work

1 files changed, 23 insertions, 23 deletions

diff --git a/index.html b/index.html
index 7b4572b..1fd52b1 100644
--- a/index.html
+++ b/index.html
@@ -35,10 +35,10 @@
 			Choose one of the following missions.
 		</p>
         <p>
-            <strong><a href="#">Nonce reuse</a>.</strong> Due to rising entropy
-            prices, Roseacrucis has started to reuse nonces. You must perform the
-            Forbidden Attack in order to recover the authentication key and
-            forge arbitrary ciphertext.
+            <strong><a href="/forbidden-salamanders/nonce-reuse">Nonce
+            reuse</a>.</strong> Due to rising entropy prices, Roseacrucis has
+            started to reuse nonces. You must perform the Forbidden Attack in order to
+            recover the authentication key and forge arbitrary ciphertext.
         </p>
         <p>
             <strong><a href="#">Nonce truncation</a>.</strong> The sorcerer
@@ -82,7 +82,7 @@
 				interpreted as the set of polynomials with coefficients in \(\mathbb{F}_2\)
 				of degree less than \(128\). Multiplication
 				is performed modulo \(m\). This field is of characteristic 2;
-				e.g., \((\alpha^5 + \alpha+1)+(\alpha^5 + \alpha+1) = 0\).
+				e.g., \((\alpha^5 + 1)+(\alpha^5 + 1) = 0\).
 			</p>
 			<p>
 				We interpret 16-byte blocks as elements in \(\mathbb{K}\)
@@ -95,40 +95,40 @@
 				the block.
 			</p>
 			<p>
-				12-byte nonces are interpreted as 96-bit integers in big-endian byte order.
-			</p>
+                12-byte nonces are interpreted as 96-bit integers in big-endian
+                byte order. Let \(\operatorname{Byte} = [0, 2^8-1]\) and
+                \(x_i\) refer to the \(i\)th 16-byte chunk of the bytestring
+                \(x\).
+            </p>
             <p>
-                Let \(\operatorname{Byte} = [0, 2^8-1]\).
+                \(\operatorname{encode_{big}}(x, n)\) encodes an integer \(x\) into \(n\) bytes in big-endian
+                byte order. \(\operatorname{pad_n}(x, p)\) pads the length of
+                the bytestring \(x\) to the nearest multiple of \(n\) with the
+                byte \(p\). \(\operatorname{AES}(k, x)\) refers to
+                the <a href="https://en.wikipedia.org/wiki/Advanced_Encryption_Standard">128-bit AES block cipher</a>.
             </p>
 			<br>
 			<div class="algorithm">
                 <p>\(\operatorname{GMAC}(h\in \mathbb{K}, s\in \mathbb{K}, aad\in \operatorname{Byte}^{y}, c\in \operatorname{Byte}^{z})\)</p>
 				<ol class="algorithm-code">
-                    <li>\( aad' = \operatorname{chunk}_{16}(aad, \operatorname{pad}=\mathtt{0x00}) \)</li>
-                    <li>\( c' = \operatorname{chunk}_{16}(c, \operatorname{pad}=\mathtt{0x00}) \)</li>
-					<li>\( len = \operatorname{encode_{big}}(128\vert aad' \vert, 8) \mathbin\Vert \operatorname{encode_{big}}(128\vert c'\vert, 8) \)</li>
-					<li>\( blocks = aad' \mathbin\Vert c' \mathbin\Vert (len) \mathbin\Vert (s) \)</li>
-					<li>\( \operatorname{return} \sum\limits_{i=1}^{\vert blocks\vert} blocks_{\vert blocks \vert-i} h^{i-1}\)</li>
+					<li>\( len = \operatorname{encode_{big}}(8y, 8) \mathbin\Vert \operatorname{encode_{big}}(8z, 8) \)</li>
+					<li>\( blocks = \operatorname{pad}_{16}(aad, 0) \mathbin\Vert \operatorname{pad}_{16}(c, 0) \mathbin\Vert len \mathbin\Vert s \)</li>
+                    <li>\( N = \frac{\vert blocks \vert}{16} \)</li>
+                    <li>\( \operatorname{return} \sum\limits_{i=1}^{N} blocks_{N-i} h^{i-1}\)</li>
 				</ol>
 			</div>
 			<br>
 			<br>
 			<div class="algorithm">
-                <p>\(\operatorname{GCM}(k\in \operatorname{Byte}^{16}, n\in \operatorname{Byte}^{12}, aad\in \operatorname{Byte}^{y}, m\in \operatorname{Byte}^{z})\)</p>
+                <p>\(\operatorname{AES-GCM}(k\in \operatorname{Byte}^{16}, n\in \operatorname{Byte}^{12}, aad\in \operatorname{Byte}^{y}, m\in \operatorname{Byte}^{z})\)</p>
 				<ol class="algorithm-code">
-					<li> \( r = \mathop{\Vert}\limits_{n'=2^{32}n+2}^{2^{32}n+2^{32}-1} \operatorname{AES-ECB}(k, n') \)</li>
+					<li> \( r = \mathop{\Vert}\limits_{n'=2^{32}n+2}^{2^{32}n+2^{32}-1} \operatorname{AES}(k, n') \)</li>
 					<li> \( c = r \oplus m \) </li>
-					<li> \( h = \operatorname{AES-ECB}(k, 0) \) </li>
-					<li> \( s = \operatorname{AES-ECB}(k, 2^{32}n + 1) \) </li>
+					<li> \( h = \operatorname{AES}(k, 0) \) </li>
+					<li> \( s = \operatorname{AES}(k, 2^{32}n + 1) \) </li>
 					<li> \( \operatorname{return} c, \operatorname{GMAC}(h, s, aad, c) \)</li>
 				</ol>
 			</div>
-            <p>
-                The authentication key \( h \) is independent of the
-                nonce \( n \). The constant term \( s \) acts as a blind to
-                hide the confidential block data in the MAC. Finally, note
-                that the polynomial computation reverses the order of the blocks.
-            </p>
 		</details>
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