Implement code word based remote authentication (#1)

Add comprehensive remote authentication system allowing users to log in from one device by authenticating from another trusted device. Features include:

- Proof of Work (PoW) protection using PBKDF2-SHA512 to prevent abuse
- Simple pairing codes (3 words) protected by dynamic PoW difficulty
- Autocomplete pairing code input with error checking
- Real-time WebSocket communication between devices

Unlike device addition links and reset links with QR codes that only allow adding an authentication method, and that work offline over the duration of several days, this mechanism is strictly online, with 5 minute time limit.

frontend/src/utils/pow.js

@@ -0,0 +1,68 @@
+/**
+ * Proof of Work utility using PBKDF2-SHA512
+ *
+ * The PoW requires finding nonces where PBKDF2(challenge, nonce) produces
+ * output with a zero first byte. Each work unit requires finding one such nonce.
+ * All valid nonces are concatenated into a solution for server verification.
+ */
+
+/**
+ * Solve a Proof of Work challenge
+ *
+ * @param {Uint8Array|ArrayBuffer} challenge - 8-byte server-provided challenge
+ * @param {number} work - Number of PBKDF2 work units required
+ * @param {object} [options] - Optional parameters
+ * @param {AbortSignal} [options.signal] - AbortSignal to cancel the operation
+ * @returns {Promise<Uint8Array>} Solution: concatenated 8-byte nonces (8 * work bytes)
+ * @throws {Error} If challenge is invalid or operation is aborted
+ */
+export async function solvePoW(challenge, work, options = {}) {
+  const { signal } = options
+  const startTime = performance.now()
+
+  // Validate inputs
+  const challengeBytes = challenge instanceof ArrayBuffer
+    ? new Uint8Array(challenge)
+    : challenge
+
+  if (!(challengeBytes instanceof Uint8Array) || challengeBytes.length !== 8) {
+    throw new Error('Challenge must be exactly 8 bytes')
+  }
+
+  // Import challenge as PBKDF2 key material
+  const baseKey = await crypto.subtle.importKey('raw', challengeBytes, 'PBKDF2', false, ['deriveBits'])
+
+  // Build solution from found nonces
+  const solution = new Uint8Array(8 * work)
+  let totalIterations = 0
+  const mask = 0x7FF  // The client must work 2048x harder than the server
+
+  // Sequential nonce starting at zero (little-endian, using Uint32Array for efficient increment)
+  const nonce = new Uint32Array(2)
+
+  for (let i = 0; i < work; i++) {
+    if (signal?.aborted) {
+      throw new DOMException('PoW operation aborted', 'AbortError')
+    }
+
+    // Find a nonce where PBKDF2 output passes the mask check
+    let result
+    do {
+      totalIterations++
+      if (++nonce[0] === 0x100000000) ++nonce[1]  // Increment 64-bit little-endian nonce
+      result = new Uint32Array(await crypto.subtle.deriveBits(
+        { name: 'PBKDF2', salt: nonce, iterations: 128, hash: 'SHA-512'},
+        baseKey,
+        32
+      ))
+    } while (result[0] & mask)
+    solution.set(new Uint8Array(nonce.buffer), i * 8)
+  }
+
+  const elapsed = (performance.now() - startTime) / 1000
+  const expectedIterations = work * (mask + 1)
+  const luckRatio = (totalIterations / expectedIterations).toFixed(1)
+  const bench = totalIterations / ((mask + 1) * elapsed)
+  console.log(`PoW work=${work} solved in ${elapsed.toFixed(2)}s (${luckRatio}x expected ${bench.toFixed(1)} work/s)`)
+  return solution
+}