From 9d2382cf5f10f06245d5f0cc7b8b250e6e19d06e Mon Sep 17 00:00:00 2001
From: Runxi Yu <me@runxiyu.org>
Date: Sun, 23 Mar 2025 18:53:35 +0800
Subject: Add MathML notation

---
 flags.go  | 1 +
 global.go | 7 ++++---
 main.go   | 4 +++-
 tmpl.go   | 1 +
 4 files changed, 9 insertions(+), 4 deletions(-)

diff --git a/flags.go b/flags.go
index 8dba141..8e3fcba 100644
--- a/flags.go
+++ b/flags.go
@@ -18,4 +18,5 @@ func init() {
 	flag.StringVar(&destHost, "upstream", "http://127.0.0.1:8080", "destination url base to proxy to")
 	flag.BoolVar(&secondary, "secondary", false, "trust X-Forwarded-For headers")
 	flag.Parse()
+	global.NeedBitsReverse = 256 - global.NeedBits
 }
diff --git a/global.go b/global.go
index b5afaa8..772dce5 100644
--- a/global.go
+++ b/global.go
@@ -4,7 +4,8 @@
 package main
 
 var global = struct {
-	NeedBits  uint
-	SourceURL string
-	Version   string
+	NeedBits        uint
+	NeedBitsReverse uint
+	SourceURL       string
+	Version         string
 }{}
diff --git a/main.go b/main.go
index 342138e..77f1456 100644
--- a/main.go
+++ b/main.go
@@ -39,11 +39,13 @@ func main() {
 		}
 
 		authPage := func(message string) {
-			_ = tmpl.Execute(writer, tparams{
+			err := tmpl.Execute(writer, tparams{
 				Identifier: base64.StdEncoding.EncodeToString(identifier),
 				Message:    message,
 				Global:     global,
 			})
+			if err != nil {
+			}
 		}
 
 		if request.ParseForm() != nil {
diff --git a/tmpl.go b/tmpl.go
index ca21b96..b6fb9e0 100644
--- a/tmpl.go
+++ b/tmpl.go
@@ -195,6 +195,7 @@ func init() {
 
 		<section>
 			<p>Select a nonce no longer than 32 bytes, such that when it is appended to the decoded form of the challenge identifier, and the entire result is hashed with SHA-256, the first {{ .Global.NeedBits }} bits of the SHA-256 hash are all zeros. Within one octet, higher bits are considered to come before lower bits.</p>
+			<p>In other words, find an nonce <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mi>N</mi><annotation encoding="application/x-tex">N</annotation></semantics></math> with <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false" form="prefix">|</mo><mi>N</mi><mo stretchy="false" form="postfix">|</mo><mo>≤</mo><mn>32</mn><mspace width="0.167em"></mspace><mi mathvariant="normal">B</mi></mrow><annotation encoding="application/x-tex">\lvert N\rvert \le 32\,\mathrm{B}</annotation></semantics></math>, such that <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">H</mi><mi mathvariant="normal">A</mi><mn mathvariant="normal">256</mn></mrow><mrow><mo stretchy="true" form="prefix">(</mo><mi>B</mi><mspace width="0.167em"></mspace><mo stretchy="false" form="postfix">∥</mo><mspace width="0.167em"></mspace><mi>N</mi><mo stretchy="true" form="postfix">)</mo></mrow><mo>&lt;</mo><msup><mn>2</mn><mn>{{ .Global.NeedBitsReverse }}</mn></msup></mrow><annotation encoding="application/x-tex">\mathrm{SHA256}(B \,\|\, N) &lt; 2^&lcub;{{ .Global.NeedBitsReverse }}&rcub;</annotation></semantics></math> in big endian.</p>
 			<label for="unsigned-identifier">Challenge identifier (read-only)</label>
 			<input id="unsigned-identifier" type="text" readonly disabled tabindex="-1" value="{{ .Identifier }}" />
 		</section>
-- 
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