{"id":55,"date":"2023-12-17T22:13:00","date_gmt":"2023-12-17T14:13:00","guid":{"rendered":"http:\/\/www.triode.cc\/?p=55"},"modified":"2025-09-28T09:40:40","modified_gmt":"2025-09-28T01:40:40","slug":"lcg-note","status":"publish","type":"post","link":"https:\/\/www.triode.cc\/index.php\/2023\/12\/17\/lcg-note\/","title":{"rendered":"LCG\u7b14\u8bb0"},"content":{"rendered":"\n<p>LCG\uff0c\u5168\u79f0\u7ebf\u6027\u540c\u4f59\u65b9\u53d1\u751f\u5668\uff08Linear congruential generator\uff09\uff0c\u662f\u4e00\u79cd\u4f2a\u968f\u673a\u5e8f\u5217\u751f\u6210\u5668\u7b97\u6cd5\uff0c\u751f\u6210\u5668\u7531\u4e0b\u5f0f\u5b9a\u4e49\uff1a<\/p>\n\n\n\n<p>$$X_{n+1}\\equiv aX_n+b\\ (mod\\ p)$$<\/p>\n\n\n\n<p>\u5728CTF\u4e2d\uff0c\u4e00\u822c\u6709\u4ee5\u4e0b\u9898\u578b\uff1a<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4e00.\u6c42\u9006<\/h2>\n\n\n\n<p>\u6240\u8c13\u6c42\u9006\uff0c\u5176\u5b9e\u5373\u4e3a\u5df2\u77e5\\(a,b,p,c\\)\u540e\u6c42\u89e3\u65b9\u7a0b\uff1a<\/p>\n\n\n\n<p>$$c\\equiv(ax+b)\\ (mod\\ p)$$<\/p>\n\n\n\n<p>\u7531\u6570\u8bba\u77e5\u8bc6\u6211\u4eec\u5f88\u5bb9\u6613\u53ef\u4ee5\u77e5\u9053\uff1a<\/p>\n\n\n\n<p>$$x\\equiv(c-b)a^{-1}\\ (mod\\ p)$$<\/p>\n\n\n\n<p>\u5bf9\u4e8e\u8fd9\u7c7b\u9898\u76ee\uff0c\u6211\u4eec\u53ea\u9700\u5229\u7528\u4ee5\u4e0a\u516c\u5f0f\u5373\u53ef\u5feb\u901f\u89e3\u51fa\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e8c.\u6c42\u53c2\u6570a,b\u540e\u6c42\u9006<\/strong><\/h2>\n\n\n\n<p>\u8fd9\u7c7b\u9898\u578b\u4e00\u822c\u90fd\u4f1a\u7ed9\u51fa\u4e00\u5217\u8fde\u7eed\u7ecf\u8fc7\u51e0\u6b21\u7ebf\u6027\u540c\u4f59\u7684\u6570\u636e\u540e\u5f97\u51fa\u7684\u6570\u636e\u548c\\(p\\)\uff0c\u6211\u4eec\u9700\u8981\u901a\u8fc7\u8fd9\u4e9b\u6709\u9650\u7684\u6570\u636e\u6765\u6c42\u89e3\u539f\u6765\u7684\u6570\u636e\uff0c\u5728\u6b64\u4e4b\u524d\u6211\u4eec\u9700\u8981\u5148\u6c42\u89e3\\(a\\)\u548c\\(b\\)\uff0c\u5927\u81f4\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/p>\n\n\n\n<p>\u5047\u8bbe\u5df2\u77e5\\(x_{n},x_{n+1},x_{n+2}\\)\uff0c\u6211\u4eec\u6709\uff1a<\/p>\n\n\n\n<p>$$x_{n+1}\\equiv ax_n+b\\ (mod\\ p)\\\\ x_{n+2}\\equiv ax_{n+1}+b\\ (mod\\ p)$$<\/p>\n\n\n\n<p>\u6240\u4ee5\u6211\u4eec\u6709\uff1a<\/p>\n\n\n\n<p>$$x_{n+2}-x_{n+1}\\equiv a(x_{n+1}-x_n)\\ (mod\\ p)$$<\/p>\n\n\n\n<p>\u6240\u4ee5\uff1a<\/p>\n\n\n\n<p>$$a\\equiv (x_{n+2}-x_{n+1})(x_{n+1}-x_n)^{-1}\\ (mod\\ p)(\u5047\u5b9a(x_{n+1}-x_n)\u4e0ep\u4e92\u8d28)$$<\/p>\n\n\n\n<p>\u90a3\u4e48\u6211\u4eec\u6709\uff1a<\/p>\n\n\n\n<p>$$b\\equiv x_{n+1}-ax_n\\ (mod\\ p)$$<\/p>\n\n\n\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u5f97\u5230\\(a,b\\)\uff0c\u518d\u901a\u8fc7\u6c42\u9006\u5f97\u51fa\u539f\u6765\u7684\u6570\u636e\u5373\u53ef\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4f8b\uff1a[Newstar CTF2023]Week3 babyrandom<\/h3>\n\n\n\n<p>\u52a0\u5bc6\u4ee3\u7801\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#2e3440ff\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" style=\"color:#d8dee9ff;display:none\" aria-label=\"\u590d\u5236\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>#!\/usr\/bin\/python3\nfrom secret import flag\nfrom Crypto.Util.number import *\nfrom random import randrange\n\np = 64999433139797068147576269731948390094958654326970231465808792590598519729077\n\na = randrange(2, p)\nb = randrange(2, p)\nx = bytes_to_long(flag)\nmenu = '''\n\nRandom as a Service with LCG backend\n\nEnter your option\n1. Reset\n2. Get\n3. Exit\n'''\n\ndef GetRandom():\n    global x\n    nx = (a*x + b) % p\n    print(nx)\n    x = nx\n    \nwhile True:\n    print(menu)\n    opt = input('> ')\n    try:\n        opt = int(opt)\n        if opt == 1:\n            x = bytes_to_long(flag)\n        elif opt == 2:\n            GetRandom()\n        elif opt == 3:\n            break\n        else:\n            print('invalid option')\n    except Exception as e:\n        print('oh no, something wrong!')\n        print(e)<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki nord\" style=\"background-color: #2e3440ff\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #616E88\">#!\/usr\/bin\/python3<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> secret <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> flag<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> Crypto<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">Util<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">number <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">*<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> random <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> randrange<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">p <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #B48EAD\">64999433139797068147576269731948390094958654326970231465808792590598519729077<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">a <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">randrange<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">2<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\"> p<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">b <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">randrange<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">2<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\"> p<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">x <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">bytes_to_long<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">flag<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">menu <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">&#39;&#39;&#39;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">Random as a Service with LCG backend<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">Enter your option<\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">1. Reset<\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">2. Get<\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">3. Exit<\/span><\/span>\n<span class=\"line\"><span style=\"color: #ECEFF4\">&#39;&#39;&#39;<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">def<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">GetRandom<\/span><span style=\"color: #ECEFF4\">():<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    <\/span><span style=\"color: #81A1C1\">global<\/span><span style=\"color: #D8DEE9FF\"> x<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    nx <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">a<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">x <\/span><span style=\"color: #81A1C1\">+<\/span><span style=\"color: #D8DEE9FF\"> b<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\"> p<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    <\/span><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">nx<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    x <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> nx<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    <\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">while<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">True<\/span><span style=\"color: #ECEFF4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    <\/span><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">menu<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    opt <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">input<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #A3BE8C\">&gt; <\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    <\/span><span style=\"color: #81A1C1\">try<\/span><span style=\"color: #ECEFF4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">        opt <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">int<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">opt<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">        <\/span><span style=\"color: #81A1C1\">if<\/span><span style=\"color: #D8DEE9FF\"> opt <\/span><span style=\"color: #81A1C1\">==<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">            x <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">bytes_to_long<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">flag<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">        <\/span><span style=\"color: #81A1C1\">elif<\/span><span style=\"color: #D8DEE9FF\"> opt <\/span><span style=\"color: #81A1C1\">==<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #B48EAD\">2<\/span><span style=\"color: #ECEFF4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">            <\/span><span style=\"color: #88C0D0\">GetRandom<\/span><span style=\"color: #ECEFF4\">()<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">        <\/span><span style=\"color: #81A1C1\">elif<\/span><span style=\"color: #D8DEE9FF\"> opt <\/span><span style=\"color: #81A1C1\">==<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #B48EAD\">3<\/span><span style=\"color: #ECEFF4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">            <\/span><span style=\"color: #81A1C1\">break<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">        <\/span><span style=\"color: #81A1C1\">else<\/span><span style=\"color: #ECEFF4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">            <\/span><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #A3BE8C\">invalid option<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    <\/span><span style=\"color: #81A1C1\">except<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #8FBCBB\">Exception<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">as<\/span><span style=\"color: #D8DEE9FF\"> e<\/span><span style=\"color: #ECEFF4\">:<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">        <\/span><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #A3BE8C\">oh no, something wrong!<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">        <\/span><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">e<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p>\u8fd9\u9053\u9898\u63d0\u4f9b\u4e86\u9776\u673a\uff0c\u53ef\u4ee5\u901a\u8fc7\u9776\u673a\u5f97\u51fa\u4e09\u4e2a\u8fde\u7eed\u52a0\u5bc6\u540e\u6570\u636e\uff0c\u89e3\u5bc6\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#2e3440ff\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" style=\"color:#d8dee9ff;display:none\" aria-label=\"\u590d\u5236\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>import pwn\nfrom Crypto.Util.number import *\nimport gmpy2\nx = []\np = 64999433139797068147576269731948390094958654326970231465808792590598519729077\nio = pwn.remote(\"node4.buuoj.cn\",25624)\nio.recv()\nio.sendline(b'1')\nio.recv()\nfor _ in range(3):\n    io.sendline(b'2')\n    data = io.recvline()\n    io.recv()\n    x.append(int(data))\nio.sendline(b'3')\na = (x&#91;2&#93;-x&#91;1&#93;)*gmpy2.invert(x&#91;1&#93;-x&#91;0&#93;,p)%p\nb = (x&#91;1&#93;-a*x&#91;0&#93;)%p\nx = (x&#91;0&#93;-b)*gmpy2.invert(a,p)%p\nprint(long_to_bytes(x))<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki nord\" style=\"background-color: #2e3440ff\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> pwn<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> Crypto<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">Util<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">number <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">*<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> gmpy2<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">x <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">[]<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">p <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #B48EAD\">64999433139797068147576269731948390094958654326970231465808792590598519729077<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">io <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> pwn<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">remote<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #ECEFF4\">&quot;<\/span><span style=\"color: #A3BE8C\">node4.buuoj.cn<\/span><span style=\"color: #ECEFF4\">&quot;<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #B48EAD\">25624<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">io<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">recv<\/span><span style=\"color: #ECEFF4\">()<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">io<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">sendline<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #81A1C1\">b<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #A3BE8C\">1<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">io<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">recv<\/span><span style=\"color: #ECEFF4\">()<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">for<\/span><span style=\"color: #D8DEE9FF\"> _ <\/span><span style=\"color: #81A1C1\">in<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">range<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">3<\/span><span style=\"color: #ECEFF4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    io<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">sendline<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #81A1C1\">b<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #A3BE8C\">2<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    data <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> io<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">recvline<\/span><span style=\"color: #ECEFF4\">()<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    io<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">recv<\/span><span style=\"color: #ECEFF4\">()<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    x<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">append<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #88C0D0\">int<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">data<\/span><span style=\"color: #ECEFF4\">))<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">io<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">sendline<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #81A1C1\">b<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #A3BE8C\">3<\/span><span style=\"color: #ECEFF4\">&#39;<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">a <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">2<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;)<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">gmpy2<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">invert<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">0<\/span><span style=\"color: #ECEFF4\">&#93;,<\/span><span style=\"color: #D8DEE9FF\">p<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\">p<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">b <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">a<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">0<\/span><span style=\"color: #ECEFF4\">&#93;)<\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\">p<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">x <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">0<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">b<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">gmpy2<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">invert<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">a<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\">p<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\">p<\/span><\/span>\n<span class=\"line\"><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #88C0D0\">long_to_bytes<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">))<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p>\u8fd0\u884c\u53ef\u5f97flag\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>flag{lcg_1s_n0t_s3cur3#fb528ba5}<\/p>\n<\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<blockquote class=\"wp-block-quote is-style-default is-layout-flow wp-block-quote-is-layout-flow\">\n<p><\/p>\n<\/blockquote>\n<\/blockquote>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>\u4e09.\u6c42\u53c2\u6570a,b,p\u540e\u6c42\u9006<\/strong><\/h2>\n\n\n\n<p>\u4e0e\u4e0a\u4e00\u79cd\u5f62\u5f0f\u76f8\u4f3c\uff0c\u4f46\u662f\u591a\u4e86\u4e2a\\(p\\)\u8981\u6c42\uff0c\u6211\u4eec\u5047\u8bbe\u4e00\u4e2a\u6570\u5217\uff1a<\/p>\n\n\n\n<p>$$\\{x_0,x_1,x_2,\\cdots,x_{n-1},x_{n},\\cdots\\}$$<\/p>\n\n\n\n<p>\u5176\u6ee1\u8db3\uff1a<\/p>\n\n\n\n<p>$$x_{n+1}\\equiv ax_n+b\\ (mod\\ p)$$<\/p>\n\n\n\n<p>\u5047\u8bbe\u6709\u4e00\u4e2a\u6570\u5217 \\(\\{t_n\\}\\) \u6709\uff1a\\(t_n\\equiv x_{n+1}-x_n\\equiv a(x_n-x_{n-1})\\equiv at_{n-1}\\ (mod\\ p)\\)<\/p>\n\n\n\n<p>\u6240\u4ee5\uff1a\\(t_{n+1}t_{n-1}\\equiv a^{2}t_{n-1}^2\\equiv t_n^2\\ (mod\\ p)\\)<\/p>\n\n\n\n<p>\u4e5f\u5c31\u662f\u8bf4\uff1a\\(t_{n+1}t_{n-1}-t_n^{2}=kp\\ (k\\in Z)\\)<\/p>\n\n\n\n<p>\u540c\u7406\uff0c\u6709\uff1a\\(t_{n+2}t_{n}-t_{n+1}^{2}=k&#8217;p\\ (k&#8217;\\in Z)\\)<\/p>\n\n\n\n<p>\u6240\u4ee5\uff1a<\/p>\n\n\n\n<p>$$p=gcd(t_{n+2}t_{n}-t_{n+1}^{2},t_{n+1}t_{n-1}-t_n^{2})$$<\/p>\n\n\n\n<p>\u6c42\u51fap\u540e\u6211\u4eec\u5c31\u53ef\u4ee5\u7531\u4e0a\u79cd\u7c7b\u578b\u7ee7\u7eed\u6c42\u89e3\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\u8981\u6ce8\u610f\uff0c\u4e0a\u9762\u6c42\u51fa\u7684\\(p\\)\u4e0d\u4e00\u5b9a\u5c31\u662f\u5b9e\u9645\u8981\u6c42\u7684\\(p\\)\uff0c\u6240\u4ee5\u9700\u8981\u7efc\u5408\u591a\u7ec4\u6570\u636e\u6c42\u89e3\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u4f8b\uff1a[PCTF2023]cgl<\/strong><\/h3>\n\n\n\n<p>\u52a0\u5bc6\u4ee3\u7801\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#2e3440ff\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" style=\"color:#d8dee9ff;display:none\" aria-label=\"\u590d\u5236\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>from Crypto.Util.number import *\nimport base64\nfrom random import *\nfrom secrets import flag,hint,key_number\n\nhint=bytes_to_long(hint)\n\na = getPrime(256)\nb = getPrime(256)\nn = getPrime(256)\n\nstate = hint\nresult = []\nfor _ in range(5):\n    state = (state * a + b) % n\n    result.append(state)\n\nprint(result)\n\n\nenc=list(base64.b64encode(flag))\nseed(key_number)\nshuffle(enc)\n\nprint(bytes(enc))\n\"\"\"\n&#91;64808739969023370119048821688797617211776674130654821075486774236651303382814, \n79259085906502785899793009961165414442137337544515472474317826031734962148580, \n47572752582229256276978761367590954300620113464013293239765792280017260371290, \n38491979589561565391093783861378040494484383004914878495301417593240442882761, \n58955289126482266943455593731576872529828229203595014577711629479455475819111&#93;\nb'QkiTMMx3St9IYTLMN2DmR0t53zd1MhmJT1hZ2YiwMZETVhwhOGYVZYcD'\n\"\"\"<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki nord\" style=\"background-color: #2e3440ff\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> Crypto<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">Util<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">number <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">*<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> base64<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> random <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">*<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> secrets <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> flag<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\">hint<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\">key_number<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">hint<\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #88C0D0\">bytes_to_long<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">hint<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">a <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">getPrime<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">256<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">b <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">getPrime<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">256<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">n <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">getPrime<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">256<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">state <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> hint<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">result <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">[]<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">for<\/span><span style=\"color: #D8DEE9FF\"> _ <\/span><span style=\"color: #81A1C1\">in<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">range<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">5<\/span><span style=\"color: #ECEFF4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    state <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">state <\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\"> a <\/span><span style=\"color: #81A1C1\">+<\/span><span style=\"color: #D8DEE9FF\"> b<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\"> n<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    result<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">append<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">state<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">result<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">enc<\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #88C0D0\">list<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">base64<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">b64encode<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">flag<\/span><span style=\"color: #ECEFF4\">))<\/span><\/span>\n<span class=\"line\"><span style=\"color: #88C0D0\">seed<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">key_number<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #88C0D0\">shuffle<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">enc<\/span><span style=\"color: #ECEFF4\">)<\/span><\/span>\n<span class=\"line\"><\/span>\n<span class=\"line\"><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #88C0D0\">bytes<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">enc<\/span><span style=\"color: #ECEFF4\">))<\/span><\/span>\n<span class=\"line\"><span style=\"color: #ECEFF4\">&quot;&quot;&quot;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">&#91;64808739969023370119048821688797617211776674130654821075486774236651303382814, <\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">79259085906502785899793009961165414442137337544515472474317826031734962148580, <\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">47572752582229256276978761367590954300620113464013293239765792280017260371290, <\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">38491979589561565391093783861378040494484383004914878495301417593240442882761, <\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">58955289126482266943455593731576872529828229203595014577711629479455475819111&#93;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #A3BE8C\">b&#39;QkiTMMx3St9IYTLMN2DmR0t53zd1MhmJT1hZ2YiwMZETVhwhOGYVZYcD&#39;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #ECEFF4\">&quot;&quot;&quot;<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p>\u8fd9\u9053\u9898\u5f88\u660e\u663e\u8981\u901a\u8fc7\u4e0a\u8ff0\u65b9\u6cd5\u6765\u6c42\u89e3hint\uff0c\u5728\u8fd9\u91cc\u6211\u4eec\u53ea\u6c42\u89e3hint\uff0c\u6c42\u89e3\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n\n\n\n<div class=\"wp-block-kevinbatdorf-code-block-pro\" data-code-block-pro-font-family=\"Code-Pro-JetBrains-Mono\" style=\"font-size:.875rem;font-family:Code-Pro-JetBrains-Mono,ui-monospace,SFMono-Regular,Menlo,Monaco,Consolas,monospace;line-height:1.25rem;--cbp-tab-width:2;tab-size:var(--cbp-tab-width, 2)\"><span style=\"display:block;padding:16px 0 0 16px;margin-bottom:-1px;width:100%;text-align:left;background-color:#2e3440ff\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"54\" height=\"14\" viewBox=\"0 0 54 14\"><g fill=\"none\" fill-rule=\"evenodd\" transform=\"translate(1 1)\"><circle cx=\"6\" cy=\"6\" r=\"6\" fill=\"#FF5F56\" stroke=\"#E0443E\" stroke-width=\".5\"><\/circle><circle cx=\"26\" cy=\"6\" r=\"6\" fill=\"#FFBD2E\" stroke=\"#DEA123\" stroke-width=\".5\"><\/circle><circle cx=\"46\" cy=\"6\" r=\"6\" fill=\"#27C93F\" stroke=\"#1AAB29\" stroke-width=\".5\"><\/circle><\/g><\/svg><\/span><span role=\"button\" tabindex=\"0\" style=\"color:#d8dee9ff;display:none\" aria-label=\"\u590d\u5236\" class=\"code-block-pro-copy-button\"><pre class=\"code-block-pro-copy-button-pre\" aria-hidden=\"true\"><textarea class=\"code-block-pro-copy-button-textarea\" tabindex=\"-1\" aria-hidden=\"true\" readonly>from Crypto.Util.number import *\nimport gmpy2\nx = &#91;64808739969023370119048821688797617211776674130654821075486774236651303382814, \n79259085906502785899793009961165414442137337544515472474317826031734962148580, \n47572752582229256276978761367590954300620113464013293239765792280017260371290, \n38491979589561565391093783861378040494484383004914878495301417593240442882761, \n58955289126482266943455593731576872529828229203595014577711629479455475819111&#93;\nt = []\nfor i in range(4):\n    t.append(x&#91;i+1&#93;-x&#91;i&#93;)\nfor i in range(1,2):\n    p = gmpy2.gcd(t&#91;i+2&#93;*t&#91;i&#93;-t&#91;i+1&#93;*t&#91;i+1&#93;,t&#91;i+1&#93;*t&#91;i-1&#93;-t&#91;i&#93;*t&#91;i&#93;)\n    a = (x&#91;2&#93;-x&#91;1&#93;)*gmpy2.invert(x&#91;1&#93;-x&#91;0&#93;,p)%p\n    b = (x&#91;1&#93;-a*x&#91;0&#93;)%p\n    x = (x&#91;0&#93; - b) * gmpy2.invert(a, p) % p\n    print(long_to_bytes(x))<\/textarea><\/pre><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"width:24px;height:24px\" fill=\"none\" viewBox=\"0 0 24 24\" stroke=\"currentColor\" stroke-width=\"2\"><path class=\"with-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2m-6 9l2 2 4-4\"><\/path><path class=\"without-check\" stroke-linecap=\"round\" stroke-linejoin=\"round\" d=\"M9 5H7a2 2 0 00-2 2v12a2 2 0 002 2h10a2 2 0 002-2V7a2 2 0 00-2-2h-2M9 5a2 2 0 002 2h2a2 2 0 002-2M9 5a2 2 0 012-2h2a2 2 0 012 2\"><\/path><\/svg><\/span><pre class=\"shiki nord\" style=\"background-color: #2e3440ff\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color: #81A1C1\">from<\/span><span style=\"color: #D8DEE9FF\"> Crypto<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">Util<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #D8DEE9FF\">number <\/span><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">*<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">import<\/span><span style=\"color: #D8DEE9FF\"> gmpy2<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">x <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">64808739969023370119048821688797617211776674130654821075486774236651303382814<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\"> <\/span><\/span>\n<span class=\"line\"><span style=\"color: #B48EAD\">79259085906502785899793009961165414442137337544515472474317826031734962148580<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\"> <\/span><\/span>\n<span class=\"line\"><span style=\"color: #B48EAD\">47572752582229256276978761367590954300620113464013293239765792280017260371290<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\"> <\/span><\/span>\n<span class=\"line\"><span style=\"color: #B48EAD\">38491979589561565391093783861378040494484383004914878495301417593240442882761<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\"> <\/span><\/span>\n<span class=\"line\"><span style=\"color: #B48EAD\">58955289126482266943455593731576872529828229203595014577711629479455475819111<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">t <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">[]<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">for<\/span><span style=\"color: #D8DEE9FF\"> i <\/span><span style=\"color: #81A1C1\">in<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">range<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">4<\/span><span style=\"color: #ECEFF4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    t<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">append<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #81A1C1\">+<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #ECEFF4\">&#93;)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #81A1C1\">for<\/span><span style=\"color: #D8DEE9FF\"> i <\/span><span style=\"color: #81A1C1\">in<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #88C0D0\">range<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #B48EAD\">2<\/span><span style=\"color: #ECEFF4\">):<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    p <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> gmpy2<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">gcd<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #81A1C1\">+<\/span><span style=\"color: #B48EAD\">2<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #81A1C1\">+<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #81A1C1\">+<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;,<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #81A1C1\">+<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">t<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #D8DEE9FF\">i<\/span><span style=\"color: #ECEFF4\">&#93;)<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    a <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">2<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;)<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">gmpy2<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">invert<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">0<\/span><span style=\"color: #ECEFF4\">&#93;,<\/span><span style=\"color: #D8DEE9FF\">p<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\">p<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    b <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">1<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\">a<\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">0<\/span><span style=\"color: #ECEFF4\">&#93;)<\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\">p<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    x <\/span><span style=\"color: #81A1C1\">=<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">&#91;<\/span><span style=\"color: #B48EAD\">0<\/span><span style=\"color: #ECEFF4\">&#93;<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">-<\/span><span style=\"color: #D8DEE9FF\"> b<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">*<\/span><span style=\"color: #D8DEE9FF\"> gmpy2<\/span><span style=\"color: #ECEFF4\">.<\/span><span style=\"color: #88C0D0\">invert<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">a<\/span><span style=\"color: #ECEFF4\">,<\/span><span style=\"color: #D8DEE9FF\"> p<\/span><span style=\"color: #ECEFF4\">)<\/span><span style=\"color: #D8DEE9FF\"> <\/span><span style=\"color: #81A1C1\">%<\/span><span style=\"color: #D8DEE9FF\"> p<\/span><\/span>\n<span class=\"line\"><span style=\"color: #D8DEE9FF\">    <\/span><span style=\"color: #88C0D0\">print<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #88C0D0\">long_to_bytes<\/span><span style=\"color: #ECEFF4\">(<\/span><span style=\"color: #D8DEE9FF\">x<\/span><span style=\"color: #ECEFF4\">))<\/span><\/span><\/code><\/pre><\/div>\n\n\n\n<p>\u8fd0\u884c\u53ef\u4ee5\u5f97\u51fahint\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>key_number=randrange(999999)<\/p>\n<\/blockquote>\n\n\n\n<p>\u8981\u6ce8\u610f\u7684\u662f\uff1a\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\\(\\{x_n\\}\\)\u7684\u5143\u7d20\u6570\u91cf\u5e94\u8be5\u81f3\u5c11\u8981\u67095\u4e2a\u624d\u80fd\u6c42\u89e3\u51fa\\(p\\)\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5173\u4e8e\u7ebf\u6027\u540c\u4f59\u53d1\u751f\u5668<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[7],"class_list":["post-55","post","type-post","status-publish","format-standard","hentry","category-3","tag-crypto"],"_links":{"self":[{"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/posts\/55","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/comments?post=55"}],"version-history":[{"count":6,"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/posts\/55\/revisions"}],"predecessor-version":[{"id":61,"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/posts\/55\/revisions\/61"}],"wp:attachment":[{"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/media?parent=55"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/categories?post=55"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.triode.cc\/index.php\/wp-json\/wp\/v2\/tags?post=55"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}