96c6<\/strong>\u7f51\u7edc<\/td><\/tr><tr><th>#\u56fe\u5c42<\/th><td><strong>7<\/strong><\/td><td><strong>2<\/strong><\/td><\/tr><tr><th>#\u795e\u7ecf\u5143<\/th><td><strong>1024<\/strong>&nbsp;LSTM<br><strong>2592<\/strong>\u5bc6\u96c6&nbsp;<\/td><td><strong>1056<\/strong>&nbsp;\u5bc6\u96c6<\/td><\/tr><tr><th>#\u53ef\u8bad\u7ec3\u53c2\u6570<\/th><td><strong>5,921,312<\/strong><br>\uff084,329,472 \u4ec5\u6765\u81ea LSTM \u5c42\uff09<\/td><td><strong>164,896<\/strong><\/td><\/tr><tr><th>\u6fc0\u6d3b\u51fd\u6570<\/th><td>\u9690\u85cf\u5c42\uff1a&nbsp;&nbsp;<strong>relu<\/strong><br>\u8f93\u51fa\u5c42\uff1a<strong>\u7ebf\u6027<\/strong><\/td><td>\u9690\u85cf\u5c42\uff1a<strong>relu<\/strong><br>\u8f93\u51fa\u5c42\uff1a<strong>sigmoid<\/strong><\/td><\/tr><tr><th>\u635f\u5931\u51fd\u6570<\/th><td><strong>\u6beb\u79d2<\/strong><\/td><td><strong>\u4e8c\u5143\u4ea4\u53c9\u71b5<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-medium-font-size\">\u6211\u4eec\u63d0\u51fa\u7684\u6a21\u578b\u4e0e<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">[1]\u4e2d\u7684\u5e16\u5b50\u6a21\u578b\u4e4b\u95f4\u7684\u6bd4\u8f83<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4.2\">4.2 \u6a21\u578b\u7ed3\u679c<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u7ecf\u8fc7\u51e0\u4e2a\u5c0f\u65f6\u7684\u6a21\u578b\u8bad\u7ec3\u548c\u8d85\u53c2\u6570\u4f18\u5316\uff0cNN \u6a21\u578b\u5df2\u7ecf\u8fbe\u5230\u4e86<strong>100%<\/strong>\u7684\u6309\u4f4d\u8bad\u7ec3\u7cbe\u5ea6\uff01\u5f53\u7136\uff0c\u6211\u4eec\u901a\u8fc7\u6a21\u578b\u8fd0\u884c\u6d4b\u8bd5\u96c6\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u76f8\u540c\u7684\u7ed3\u679c\uff0c\u5e76\u4e14\u5177\u6709 100% \u7684\u4f4d\u7cbe\u5ea6\u3002\u4e3a\u4e86\u5bf9\u6211\u4eec\u53d6\u5f97\u7684\u6210\u5c31\u66f4\u6709\u4fe1\u5fc3\uff0c\u6211\u4eec\u751f\u6210\u4e86\u4e00\u4e2a\u5305\u542b 100,000 \u4e2a\u968f\u673a\u6570\u7684\u65b0\u6837\u672c\uff0c\u5176\u79cd\u5b50\u4e0e\u7528\u4e8e\u751f\u6210\u5148\u524d\u6570\u636e\u7684\u79cd\u5b50\u4e0d\u540c\uff0c\u5e76\u4e14\u6211\u4eec\u5f97\u5230\u4e86\u76f8\u540c\u7684 100% \u4f4d\u7cbe\u5ea6\u7ed3\u679c\u3002\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0c\u867d\u7136\u53c2\u8003\u6587\u7ae0\u8fbe\u5230\u4e86<strong>95%+&nbsp;<\/strong>\u6309\u4f4d\u7cbe\u5ea6\uff0c\u8fd9\u770b\u8d77\u6765\u662f\u4e00\u4e2a\u5f88\u6709\u5e0c\u671b\u7684\u7ed3\u679c\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u8bc4\u4f30\u6a21\u578b\u7cbe\u5ea6\uff08\u76f8\u5bf9\u4e8e\u4f4d\u7cbe\u5ea6\uff09\u65f6\uff0c\u5373\u5b83\u80fd\u591f\u5728\u4e0d\u7ffb\u8f6c\u4efb\u4f55\u4f4d\u7684\u60c5\u51b5\u4e0b\u751f\u6210\u7cbe\u786e\u7684\u4e0b\u4e00\u4e2a\u968f\u673a\u6570\uff0c\u6211\u4eec\u53d1\u73b0\u6a21\u578b\u7684\u7cbe\u5ea6\u4e0b\u964d\u5230<strong>26% \u5de6\u53f3<\/strong>\u3002\u4e0e\u6211\u4eec\u7684\u6a21\u578b\u76f8\u6bd4\uff0c\u6211\u4eec\u6709<strong>100%<\/strong>\u7684\u51c6\u786e\u7387\u3002<strong>95%+&nbsp;<\/strong>\u6309\u4f4d\u5e76\u4e0d\u50cf\u5b83\u53ef\u80fd\u51fa\u73b0\u7684\u90a3\u6837\u4ec5\u5728 2 \u4f4d\u4e0a\u5931\u8d25\uff0832 \u4f4d\u7684 95% \u5c0f\u4e8e 2\uff09\uff0c\u800c\u662f\u8fd9\u4e9b 5% \u7684\u9519\u8bef\u5206\u6563\u5728<strong>14 \u4f4d<\/strong>\u4e2d\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5c3d\u7ba1\u53c2\u8003\u6a21\u578b\u7684\u6309\u4f4d\u7cbe\u5ea6\u4e3a<strong>95%+<\/strong>\uff0c\u4f46\u53ea\u6709 18 \u4f4d\u662f 100% \u6b63\u786e\u7684\uff0c\u5e73\u5747\u800c\u8a00\uff0c\u5176\u4f59 14 \u4f4d\u4e2d\u7684 2 \u4f4d\u4f1a\u88ab\u6a21\u578b\u66f4\u6539\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u4e0b\u8868\u603b\u7ed3\u4e86\u4e24\u79cd\u6a21\u578b\u7684\u6bd4\u8f83\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th><\/th><th><a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">[1]<\/a>\u4e2d\u7684 NN \u6a21\u578b<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\"><\/a><\/th><th>\u6211\u4eec\u7684\u6a21\u578b<\/th><\/tr><tr><th>\u4f4d\u7cbe\u5ea6<\/th><td><strong>95<\/strong>&nbsp;% +<\/td><td><strong>100<\/strong>&nbsp;%<\/td><\/tr><tr><th>\u51c6\u786e\u6027<\/th><td><strong>26<\/strong>&nbsp;%<\/td><td><strong>100<\/strong>&nbsp;%<\/td><\/tr><tr><th>\u4f4d\u53ef\u4ee5\u7ffb\u8f6c\uff08\u5171 32 \u4e2a\uff09<\/th><td><strong>14<\/strong><\/td><td><strong>0<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-medium-font-size\">\u6a21\u578b\u7cbe\u5ea6\u6bd4\u8f83<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u5728\u673a\u5668\u5b66\u4e60\u4e2d\uff0c\u83b7\u5f97 100% \u7684\u51c6\u786e\u7387\u901a\u5e38\u4e0d\u662f\u597d\u6d88\u606f\u3002\u8fd9\u901a\u5e38\u610f\u5473\u7740\u8981\u4e48\u6211\u4eec\u6ca1\u6709\u5f88\u597d\u5730\u8868\u793a\u6574\u4e2a\u6570\u636e\u96c6\uff0c\u8981\u4e48\u6211\u4eec\u8fc7\u5ea6\u62df\u5408\u6837\u672c\u6570\u636e\u7684\u6a21\u578b\uff0c\u8981\u4e48\u95ee\u9898\u662f\u786e\u5b9a\u6027\u7684\uff0c\u5b83\u4e0d\u9700\u8981\u673a\u5668\u5b66\u4e60\u3002\u5728\u6211\u4eec\u7684\u4f8b\u5b50\u4e2d\uff0c\u5b83\u63a5\u8fd1\u4e8e\u7b2c\u4e09\u79cd\u9009\u62e9\u3002xorshift128 PRNG \u7b97\u6cd5\u662f\u786e\u5b9a\u6027\u7684\uff1b\u6211\u4eec\u9700\u8981\u77e5\u9053\u54ea\u4e9b\u8f93\u5165\u4f4d\u7528\u4e8e\u751f\u6210\u8f93\u51fa\u4f4d\uff0c\u4f46\u662f\u8fde\u63a5\u5b83\u4eec\u7684\u51fd\u6570 XOR \u662f\u5df2\u77e5\u7684\u3002\u6240\u4ee5\uff0c\u5728\u67d0\u79cd\u7a0b\u5ea6\u4e0a\uff0c\u8fd9\u4e2a\u7b97\u6cd5\u5f88\u5bb9\u6613\u88ab\u673a\u5668\u5b66\u4e60\u7834\u89e3\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u95ee\u9898\uff0c\u83b7\u5f97 100% \u51c6\u786e\u7684\u6a21\u578b\u610f\u5473\u7740 ML \u6a21\u578b\u5df2\u7ecf\u5b66\u4e60\u4e86\u8f93\u5165\u548c\u8f93\u51fa\u4f4d\u4e4b\u95f4\u7684\u4f4d\u8fde\u63a5\u6620\u5c04\u3002\u6240\u4ee5\uff0c\u5982\u679c\u6211\u4eec\u4ece\u8fd9\u4e2a\u7b97\u6cd5\u4e2d\u5f97\u5230\u4efb\u4f55\u7ed3\u679c\u7684\u56db\u4e2a\u968f\u673a\u6570\uff0c<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"4.3\">4.3 \u6a21\u578b\u6df1\u6f5c<\/h3>\n\n\n\n<p class=\"has-medium-font-size\">\u672c\u8282\u5c06\u6df1\u5165\u7814\u7a76\u8be5\u6a21\u578b\uff0c\u4ee5\u4e86\u89e3\u5b83\u4ece PRNG \u6570\u636e\u4e2d\u5b66\u5230\u7684\u66f4\u591a\u5185\u5bb9\uff0c\u4ee5\u53ca\u5b83\u662f\u5426\u7b26\u5408\u6211\u4eec\u7684\u9884\u671f\u3002&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"4.3.1\">4.3.1 \u6a21\u578b\u7b2c\u4e00\u5c42\u8fde\u63a5<\/h3>\n\n\n\n<p class=\"has-medium-font-size\">\u5982<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#CrackingRandomNumberGeneratorsusingMachineLearning-Section2\">\u7b2c 2 \u8282<\/a>\u6240\u8ff0\uff0cxorshift128 PRNG \u4f7f\u7528\u6700\u540e\u56db\u4e2a\u751f\u6210\u7684\u6570\u5b57\u6765\u751f\u6210\u65b0\u7684\u968f\u673a\u6570\u3002\u66f4\u5177\u4f53\u5730\u8bf4\uff0cxorshift128 PRNG \u7684\u5b9e\u73b0\u4ec5\u4f7f\u7528\u56db\u4e2a\u6570\u5b57\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u6570\u5b57<strong>w<\/strong>\u548c<strong>x<\/strong>\u6765\u751f\u6210\u65b0\u7684\u968f\u673a\u6570<strong>o<\/strong>\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u8981\u68c0\u67e5\u8fde\u63a5<strong>128\u7684\u6743\u91cd<\/strong>\u8f93\u5165\uff0c\u6700\u540e\u56db\u4e2a\u751f\u6210\u7684\u6570\u5b57\u5408\u5e76\uff0c\u4ece\u8f93\u5165\u5c42\u5230\u9690\u85cf\u5c42\uff0c\u6211\u4eec\u8bad\u7ec3\u7684\u6a21\u578b\u7684 1024 \u4e2a\u9690\u85cf\u8282\u70b9\uff0c\u4ee5\u67e5\u770b\u5b83\u4eec\u7684\u8fde\u63a5\u5f3a\u5ea6\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u9a8c\u8bc1\u54ea\u4e9b\u4f4d\u7528\u4e8e\u751f\u6210\u8f93\u51fa\u3002\u4e0b\u56fe\u663e\u793a\u4e86\u5c06\u6bcf\u4e2a\u8f93\u5165\uff08\u4ee5 x \u8f74\u8868\u793a\uff09\u8fde\u63a5\u5230\u9690\u85cf\u5c42\u4e2d\u7684 1024 \u4e2a\u9690\u85cf\u8282\u70b9\u7684 y \u8f74\u4e0a\u7684\u6743\u91cd\u503c\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u56fe\u4e0a\u7684\u6bcf\u4e2a\u70b9\u4ee3\u8868\u4ece\u4efb\u4f55\u9690\u85cf\u8282\u70b9\u5230 x \u8f74\u8f93\u5165\u7684\u6743\u91cd\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"523\" src=\"http:\/\/127.0.0.1\/wp-content\/uploads\/2022\/06\/img4-1.webp\" alt=\"\" class=\"wp-image-354\" srcset=\"https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img4-1.webp 1024w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img4-1-300x153.webp 300w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img4-1-768x392.webp 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-medium-font-size\">\u6b63\u5982\u6211\u4eec\u6240\u770b\u5230\u7684\uff0c\u5f88\u5c11\u6709\u9690\u85cf\u8282\u70b9\u8fde\u63a5\u5230\u5176\u4e2d\u6743\u91cd\u5927\u4e8e~2\u200b\u200b.5 \u6216\u5c0f\u4e8e~-2.5 \u7684\u8f93\u5165\u4e4b\u4e00\u3002\u5176\u4f59\u5728 -2 \u548c 2 \u4e4b\u95f4\u7684\u4f4e\u6743\u91cd\u8282\u70b9\u53ef\u4ee5\u8ba4\u4e3a\u662f\u672a\u8fde\u63a5\u7684\u3002\u6211\u4eec\u8fd8\u53ef\u4ee5\u6ce8\u610f\u5230\u4f4d 32 \u548c 95 \u4e4b\u95f4\u7684\u8f93\u5165\u6ca1\u6709\u8fde\u63a5\u5230\u4efb\u4f55\u9690\u85cf\u5c42\u3002\u8fd9\u662f\u56e0\u4e3a\u6211\u4eec\u4e4b\u524d\u6240\u8bf4\u7684 xorshift128 PRNG \u7684\u5b9e\u73b0\u4ec5\u4f7f\u7528\u6765\u81ea\u8f93\u5165\u7684<strong>x<\/strong>\uff08\u4ece 0 \u5230 31 \u7684\u4f4d\uff09\u548c<strong>w<\/strong>\uff08\u4ece 96 \u5230 127 \u7684\u4f4d\uff09\uff0c\u800c\u53e6\u5916\u4e24\u4e2a\u8f93\u5165<strong>y<\/strong>&nbsp;\u548c<strong>z<\/strong>\u8868\u793a\u6765\u81ea 32 \u7684\u4f4d\u5230 95\uff0c\u4e0d\u7528\u4e8e\u751f\u6210\u8f93\u51fa\uff0c\u8fd9\u6b63\u662f\u6a21\u578b\u5b66\u5230\u7684\u3002\u8fd9\u610f\u5473\u7740\u6a21\u578b\u5df2\u7ecf\u4ece\u8bad\u7ec3\u9636\u6bb5\u7ed9\u51fa\u7684\u6570\u636e\u4e2d\u51c6\u786e\u5730\u5b66\u4e60\u4e86\u8be5\u6a21\u5f0f\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"4.3.2\">4.3.2 \u6a21\u578b\u8f93\u51fa\u89e3\u6790<\/h3>\n\n\n\n<p class=\"has-medium-font-size\">\u4e0e\u6211\u4eec\u5728\u4e0a\u4e00\u8282\u4e2d\u6240\u505a\u7684\u7c7b\u4f3c\uff0c\u4e0b\u56fe\u663e\u793a\u4e86\u5c06\u6bcf\u4e2a\u8f93\u51fa\uff08\u4ee5 x \u8f74\u8868\u793a\uff09\u8fde\u63a5\u5230\u9690\u85cf\u5c42\u4e2d\u7684 1024 \u4e2a\u9690\u85cf\u8282\u70b9\u7684\u6743\u91cd\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"523\" src=\"http:\/\/127.0.0.1\/wp-content\/uploads\/2022\/06\/img5-1.webp\" alt=\"\" class=\"wp-image-355\" srcset=\"https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img5-1.webp 1024w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img5-1-300x153.webp 300w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img5-1-768x392.webp 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-medium-font-size\">\u5c31\u50cf\u6211\u4eec\u4e4b\u524d\u7684\u89c2\u5bdf\u4e00\u6837\uff0c\u6bcf\u4e2a\u8f93\u51fa\u4f4d\u53ea\u8fde\u63a5\u5230\u9690\u85cf\u5c42\u7684\u6781\u5c11\u6570\u8282\u70b9\uff0c\u53ef\u80fd\u9664\u4e86\u7b2c 11 \u4f4d\u4e4b\u5916\uff0c\u5b83\u7684\u51b3\u5b9a\u6027\u8f83\u5c0f\uff0c\u53ef\u80fd\u9700\u8981\u66f4\u591a\u7684\u8bad\u7ec3\u624d\u80fd\u51cf\u5c11\u51fa\u9519\u7684\u53ef\u80fd\u6027\u3002\u6211\u4eec\u73b0\u5728\u8981\u68c0\u67e5\u7684\u662f\u8fd9\u4e9b\u8f93\u51fa\u4f4d\u662f\u5982\u4f55\u8fde\u63a5\u5230\u8f93\u5165\u4f4d\u7684\u3002\u6211\u4eec\u5c06\u5728\u8fd9\u91cc\u53ea\u63a2\u7d22\u7b2c\u4e00\u90e8\u5206\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u4ee5\u540c\u6837\u7684\u65b9\u5f0f\u5b8c\u6210\u5176\u4f59\u90e8\u5206\u3002\u5982\u679c\u6211\u4eec\u53ea\u5173\u6ce8\u56fe\u4e2d\u7684\u7b2c 0 \u4f4d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u5b83\u53ea\u8fde\u63a5\u5230\u6765\u81ea\u9690\u85cf\u5c42\u7684<strong>\u4e94\u4e2a\u8282\u70b9\uff0c\u4e24\u4e2a\u5177\u6709\u6b63<\/strong>\u6743\u91cd\uff0c<strong>\u4e09\u4e2a\u5177\u6709\u8d1f<\/strong>\u6743\u91cd\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"523\" src=\"http:\/\/127.0.0.1\/wp-content\/uploads\/2022\/06\/img6-1.webp\" alt=\"\" class=\"wp-image-356\" srcset=\"https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img6-1.webp 1024w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img6-1-300x153.webp 300w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img6-1-768x392.webp 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p class=\"has-medium-font-size\">\u90a3\u4e9b\u8fde\u63a5\u7684\u9690\u85cf\u8282\u70b9\u662f<strong>120\u3001344\u3001395\u3001553<\/strong>\u548c<strong>788<\/strong>\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u8282\u70b9\u770b\u8d77\u6765\u662f\u968f\u673a\u7684\uff0c\u4f46\u5982\u679c\u6211\u4eec\u7ed8\u5236\u5b83\u4eec\u4e0e\u8f93\u5165\u7684\u8fde\u63a5\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u4e0b\u56fe\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"523\" src=\"http:\/\/127.0.0.1\/wp-content\/uploads\/2022\/06\/img7.webp\" alt=\"\" class=\"wp-image-357\" srcset=\"https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img7.webp 1024w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img7-300x153.webp 300w, https:\/\/rngrb.com\/wp-content\/uploads\/2022\/06\/img7-768x392.webp 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"has-medium-font-size\">\u6b63\u5982\u6211\u4eec\u6240\u770b\u5230\u7684\uff0c\u5f88\u5c11\u6709\u4f4d\u4f1a\u5f71\u54cd\u6211\u4eec\u5728\u56fe\u4e2d\u5708\u51fa\u7684\u90a3\u4e9b\u9690\u85cf\u8282\u70b9\u3002\u5b83\u4eec\u662f\u4f4d 0\u30018\u300196 \u548c 115\uff0c\u5982\u679c\u6211\u4eec\u5c06\u5b83\u4eec\u4ee5 32<strong>\u4e3a\u6a21\uff0c\u6211\u4eec\u4f1a\u4ece\u7b2c\u4e00\u4e2a\u6570\u5b57<\/strong><strong>x<\/strong>\u4e2d\u83b7\u5f97\u4f4d 0 \u548c 8\uff0c\u4ece\u7b2c\u56db\u4e2a\u6570\u5b57<strong>w<\/strong>\u4e2d\u83b7\u5f97 0 \u548c 19 \u4f4d\u3002<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#CrackingRandomNumberGeneratorsusingMachineLearning-Section2\">\u8fd9\u4e0e\u6211\u4eec\u5728\u7b2c 2 \u8282<\/a>\u4e2d\u63a8\u5bfc\u51fa\u7684 xorshift128 PRNG \u51fd\u6570\u76f8\u5339\u914d\uff0c\u8f93\u51fa\u7684\u7b2c\u4e00\u4f4d\u662f\u8fd9\u4e9b\u4f4d\u7684 XOR\uff0cO&nbsp;<sub>0<\/sub>&nbsp;= W&nbsp;<sub>0<\/sub>&nbsp;^ W&nbsp;<sub>19<\/sub>&nbsp;^ X&nbsp;<sub>0<\/sub>&nbsp;^ X&nbsp;<sub>8<\/sub>.&nbsp;\u6211\u4eec\u671f\u671b\u5177\u6709\u4e00\u4e2a\u8f93\u51fa\u8282\u70b9\u7684\u4e94\u4e2a\u9690\u85cf\u8282\u70b9\u7c7b\u4f3c\u4e8e\u8fd9\u56db\u4e2a\u8f93\u5165\u4f4d\u7684 XOR \u529f\u80fd\u3002\u56e0\u6b64\uff0c\u5982\u679c\u7ed9\u5b9a\u8db3\u591f\u7684\u8bad\u7ec3\u6570\u636e\uff0cML \u6a21\u578b\u53ef\u4ee5\u5b66\u4e60\u4efb\u610f\u8f93\u5165\u4f4d\u96c6\u5408\u7684 XOR \u51fd\u6570\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5.\">5. \u521b\u5efa\u6297\u673a\u5668\u5b66\u4e60\u7248\u672c\u7684 xorshift128<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u5728\u5206\u6790\u4e86 xorshift128 PRNG \u7684\u5de5\u4f5c\u539f\u7406\u4ee5\u53ca NN \u5982\u4f55\u8f7b\u677e\u7834\u89e3\u5b83\u4e4b\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u5efa\u8bae\u5bf9\u7b97\u6cd5\u8fdb\u884c\u7b80\u5355\u7684\u66f4\u65b0\uff0c\u4f7f\u5176\u66f4\u96be\u4f7f\u7528 ML \u7834\u89e3\u3002\u8fd9\u4e2a\u60f3\u6cd5\u662f\u5728\u79cd\u5b50\u4e2d\u5f15\u5165\u53e6\u4e00\u4e2a\u53d8\u91cf\uff0c\u5b83\u5c06\u51b3\u5b9a\uff1a<\/p>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>\u8981\u4f7f\u7528<strong>x<\/strong>\u3001<strong>y<\/strong>\u3001<strong>z<\/strong>\u548c<strong>w<\/strong>\u4e2d\u7684\u54ea\u4e9b\u53d8\u91cf\u6765\u751f\u6210<strong>o<\/strong>\u3002<\/li><li>\u5c06\u8fd9\u4e9b\u53d8\u91cf\u4e2d\u7684\u6bcf\u4e00\u4e2a\u79fb\u4f4d\u591a\u5c11\u4f4d\u3002<\/li><li>\u5411\u5de6\u6216\u5411\u53f3\u79fb\u52a8\u8fd9\u4e9b\u53d8\u91cf\u7684\u65b9\u5411\u3002<\/li><\/ol>\n\n\n\n<p class=\"has-medium-font-size\">\u8fd9\u53ef\u4ee5\u7528\u5c11\u4e8e 32 \u4f4d\u7684\u4e8c\u8fdb\u5236\u7f16\u7801\u3002\u4f8b\u5982\uff0c\u5728\u524d\u9762\u663e\u793a\u7684\u793a\u4f8b\u4ee3\u7801\u4e2d\uff0c\u53ea\u6709<strong>w<\/strong>\u548c<strong>x<\/strong>\u53d8\u91cf\u751f\u6210\u8f93\u51fa\uff0c\u53ef\u4ee5\u4e8c\u8fdb\u5236\u7f16\u7801\u4e3a 1001\u3002\u53d8\u91cf w \u5411\u53f3\u79fb\u52a8 11 \u4f4d\uff0c\u53ef\u4ee5\u4e8c\u8fdb\u5236\u7f16\u7801\u4e3a 01011&nbsp;<strong>0<\/strong>\uff0c\u5176\u4e2d\u6700\u4f4e\u6709\u6548\u4f4d\uff0c0\uff0c\u4ee3\u8868\u6b63\u786e\u7684\u65b9\u5411\u3002\u53d8\u91cf x \u5411\u53f3\u79fb\u52a8 19 \u4f4d\uff0c\u53ef\u4ee5\u4e8c\u8fdb\u5236\u7f16\u7801\u4e3a 10011&nbsp;<strong>1<\/strong>\uff0c\u5176\u4e2d\u6700\u4f4e\u6709\u6548\u4f4d 1 \u8868\u793a\u5411\u5de6\u65b9\u5411\u3002\u8fd9\u79cd\u8868\u793a\u5c06\u5360\u7528 4 \u4f4d + 4\u00d76 \u4f4d = 28 \u4f4d\u3002\u5f53\u7136\uff0c\u6211\u4eec\u9700\u8981\u786e\u4fdd\u9009\u62e9\u53d8\u91cf\u7684 4 \u4f4d\u4e0d\u5177\u6709\u4ee5\u4e0b\u503c\uff1a0000\u30010001\u30010010\u30010100 \u548c 1000\uff0c\u56e0\u4e3a\u5b83\u4eec\u4f1a\u9009\u62e9\u4e00\u4e2a\u6216\u6ca1\u6709\u53d8\u91cf\u8fdb\u884c\u5f02\u6216\u3002&nbsp;<\/p>\n\n\n\n<p class=\"has-medium-font-size\">\u4f7f\u7528\u8fd9\u4e2a\u7b80\u5355\u7684\u66f4\u65b0\u5c06\u589e\u52a0 PRNG \u7b97\u6cd5\u5b9e\u73b0\u7684\u5c0f\u590d\u6742\u6027\u3002\u5b83\u4ecd\u7136\u4f1a\u4f7f ML \u6a21\u578b\u53ea\u5b66\u4e60\u4e00\u4e2a\u53ef\u80fd\u7684\u5e8f\u5217\uff0c\u5176\u4e2d\u5927\u7ea6 1600 \u4e07\u4e2a\u4e0d\u540c\u7684\u5e8f\u5217\u662f\u7528\u76f8\u540c\u7684\u7b97\u6cd5\u548c\u4e0d\u540c\u7684\u79cd\u5b50\u751f\u6210\u7684\u3002\u597d\u50cf\u673a\u5668\u5b66\u4e60\u53ea\u4f1a\u5b66\u4e60\u7b97\u6cd5\u7684\u79cd\u5b50\uff0c\u800c\u4e0d\u662f\u7b97\u6cd5\u672c\u8eab\u3002\u8bf7\u6ce8\u610f\uff0c\u6b64\u66f4\u65b0\u7684\u76ee\u7684\u662f\u4f7f\u7b97\u6cd5\u5bf9 ML \u653b\u51fb\u66f4\u5177\u5f39\u6027\uff0c\u4f46\u7ed3\u679c PRNG \u7684\u5176\u4ed6\u5c5e\u6027\uff0c\u4f8b\u5982\u5468\u671f\u6027\uff0c\u8fd8\u6709\u5f85\u7814\u7a76\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6.\">\u516d\uff0c\u7ed3\u8bba<\/h2>\n\n\n\n<p class=\"has-medium-font-size\">\u8fd9\u7bc7\u6587\u7ae0\u8ba8\u8bba\u4e86 xorshift128 PRNG \u7684\u5de5\u4f5c\u539f\u7406\u4ee5\u53ca\u5982\u4f55\u6784\u5efa\u4e00\u4e2a\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff0c\u8be5\u6a21\u578b\u53ef\u4ee5\u4ece PRNG \u7684\u201c\u968f\u673a\u201d\u751f\u6210\u7684\u6570\u5b57\u4e2d\u5b66\u4e60\uff0c\u4ece\u800c\u4ee5 100% \u7684\u51c6\u786e\u5ea6\u9884\u6d4b\u5b83\u4eec\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5982\u679c ML \u6a21\u578b\u53ef\u4ee5\u8bbf\u95ee\u4ece\u6b64 PRNG \u751f\u6210\u7684\u4efb\u4f55\u56db\u4e2a\u7ed3\u679c\u6570\uff0c\u5b83\u53ef\u4ee5\u751f\u6210\u786e\u5207\u7684\u5e8f\u5217\u800c\u65e0\u9700\u8bbf\u95ee\u79cd\u5b50\u3002\u6211\u4eec\u8fd8\u7814\u7a76\u4e86\u5982\u4f55\u8bbe\u8ba1\u4e00\u4e2a\u6700\u80fd\u4ee3\u8868\u8fd9\u4e2a PRNG \u7684 NN \u6a21\u578b\u3002\u4ee5\u4e0b\u662f\u4ece\u8fd9\u7bc7\u6587\u7ae0\u4e2d\u5b66\u5230\u7684\u4e00\u4e9b\u6559\u8bad\uff1a<\/p>\n\n\n\n<ol class=\"has-medium-font-size wp-block-list\"><li>\u5c3d\u7ba1 xorshift128 PRNG \u5728\u4eba\u7c7b\u770b\u6765\u4f3c\u4e4e\u4e0d\u9075\u5faa\u4efb\u4f55\u6a21\u5f0f\uff0c\u4f46\u673a\u5668\u5b66\u4e60\u53ef\u7528\u4e8e\u9884\u6d4b\u7b97\u6cd5\u7684\u8f93\u51fa\uff0c\u56e0\u4e3a PRNG \u4ecd\u7136\u9075\u5faa\u9690\u85cf\u6a21\u5f0f\u3002<\/li><li>&nbsp;\u5e94\u7528\u6df1\u5ea6\u5b66\u4e60\u6765\u9884\u6d4b PRNG \u8f93\u51fa\u9700\u8981\u4e86\u89e3\u7279\u5b9a\u5e95\u5c42\u7b97\u6cd5\u7684\u8bbe\u8ba1\u3002<\/li><li>\u5927\u578b\u590d\u6742\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\u4e0d\u4e00\u5b9a\u4f1a\u83b7\u5f97\u6bd4\u7b80\u5355\u6a21\u578b\u66f4\u9ad8\u7684\u51c6\u786e\u6027\u3002<\/li><li>\u7b80\u5355\u7684\u795e\u7ecf\u7f51\u7edc (NN) \u6a21\u578b\u53ef\u4ee5\u8f7b\u677e\u5b66\u4e60 XOR \u51fd\u6570\u3002<\/li><\/ol>\n\n\n\n<p class=\"has-medium-font-size\"><a href=\"https:\/\/github.com\/nccgroup\/ML-for-RNGs\/tree\/main\/rng_xorshift128\" target=\"_blank\" rel=\"noreferrer noopener\">\u672c\u6587\u4e2d\u6982\u8ff0\u7684\u7528\u4e8e\u8bad\u7ec3\u548c\u6d4b\u8bd5\u6a21\u578b\u7684 Python \u4ee3\u7801\u4ee5Jupyter<\/a>\u7b14\u8bb0\u672c\u7684\u5f62\u5f0f\u5728\u6b64\u5b58\u50a8\u5e93\u4e2d\u5171\u4eab\u3002\u8bf7\u6ce8\u610f\uff0c\u6b64\u4ee3\u7801\u57fa\u4e8e<a href=\"https:\/\/research.nccgroup.com\/2021\/10\/15\/cracking-random-number-generators-using-machine-learning-part-1-xorshift128\/#[1]\">[1]<\/a>\u4e2d\u7684\u5e16\u5b50\u4e2d\u5171\u4eab\u7684<a href=\"https:\/\/github.com\/airza\/RngPredictor\/tree\/c726a72a8c561eaeaf0d875559b63b45dbd10ed3\" target=\"_blank\" rel=\"noreferrer noopener\">\u65e7\u7248\u672c<\/a>\u4ee3\u7801\uff0c\u5e76\u5728\u6b64\u5e16\u5b50\u4e2d\u89e3\u91ca\u4e86\u66f4\u6539\u3002\u8fd9\u6837\u505a\u662f\u4e3a\u4e86\u4fdd\u6301\u76f8\u540c\u7684\u6570\u636e\u548c\u5176\u4ed6\u53c2\u6570\u4e0d\u53d8\uff0c\u4ee5\u4fbf\u8fdb\u884c\u516c\u5e73\u6bd4\u8f83\u3002<\/p>\n        <div class=\"booster-block booster-reactions-block\">\r\n            <div class=\"twp-reactions-icons\">\r\n                \r\n                <div class=\"twp-reacts-wrap\">\r\n                    <a react-data=\"be-react-1\" post-id=\"350\" class=\"be-face-icons un-reacted\" href=\"javascript:void(0)\">\r\n                        <img decoding=\"async\" src=\"https:\/\/rngrb.com\/wp-content\/plugins\/booster-extension\/\/assets\/icon\/happy.svg\" alt=\"Happy\">\r\n                    <\/a>\r\n                    <div class=\"twp-reaction-title\">\r\n                        Happy                    <\/div>\r\n                    <div class=\"twp-count-percent\">\r\n                                                    <span style=\"display: none;\" class=\"twp-react-count\">0<\/span>\r\n                        \r\n                                                <span class=\"twp-react-percent\"><span>0<\/span> %<\/span>\r\n                                            <\/div>\r\n                <\/div>\r\n\r\n                <div class=\"twp-reacts-wrap\">\r\n                    <a react-data=\"be-react-2\" post-id=\"350\" class=\"be-face-icons un-reacted\" href=\"javascript:void(0)\">\r\n                        <img decoding=\"async\" src=\"https:\/\/rngrb.com\/wp-content\/plugins\/booster-extension\/\/assets\/icon\/sad.svg\" alt=\"Sad\">\r\n                    <\/a>\r\n                    <div class=\"twp-reaction-title\">\r\n                        Sad                    <\/div>\r\n                    <div class=\"twp-count-percent\">\r\n                                                    <span style=\"display: none;\" class=\"twp-react-count\">0<\/span>\r\n                                                                        <span class=\"twp-react-percent\"><span>0<\/span> %<\/span>\r\n                                            <\/div>\r\n                <\/div>\r\n\r\n                <div class=\"twp-reacts-wrap\">\r\n                    <a react-data=\"be-react-3\" post-id=\"350\" 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