diff --git a/web/src/app/login/login-form.tsx b/web/src/app/login/login-form.tsx
index 7f12e1b..a7134a4 100644
--- a/web/src/app/login/login-form.tsx
+++ b/web/src/app/login/login-form.tsx
@@ -1,12 +1,14 @@
 "use client";
 
 import { useState } from "react";
-import { useRouter, useSearchParams } from "next/navigation";
+import { useSearchParams } from "next/navigation";
 
 export function LoginForm() {
-  const router = useRouter();
   const params = useSearchParams();
-  const next = params.get("next") || "/";
+  // Only allow same-origin relative paths, so a crafted ?next=https://evil or ?next=//evil
+  // can't turn login into an open redirect.
+  const raw = params.get("next") || "/";
+  const next = raw.startsWith("/") && !raw.startsWith("//") ? raw : "/";
   const [password, setPassword] = useState("");
   const [error, setError] = useState("");
   const [busy, setBusy] = useState(false);
diff --git a/web/src/lib/auth.ts b/web/src/lib/auth.ts
index d43e733..edeb2b6 100644
--- a/web/src/lib/auth.ts
+++ b/web/src/lib/auth.ts
@@ -13,11 +13,16 @@ function toB64(bytes: Uint8Array): string {
   return btoa(s);
 }
 
+// Memoize the derived token so the middleware doesn't recompute an HMAC on every request
+// (password/secret don't change at runtime; keyed on both so a change still recomputes).
+let _cache: { password: string; secret: string; token: string } | null = null;
+
 /** The token a valid session cookie must carry, or "" when auth is disabled (no password). */
 export async function expectedToken(): Promise<string> {
   const password = process.env.LYRA_PASSWORD;
   if (!password) return "";
   const secret = process.env.LYRA_SECRET_KEY ?? "lyra";
+  if (_cache && _cache.password === password && _cache.secret === secret) return _cache.token;
   const enc = new TextEncoder();
   const key = await crypto.subtle.importKey(
     "raw",
@@ -27,7 +32,9 @@ export async function expectedToken(): Promise<string> {
     ["sign"],
   );
   const sig = await crypto.subtle.sign("HMAC", key, enc.encode(password));
-  return toB64(new Uint8Array(sig));
+  const token = toB64(new Uint8Array(sig));
+  _cache = { password, secret, token };
+  return token;
 }
 
 /** Constant-time string compare (both operands are our own derived tokens). */