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diff --git a/2024/11/01/binius-02/index.html b/2024/11/01/binius-02/index.html
@@ -76,7 +76,7 @@
   <meta property="og:type" content="article">
     <meta property="article:section" content="post">
     <meta property="article:published_time" content="2024-11-01T08:00:00+08:00">
-    <meta property="article:modified_time" content="2024-11-04T15:03:16+08:00">
+    <meta property="article:modified_time" content="2024-11-04T16:03:21+08:00">
     <meta property="article:tag" content="Cryptography">
     <meta property="article:tag" content="Finite Fields">
     <meta property="article:tag" content="SNARK">
@@ -85,8 +85,8 @@
   <meta itemprop="name" content="Notes on Binius (Part II): Subspace Polynomial">
   <meta itemprop="description" content="FRI-Binus 论文 [DP24] 中讨论了基于 Subspace Polynomial 的 Additive FFT 算法，并给出了用奇偶项分解的视角来理解 [LCH14] 中的基于 Novel Polynomial Basis 的 Additive FFT 算法。本文直接介绍子空间多项式 Subspace Polynomial，然后据此介绍奇偶项分解视角的 Additive FFT 算法。本文省去了 Normalized Subspace Polynomial 的定义，方便读者理解。Normalization 只是影响 FFT 算法的性能，和本文介绍的简化版算法并没有本质的区别。">
   <meta itemprop="datePublished" content="2024-11-01T08:00:00+08:00">
-  <meta itemprop="dateModified" content="2024-11-04T15:03:16+08:00">
-  <meta itemprop="wordCount" content="3275">
+  <meta itemprop="dateModified" content="2024-11-04T16:03:21+08:00">
+  <meta itemprop="wordCount" content="5561">
   <meta itemprop="keywords" content="Cryptography,Finite Fields,SNARK,Binius">
   <meta name="twitter:card" content="summary">
   <meta name="twitter:title" content="Notes on Binius (Part II): Subspace Polynomial">
@@ -585,7 +585,7 @@ <h2 id="s_1-映射的复合">${s}_1$ 映射的复合</h2>
 $$
 s^{(i)}_{j}(X) = s^{(i+j-1)}_1\circ s^{(i+j-2)}_1\circ \cdots \circ s^{(i)}_1
 $$<h2 id="多项式的-polynomial-basis">多项式的 Polynomial Basis</h2>
-<p>对于一个次数小于 $N=2^n$ 的一元多项式 $f(X) \in \mathbb{F}[X]^{<N}$，它有两种常见的表达形式，「系数式」与「点值式」。其中系数式是我们最常见的形式：</p>
+<p>对于一个次数小于 $N=2^n$ 的一元多项式 $f(X) \in \mathbb{F}[X]^{\lt N}$，它有两种常见的表达形式，「系数式」与「点值式」。其中系数式是我们最常见的形式：</p>
 $$
 f(X) = c_0 + c_1X + c_2X^2 + \ldots + c_{N-1}X^{N-1}
 $$<p>其中 $\vec{c}=(c_0, c_1, \ldots, c_{N-1})$ 为多项式的系数向量。另外未知数的向量 $(1, X, X^2, \ldots, X^{N-1})$ 则构成了一组多项式的基（Basis），按惯例称之为 Monomial Basis，记为 $\mathcal{B}^{mono}$ :</p>
@@ -804,11 +804,11 @@ <h2 id="references">References</h2>
     <span class="item-content">
       2024-11-04
 
-        <a href="https://github.com/sec-bit/blog/commit/317852adf7d5d4f606383f27407fa151523f4ff1" title="fix: support html in md">
-          (317852a)
+        <a href="https://github.com/sec-bit/blog/commit/261e110b7ce432ad2a0380610ba6a30b516b9efe" title="fix: &lt; to \lt">
+          (261e110)
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-          <br>fix: support html in md
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     </span>

diff --git a/categories/index.html b/categories/index.html
@@ -78,7 +78,7 @@
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+  <meta itemprop="dateModified" content="2024-11-04T16:03:21+08:00">
   <meta name="twitter:card" content="summary">
   <meta name="twitter:title" content="Categories">
   <meta name="twitter:description" content="SECBIT THE WORLD">

diff --git a/categories/index.xml b/categories/index.xml
@@ -6,7 +6,7 @@
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     <generator>Hugo</generator>
     <language>zh-cn</language>
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diff --git a/categories/mle-pcs/index.html b/categories/mle-pcs/index.html
@@ -78,7 +78,7 @@
   <meta itemprop="name" content="Mle-Pcs">
   <meta itemprop="description" content="SECBIT THE WORLD">
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+  <meta itemprop="dateModified" content="2024-11-04T16:03:21+08:00">
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diff --git a/categories/mle-pcs/index.xml b/categories/mle-pcs/index.xml
@@ -6,7 +6,7 @@
     <description>Recent content in Mle-Pcs on SECBIT Blog</description>
     <generator>Hugo</generator>
     <language>zh-cn</language>
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+    <lastBuildDate>Mon, 04 Nov 2024 16:03:21 +0800</lastBuildDate>
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       <title>Notes on Binius (Part II): Subspace Polynomial</title>

diff --git a/en/2024/11/01/binius-02/index.html b/en/2024/11/01/binius-02/index.html
@@ -76,7 +76,7 @@
   <meta property="og:type" content="article">
     <meta property="article:section" content="post">
     <meta property="article:published_time" content="2024-11-01T08:00:00+08:00">
-    <meta property="article:modified_time" content="2024-11-04T15:03:16+08:00">
+    <meta property="article:modified_time" content="2024-11-04T16:03:21+08:00">
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     <meta property="article:tag" content="Finite Fields">
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@@ -85,8 +85,8 @@
   <meta itemprop="name" content="Notes on Binius (Part II): Subspace Polynomial">
   <meta itemprop="description" content="The FRI-Binus paper [DP24] discusses the Additive FFT algorithm based on Subspace Polynomial and provides a perspective to understand the Additive FFT algorithm based on Novel Polynomial Basis in [LCH14] using odd-even decomposition. This article directly introduces the Subspace Polynomial, and then introduces the Additive FFT algorithm from the perspective of odd-even decomposition. This article omits the definition of Normalized Subspace Polynomial for easier understanding. Normalization only affects the performance of the FFT algorithm and has no essential difference from the simplified algorithm introduced in this article.">
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   <meta itemprop="keywords" content="Cryptography,Finite Fields,SNARK,Binius">
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   <meta name="twitter:title" content="Notes on Binius (Part II): Subspace Polynomial">
@@ -585,7 +585,7 @@ <h2 id="composition-of-s_1-mappings">Composition of ${s}_1$ Mappings</h2>
 $$
 s^{(i)}_{j}(X) = s^{(i+j-1)}_1\circ s^{(i+j-2)}_1\circ \cdots \circ s^{(i)}_1
 $$<h2 id="polynomial-basis">Polynomial Basis</h2>
-<p>For a univariate polynomial $f(X) \in \mathbb{F}[X]^{<N}$ of degree less than $N=2^n$, it has two common forms of expression, &ldquo;coefficient form&rdquo; and &ldquo;point value form&rdquo;. The coefficient form is the most common form we see:</p>
+<p>For a univariate polynomial $f(X) \in \mathbb{F}[X]^{\lt N}$ of degree less than $N=2^n$, it has two common forms of expression, &ldquo;coefficient form&rdquo; and &ldquo;point value form&rdquo;. The coefficient form is the most common form we see:</p>
 $$
 f(X) = c_0 + c_1X + c_2X^2 + \ldots + c_{N-1}X^{N-1}
 $$<p>where $\vec{c}=(c_0, c_1, \ldots, c_{N-1})$ is the coefficient vector of the polynomial. In addition, the vector of unknowns $(1, X, X^2, \ldots, X^{N-1})$ forms a basis of polynomials, conventionally called the Monomial Basis, denoted as $\mathcal{B}^{mono}$:</p>
@@ -804,11 +804,11 @@ <h2 id="references">References</h2>
     <span class="item-content">
       2024-11-04
 
-        <a href="https://github.com/sec-bit/blog/commit/317852adf7d5d4f606383f27407fa151523f4ff1" title="fix: support html in md">
-          (317852a)
+        <a href="https://github.com/sec-bit/blog/commit/261e110b7ce432ad2a0380610ba6a30b516b9efe" title="fix: &lt; to \lt">
+          (261e110)
         </a>
 
-          <br>fix: support html in md
+          <br>fix: &lt; to \lt
 
 
     </span>

diff --git a/en/categories/index.html b/en/categories/index.html
@@ -78,7 +78,7 @@
   <meta itemprop="name" content="Categories">
   <meta itemprop="description" content="SECBIT THE WORLD">
   <meta itemprop="datePublished" content="2024-11-01T08:00:00+08:00">
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+  <meta itemprop="dateModified" content="2024-11-04T16:03:21+08:00">
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diff --git a/en/categories/index.xml b/en/categories/index.xml
@@ -6,7 +6,7 @@
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diff --git a/en/categories/mle-pcs/index.html b/en/categories/mle-pcs/index.html
@@ -78,7 +78,7 @@
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diff --git a/en/categories/mle-pcs/index.xml b/en/categories/mle-pcs/index.xml
@@ -6,7 +6,7 @@
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diff --git a/en/index.html b/en/index.html
@@ -78,7 +78,7 @@
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diff --git a/en/index.xml b/en/index.xml
@@ -170,7 +170,7 @@ $$&lt;p&gt;More generally, we can prove the following important property, that i
 $$
 s^{(i)}_{j}(X) = s^{(i+j-1)}_1\circ s^{(i+j-2)}_1\circ \cdots \circ s^{(i)}_1
 $$&lt;h2 id=&#34;polynomial-basis&#34;&gt;Polynomial Basis&lt;/h2&gt;
-&lt;p&gt;For a univariate polynomial $f(X) \in \mathbb{F}[X]^{&lt;N}$ of degree less than $N=2^n$, it has two common forms of expression, &amp;ldquo;coefficient form&amp;rdquo; and &amp;ldquo;point value form&amp;rdquo;. The coefficient form is the most common form we see:&lt;/p&gt;
+&lt;p&gt;For a univariate polynomial $f(X) \in \mathbb{F}[X]^{\lt N}$ of degree less than $N=2^n$, it has two common forms of expression, &amp;ldquo;coefficient form&amp;rdquo; and &amp;ldquo;point value form&amp;rdquo;. The coefficient form is the most common form we see:&lt;/p&gt;
 $$
 f(X) = c_0 + c_1X + c_2X^2 + \ldots + c_{N-1}X^{N-1}
 $$&lt;p&gt;where $\vec{c}=(c_0, c_1, \ldots, c_{N-1})$ is the coefficient vector of the polynomial. In addition, the vector of unknowns $(1, X, X^2, \ldots, X^{N-1})$ forms a basis of polynomials, conventionally called the Monomial Basis, denoted as $\mathcal{B}^{mono}$:&lt;/p&gt;

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diff --git a/en/post/index.xml b/en/post/index.xml
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diff --git a/en/tags/binius/index.xml b/en/tags/binius/index.xml
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diff --git a/en/tags/cryptography/index.html b/en/tags/cryptography/index.html
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diff --git a/en/tags/finite-fields/index.html b/en/tags/finite-fields/index.html
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diff --git a/en/tags/finite-fields/index.xml b/en/tags/finite-fields/index.xml
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@@ -6,7 +6,7 @@
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