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<!doctype html><html lang="zh-CN"><head><meta charset="utf-8" /><meta name="viewport" content="width=device-width,initial-scale=1" /><meta name="generator" content="VuePress 2.0.0-rc.24" /><meta name="theme" content="VuePress Theme Plume 1.0.0-rc.164" /><script id="check-mac-os">document.documentElement.classList.toggle('mac', /Mac|iPhone|iPod|iPad/i.test(navigator.platform))</script><script id="check-dark-mode">;(function () {const um= localStorage.getItem('vuepress-theme-appearance') || 'auto';const sm = window.matchMedia && window.matchMedia('(prefers-color-scheme: dark)').matches;const isDark = um === 'dark' || (um !== 'light' && sm);document.documentElement.dataset.theme = isDark ? 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data-v-12048f0f>替换密码</span><!----></p><!--]--><!----></a><!----></div><!----></div><div class="vp-sidebar-item sidebar-item level-1 is-link" data-v-12048f0f data-v-12048f0f><div class="item" data-v-12048f0f><div class="indicator" data-v-12048f0f></div><!----><a class="vp-link link link" href="/theory/cryptography/permutation-encryption/" data-v-12048f0f><!--[--><p class="text" data-v-12048f0f><span data-v-12048f0f>置换密码</span><!----></p><!--]--><!----></a><!----></div><!----></div><!--]--></div></div></section></div><!--]--><!--[--><!--]--></nav></aside><!--[--><div id="VPContent" vp-content class="vp-content has-sidebar" data-v-f73ca3da data-v-b2beaca7><div class="vp-doc-container has-sidebar has-aside" data-v-b2beaca7 data-v-23f6ad98><!--[--><!--]--><div class="container" data-v-23f6ad98><div class="aside" vp-outline data-v-23f6ad98><div class="aside-curtain" data-v-23f6ad98></div><div class="aside-container" data-v-23f6ad98><div class="aside-content" data-v-23f6ad98><div 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data-v-1ae4ad7a><a class="vp-link link breadcrumb" href="/" property="item" typeof="WebPage" data-v-1ae4ad7a><!--[-->首页<!--]--><!----></a><span class="vpi-chevron-right" data-v-1ae4ad7a></span><meta property="name" content="首页" data-v-1ae4ad7a><meta property="position" content="1" data-v-1ae4ad7a></li><li property="itemListElement" typeof="ListItem" data-v-1ae4ad7a><span class="vp-link breadcrumb" property="item" typeof="WebPage" data-v-1ae4ad7a><!--[-->古典加密算法<!--]--><!----></span><span class="vpi-chevron-right" data-v-1ae4ad7a></span><meta property="name" content="古典加密算法" data-v-1ae4ad7a><meta property="position" content="2" data-v-1ae4ad7a></li><li property="itemListElement" typeof="ListItem" data-v-1ae4ad7a><a class="vp-link link breadcrumb current" href="/theory/cryptography/permutation-encryption/" property="item" typeof="WebPage" data-v-1ae4ad7a><!--[-->置换密码 - 等待完善<!--]--><!----></a><!----><meta property="name" content="置换密码 - 等待完善" data-v-1ae4ad7a><meta property="position" content="3" data-v-1ae4ad7a></li><!--]--></ol></nav><!--[--><!--]--><!--[--><h1 class="vp-doc-title page-title" data-v-ba8d1a1e><!----> 置换密码 - 等待完善 <!----></h1><div class="vp-doc-meta" data-v-ba8d1a1e><!--[--><!--]--><p class="reading-time" data-v-ba8d1a1e><span class="vpi-books icon" data-v-ba8d1a1e></span><span data-v-ba8d1a1e>约 1022 字</span><span data-v-ba8d1a1e>大约 3 分钟</span></p><!----><!--[--><!--]--><p class="create-time" data-v-ba8d1a1e><span class="vpi-clock icon" data-v-ba8d1a1e></span><span data-v-ba8d1a1e>2025-10-29</span></p></div><!--]--><!--[--><!--]--><div class="_theory_cryptography_permutation-encryption_ external-link-icon-enabled vp-doc plume-content" vp-content data-v-23f6ad98><!--[--><!--]--><div data-v-23f6ad98><p>置换密码的核心思想不是“把字母换成别的字母”（替换），而是<strong>重新排列明文字符的位置</strong>。也就是说：</p><ul><li>明文字母的集合不变，顺序发生了改变；</li><li>由于字母频率不变，置换密码依然会暴露统计特征，但单词的结构与位置模式被打散。</li></ul><p>与“替换密码”相比，置换密码更像是“洗牌”：把原本顺序排列的牌重新打乱。单独使用时并不安全，但与替换联合使用（乘积密码）能显著增强安全性。</p><!--[--><div class="mermaid-actions"><button class="preview-button" title="preview"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1316 1024" fill="currentColor"><path d="M658.286 0C415.89 0 0 297.106 0 512c0 214.82 415.89 512 658.286 512 242.322 0 658.285-294.839 658.285-512S900.608 0 658.286 0zm0 877.714c-161.573 0-512-221.769-512-365.714 0-144.018 350.427-365.714 512-365.714 161.572 0 512 217.16 512 365.714s-350.428 365.714-512 365.714z"/><path d="M658.286 292.571a219.429 219.429 0 1 0 0 438.858 219.429 219.429 0 0 0 0-438.858zm0 292.572a73.143 73.143 0 1 1 0-146.286 73.143 73.143 0 0 1 0 146.286z"/></svg></button><button class="download-button" title="download"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1024 1024" fill="currentColor"><path d="M828.976 894.125H190.189c-70.55 0-127.754-57.185-127.754-127.753V606.674c0-17.634 14.31-31.933 31.933-31.933h63.889c17.634 0 31.932 14.299 31.932 31.933v95.822c0 35.282 28.596 63.877 63.877 63.877h511.033c35.281 0 63.877-28.595 63.877-63.877v-95.822c0-17.634 14.298-31.933 31.943-31.933h63.878c17.635 0 31.933 14.299 31.933 31.933v159.7c0 70.566-57.191 127.751-127.754 127.751zM249.939 267.51c12.921-12.92 33.885-12.92 46.807 0l148.97 148.972V94.893c0-17.634 14.302-31.947 31.934-31.947h63.876c17.638 0 31.946 14.313 31.946 31.947v321.589l148.97-148.972c12.922-12.92 33.876-12.92 46.797 0l46.814 46.818c12.922 12.922 12.922 33.874 0 46.807L552.261 624.93c-1.14 1.138-21.664 13.684-42.315 13.693-20.877.01-41.88-12.542-43.021-13.693L203.122 361.135c-12.923-12.934-12.923-33.885 0-46.807l46.817-46.818z"/></svg></button></div><div class="mermaid-wrapper"><div style="display:flex;align-items:center;justify-content:center;height:96px;" class="mermaid-loading"><span style="--loading-icon: url("data:image/svg+xml;utf8,%3Csvg xmlns='http://www.w3.org/2000/svg' preserveAspectRatio='xMidYMid' viewBox='25 25 50 50'%3E%3CanimateTransform attributeName='transform' type='rotate' dur='2s' keyTimes='0;1' repeatCount='indefinite' values='0;360'%3E%3C/animateTransform%3E%3Ccircle cx='50' cy='50' r='20' fill='none' stroke='currentColor' stroke-width='4' stroke-linecap='round'%3E%3Canimate attributeName='stroke-dasharray' dur='1.5s' keyTimes='0;0.5;1' repeatCount='indefinite' values='1,200;90,200;1,200'%3E%3C/animate%3E%3Canimate attributeName='stroke-dashoffset' dur='1.5s' keyTimes='0;0.5;1' repeatCount='indefinite' values='0;-35px;-125px'%3E%3C/animate%3E%3C/circle%3E%3C/svg%3E");--icon-size: 48px;display: inline-block;width: var(--icon-size);height: var(--icon-size);background-color: currentcolor;-webkit-mask-image: var(--loading-icon);mask-image: var(--loading-icon)"></span></div></div><!--]--><h2 id="一、栅栏密码-rail-fence-cipher" tabindex="-1"><a class="header-anchor" href="#一、栅栏密码-rail-fence-cipher"><span>一、栅栏密码（Rail Fence Cipher）</span></a></h2><p><strong>工作原理</strong>： 将明文按“Z字形”写入若干行（称为“栅栏/轨道”），再按行依次读出即得到密文。轨道数即为密钥。</p><p><strong>示意</strong>（以 3 轨为例）：</p><div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#393a34;--shiki-dark:#dbd7caee;--shiki-light-bg:#ffffff;--shiki-dark-bg:#121212;"><pre class="shiki shiki-themes vitesse-light vitesse-dark vp-code"><code class="language-"><span class="line"><span>轨1: 0 4 8 ...</span></span>
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<span class="line"><span>轨2: 1 3 5 7 9 ...</span></span>
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<span class="line"><span>轨3: 2 6 ...</span></span></code></pre><div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0;"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p><strong>示例</strong>： 明文：<code>HELLOWORLD</code> 轨道数：<code>3</code></p><ul><li>轨1（索引 0,4,8）：<code>H O L</code></li><li>轨2（索引 1,3,5,7,9）：<code>E L W R D</code></li><li>轨3（索引 2,6）：<code>L O</code></li></ul><p>密文为各轨串联：<code>HOL</code> + <code>ELWRD</code> + <code>LO</code> → <code>HOLELWRDLO</code></p><p><strong>数学表示</strong>： 设明文 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mo>=</mo><msub><mi>p</mi><mn>0</mn></msub><msub><mi>p</mi><mn>1</mn></msub><mo>…</mo><msub><mi>p</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">P = p_0 p_1 \dots p_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6389em;vertical-align:-0.2083em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span></span></span></span>，根据密钥生成一个位置序列 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>s</mi><mn>0</mn></msub><mo separator="true">,</mo><msub><mi>s</mi><mn>1</mn></msub><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><msub><mi>s</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">s_0, s_1, \dots, s_{n-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6389em;vertical-align:-0.2083em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em;"><span></span></span></span></span></span></span></span></span></span>（即置换次序），则：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>C</mi><mi>j</mi></msub><mo>=</mo><msub><mi>p</mi><msub><mi>s</mi><mi>j</mi></msub></msub><mo separator="true">,</mo><mspace width="1em"></mspace><mi>j</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">C_j = p_{s_j}, \quad j = 0,1,\dots,n-1 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0068em;vertical-align:-0.3473em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2819em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.3473em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p><p>解密使用逆序列 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>=</mo><msup><mi>s</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">t = s^{-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span>：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub><mo>=</mo><msub><mi>C</mi><msub><mi>t</mi><mi>i</mi></msub></msub><mo separator="true">,</mo><mspace width="1em"></mspace><mi>i</mi><mo>=</mo><mn>0</mn><mo separator="true">,</mo><mn>1</mn><mo separator="true">,</mo><mo>…</mo><mo separator="true">,</mo><mi>n</mi><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">p_i = C_{t_i}, \quad i = 0,1,\dots,n-1 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.9334em;vertical-align:-0.2501em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3281em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span></span></p><p><strong>特点</strong>：</p><ul><li>实现简单，直观“打乱顺序”</li><li>频率不变，难以抵抗纯统计分析；但位置模式被破坏，较难直接猜词</li><li>作为教学与与替换密码的组合（乘积密码）更有价值</li></ul><h2 id="二、列移位置换-columnar-transposition" tabindex="-1"><a class="header-anchor" href="#二、列移位置换-columnar-transposition"><span>二、列移位置换（Columnar Transposition）</span></a></h2><p><strong>工作原理</strong>： 选择一个关键词，将明文按列填入表格，再按关键词的字母排序对列进行重排，最终按列或按行读出密文。</p><!--[--><div class="mermaid-actions"><button class="preview-button" title="preview"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1316 1024" fill="currentColor"><path d="M658.286 0C415.89 0 0 297.106 0 512c0 214.82 415.89 512 658.286 512 242.322 0 658.285-294.839 658.285-512S900.608 0 658.286 0zm0 877.714c-161.573 0-512-221.769-512-365.714 0-144.018 350.427-365.714 512-365.714 161.572 0 512 217.16 512 365.714s-350.428 365.714-512 365.714z"/><path d="M658.286 292.571a219.429 219.429 0 1 0 0 438.858 219.429 219.429 0 0 0 0-438.858zm0 292.572a73.143 73.143 0 1 1 0-146.286 73.143 73.143 0 0 1 0 146.286z"/></svg></button><button class="download-button" title="download"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1024 1024" fill="currentColor"><path d="M828.976 894.125H190.189c-70.55 0-127.754-57.185-127.754-127.753V606.674c0-17.634 14.31-31.933 31.933-31.933h63.889c17.634 0 31.932 14.299 31.932 31.933v95.822c0 35.282 28.596 63.877 63.877 63.877h511.033c35.281 0 63.877-28.595 63.877-63.877v-95.822c0-17.634 14.298-31.933 31.943-31.933h63.878c17.635 0 31.933 14.299 31.933 31.933v159.7c0 70.566-57.191 127.751-127.754 127.751zM249.939 267.51c12.921-12.92 33.885-12.92 46.807 0l148.97 148.972V94.893c0-17.634 14.302-31.947 31.934-31.947h63.876c17.638 0 31.946 14.313 31.946 31.947v321.589l148.97-148.972c12.922-12.92 33.876-12.92 46.797 0l46.814 46.818c12.922 12.922 12.922 33.874 0 46.807L552.261 624.93c-1.14 1.138-21.664 13.684-42.315 13.693-20.877.01-41.88-12.542-43.021-13.693L203.122 361.135c-12.923-12.934-12.923-33.885 0-46.807l46.817-46.818z"/></svg></button></div><div class="mermaid-wrapper"><div style="display:flex;align-items:center;justify-content:center;height:96px;" class="mermaid-loading"><span style="--loading-icon: url("data:image/svg+xml;utf8,%3Csvg xmlns='http://www.w3.org/2000/svg' preserveAspectRatio='xMidYMid' viewBox='25 25 50 50'%3E%3CanimateTransform attributeName='transform' type='rotate' dur='2s' keyTimes='0;1' repeatCount='indefinite' values='0;360'%3E%3C/animateTransform%3E%3Ccircle cx='50' cy='50' r='20' fill='none' stroke='currentColor' stroke-width='4' stroke-linecap='round'%3E%3Canimate attributeName='stroke-dasharray' dur='1.5s' keyTimes='0;0.5;1' repeatCount='indefinite' values='1,200;90,200;1,200'%3E%3C/animate%3E%3Canimate attributeName='stroke-dashoffset' dur='1.5s' keyTimes='0;0.5;1' repeatCount='indefinite' values='0;-35px;-125px'%3E%3C/animate%3E%3C/circle%3E%3C/svg%3E");--icon-size: 48px;display: inline-block;width: var(--icon-size);height: var(--icon-size);background-color: currentcolor;-webkit-mask-image: var(--loading-icon);mask-image: var(--loading-icon)"></span></div></div><!--]--><p><strong>简例（概念演示）</strong>： 明文：<code>ATTACKATDAWN</code> 关键词：<code>ZEBRA</code>（按字母表排序为 <code>A B E R Z</code>）</p><ol><li>将明文逐行填入 5 列表格；</li><li>按关键词排序（A→B→E→R→Z）重排列；</li><li>按重排后的列依次读出密文。</li></ol><p>（实际实现时需要处理明文长度不足一整行的填充策略，如使用 <code>X</code> 或留空。）</p><p><strong>数学表示（一般置换模型）</strong>： 关键词决定一个列置换 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span></span></span></span>，其作用是重新排列列索引。若把明文按列读取为序列 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi></mrow><annotation encoding="application/x-tex">P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>，加密可抽象为：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>C</mi><mo>=</mo><msub><mrow><mi mathvariant="normal">Permute</mi><mo></mo></mrow><mi>π</mi></msub><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">)</mo><mo separator="true">,</mo><mspace width="1em"></mspace><mi>P</mi><mo>=</mo><msub><mrow><mi mathvariant="normal">Permute</mi><mo></mo></mrow><msup><mi>π</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></msub><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">C = \operatorname{Permute}_{\pi}(P), \quad P = \operatorname{Permute}_{\pi^{-1}}(C) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop"><span class="mop"><span class="mord mathrm">Permute</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">π</span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mclose">)</span><span class="mpunct">,</span><span class="mspace" style="margin-right:1em;"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop"><span class="mop"><span class="mord mathrm">Permute</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.5224em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">π</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463em;"><span style="top:-2.786em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.1776em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mclose">)</span></span></span></span></span></p><p><strong>特点</strong>：</p><ul><li>比栅栏更灵活，关键词让置换更“难猜”</li><li>仍保留频率分布，易受已知明文/选择明文的结构分析攻击</li><li>常与替换结合形成更强的乘积密码（如 ADFGX/ADFGVX 密码）</li></ul><h2 id="三、联合与加固-置换-×-替换" tabindex="-1"><a class="header-anchor" href="#三、联合与加固-置换-×-替换"><span>三、联合与加固：置换 × 替换</span></a></h2><p>将“替换”与“置换”组合（先替换后置换，或多轮交替）能显著增强安全性：</p><ul><li>替换打乱统计特征（字母频率分布变平）</li><li>置换打乱位置结构（模式与相邻关系被破坏）</li></ul><p>这种思路在现代密码设计中仍然常见（“混淆与扩散”理念），尽管算法形式已经大为不同。</p><h2 id="四、安全性与弱点-直观理解" tabindex="-1"><a class="header-anchor" href="#四、安全性与弱点-直观理解"><span>四、安全性与弱点（直观理解）</span></a></h2><ul><li>单独的置换密码不改变字母频率，抵抗统计攻击能力有限</li><li>容易受到已知明文/选择明文攻击（通过结构猜测置换）</li><li>多轮、复杂置换能提高攻击成本，但不建议单独用于实际安全场景</li></ul><h2 id="五、小练习-可选" tabindex="-1"><a class="header-anchor" href="#五、小练习-可选"><span>五、小练习（可选）</span></a></h2><p>试着把你自己的名字用 3 轨栅栏加密；然后写出解密过程（先确定轨道索引，再按逆序重建原文）。</p><h2 id="附件" tabindex="-1"><a class="header-anchor" href="#附件"><span>附件：</span></a></h2><p>具体的使用样例代码请参考：<a href="https://gitea.simengweb.com/si-meng-spec/cryptography-example-code" target="_blank" rel="noopener noreferrer">https://gitea.simengweb.com/si-meng-spec/cryptography-example-code</a></p></div><!----><!----><!----></div></main><footer class="vp-doc-footer" data-v-23f6ad98 data-v-7138e2cb><!--[--><!--]--><!----><div class="contributors" aria-label="Contributors" data-v-7138e2cb><span class="contributors-label" data-v-7138e2cb>贡献者: </span><span class="contributors-info" data-v-7138e2cb><!--[--><!--[--><span class="contributor" data-v-7138e2cb>祀梦</span><!----><!--]--><!--]--></span></div><nav class="prev-next" data-v-7138e2cb><div class="pager" data-v-7138e2cb><a class="vp-link link pager-link prev" href="/theory/cryptography/substitution-ciphers/" 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