How TOTP 2FA Codes Work: RFC 6238 Math, Base32 Secrets, and Clock Drift

What TOTP Actually Is

Time-based One-Time Password (TOTP) is defined in RFC 6238. It is not a new algorithm — it is a thin wrapper around HMAC-based One-Time Password (HOTP), specified in RFC 4226. HOTP derives a code from a shared secret and a moving counter. TOTP simply says: use the clock as the counter.

That one substitution is what makes authenticator apps work offline. There is no request to Google, Authy, or your identity provider when a code appears. The phone holds the secret, reads its own clock, and computes the answer. The server does the identical computation and compares.

What you get from this guide: the exact formula, the truncation step almost every explanation skips, the enrolment URI format, and the three failure modes that generate support tickets.

The RFC 6238 Formula, Step by Step

Step 1: Derive the time counter

T = floor((Current Unix Time - T0) / X)

At Unix time 1789000000, with defaults, T = floor(1789000000 / 30) = 59633333.

Step 2: Compute the HMAC

T is encoded as an 8-byte big-endian unsigned integer and passed as the message to HMAC, keyed with the raw secret:

HS = HMAC-SHA1(K, T)      // 20-byte digest

The default hash is SHA-1. RFC 6238 explicitly permits HMAC-SHA256 and HMAC-SHA512. Using SHA-1 here is not the weakness people assume — HMAC’s security relies on the pseudorandomness of the compression function, not on collision resistance, so the known SHA-1 collision attacks do not translate into TOTP forgery. Read the underlying construction in the HMAC signature guide.

Step 3: Dynamic truncation

This is the step most tutorials omit, and the reason a naive implementation produces codes the server rejects.

offset  = HS[19] & 0x0F                      // low 4 bits of the last byte
P       = HS[offset..offset+3]               // 4 consecutive bytes
binCode = P & 0x7FFFFFFF                     // clear the most significant bit

Masking the high bit removes any signed-integer ambiguity across language implementations. The result is a 31-bit integer.

Step 4: Reduce to digits

Code = binCode mod 10^Digits

With Digits = 6, binCode = 1284755224 yields 755224 — the canonical RFC 4226 test vector. Codes are zero-padded to the full width: 000042 is a valid code, 42 is not.

Reference implementation

// Browser-native TOTP with Web Crypto. rawKey = Base32-decoded secret bytes.
async function totp(rawKey, { digits = 6, step = 30, algo = "SHA-1" } = {}) {
  const counter = Math.floor(Date.now() / 1000 / step);

  // 8-byte big-endian counter
  const msg = new DataView(new ArrayBuffer(8));
  msg.setUint32(0, Math.floor(counter / 2 ** 32));
  msg.setUint32(4, counter >>> 0);

  const key = await crypto.subtle.importKey(
    "raw", rawKey, { name: "HMAC", hash: algo }, false, ["sign"]
  );
  const hs = new Uint8Array(await crypto.subtle.sign("HMAC", key, msg.buffer));

  const offset = hs[hs.length - 1] & 0x0f;
  const bin =
    ((hs[offset] & 0x7f) << 24) |
    (hs[offset + 1] << 16) |
    (hs[offset + 2] << 8) |
    hs[offset + 3];

  return String(bin % 10 ** digits).padStart(digits, "0");
}

Base32 Secrets: Why Not Base64?

The shared secret is transported as Base32 (RFC 4648, the same document that defines Base64 — see the Base64 encoding guide for the shared 5-bit and 6-bit chunking mechanics).

Base32 is the deliberate choice for three reasons:

1. Case-insensitive alphabet (A-Z and 2-7) — a user can retype it from a printed backup without shift-key errors.
2. No visually ambiguous characters — 0, 1, and 8 are excluded, so O/0 and l/1 confusion disappears.
3. Safe in URIs and QR codes without percent-encoding.

Practical detail that breaks implementations: Base32 padding (=) is optional in authenticator secrets, and most apps strip whitespace and lowercase before decoding. A 160-bit secret encodes to 32 Base32 characters. RFC 4226 requires a minimum of 128 bits and recommends 160 bits.

The Enrolment QR Code: otpauth:// URI

The QR code you scan is a plain text URI in the Key Uri Format:

otpauth://totp/Acme%20Inc:alice@example.com?secret=JBSWY3DPEHPK3PXP&issuer=Acme%20Inc&algorithm=SHA1&digits=6&period=30

Design consequence: if your server issues algorithm=SHA256&digits=8 and your users authenticate with an app that silently assumes SHA-1 and 6 digits, every code fails and the failure is indistinguishable from a wrong password. Unless you control the client, stay on the SHA-1 / 6-digit / 30-second defaults.

Clock Drift, Validation Windows, and Replay

TOTP has no synchronisation channel. The protocol’s entire tolerance mechanism is the server checking neighbouring time steps.

Three rules that separate a correct deployment from a fragile one:

1. Run NTP on the server. Client drift is the user’s problem; server drift breaks every user at once.
2. Burn the code after use. RFC 6238 § 5.2 is explicit: accept each code once per user per time step. Without this, a code intercepted at second 1 stays replayable for the rest of the window.
3. Rate-limit attempts. A 6-digit code is 1,000,000 possibilities. At an unlimited request rate, an attacker inside a 90-second window has real odds. Cap at roughly 5 failures, then lock or back off exponentially.

Where TOTP Fits in 2026

TOTP’s structural weakness is the shared secret at rest. The server must store the key in a form it can compute with, so a database breach exposes every enrolled seed unless the seeds are encrypted with a key held outside the database. Store them encrypted, and treat the enrolment QR code as a credential — a screenshot in a chat thread is a bypassed second factor.

Step-by-Step: Testing TOTP Codes with Toolbox

1. Open the tool: visit the Toolbox TOTP Authenticator Simulator.
2. Paste the Base32 secret produced by your enrolment endpoint (spacing and case are normalised for you).
3. Set algorithm, digits, and period to match your server configuration — this is where SHA-256 or 8-digit mismatches surface immediately.
4. Compare against your backend: call your verification endpoint with the displayed code while the countdown ring is above roughly 5 seconds, so a step boundary does not confuse the result.
5. Reproduce drift deliberately: verify a code just as the ring empties to confirm your server actually accepts T-1 and does not silently reject late submissions.

Outcome: you can prove whether a failing 2FA flow is a secret-encoding bug, an algorithm mismatch, or a clock/window problem — without installing a mobile app or exposing the seed to a third-party service.

Related guides: HMAC signature verification · SHA-256 and MD5 hashing · JWT claims inspection