Behind GitHub’s Two-Factor-Auth

For those who wonder how GitHub’s Two-Factor-Auth ‘style 2’ codes work, there is an article which explains the basic mechanism. It will explain the magic from getting the QR code to getting a spinning 6-digit pin code. Like magic,… like magic.

GitHub ssh
From QR to code, but how?!


Scanning the QR code will tell you the protocol, TOTP who is issuing this OTP code (Github), and most importantly the shared secret

secret = 'onswg4tforrw6zdf'

Now that’s it – End of article, let me drink my coffee and never come back. No, of course not! How is the 6-digit code now generated?

The magic behind the code

Based on this python script:

  • time_chunk is based on the current time local time
  • time_chunk and your shared secret (based on the hmac) will be combined. It’s a sha1-hmac, which means we’ll get a 20-byte digest.
  • Take the last 4-bits of the digest, these become the main-offset. Eg. if the last 4 bits are 0010, then we would start at the 4th byte. It’s required to read 4 bytes starting from the offset to get a correct value.
  • Convert the 4 byte section into a n digit integer. This is your two-factor code.

The algorithm works by finding what 30 second time slice we’re in, starting from the Unix Epoch via time_chunk = int(time.time() / 30)time_bytes = struct.pack('>q', time_chunk).

HOTP algorithm

The default hash function in Python for HMACs is MD5, I only mention it because it’s maybe not widely known.

HOTP is an algorithm for using HMAC to generate one-time-passwords based on a counter. In the case of TOTP, the counter is the time chunk we’re in. First, we need to create a hmac of our secret key and the count:

key = base64.b32decode(secret.upper())
hm =, time_bytes, hashlib.sha1)
hex_digest = hm.hexdigest()

Now we need to determine the offset in the array we’ll be reading from. This offset is chosen based on the last 4-bit chunk of the array: offset = int(hex_digest[-1:], 16).

Starting at the offset, read 4 bytes. This will be the basis of our 6 digit code: relevant_bytes = int(hex_digest[offset*2:offset*2+8], 16). Drop the highest order bit (the sign). Dropping this makes it easier to implement in different programming languages which may have differing behavior on signed module operations: unsigned_bytes = relevant_bytes & 0x7FFFFFFF.

Last but not least, take the unsigned result % 10**d where d is the number of digits you want. In our case, that’s 6:

num_digits = 6
final = masked % (10 ** num_digits)
final_str = str(final).zfill(6)
return final_str

The Google implementation derives them by taking 4-byte sections of the secret and converting them into digits by the same process as the time-based system: bignum % (10 ** d). This means they’re also derivable in a predictable way from the original key so they don’t need to by stored separately by the server. Some other systems use hex-based codes instead, but presumably it’s a similar process.

Final Words

  • Make sure your comparison method is safe from timing attacks in case you want to implement 2-factor authentication.
  • Check if the libraries offering verify methods, if not stay away from them!
  • he easiest way to compare 2-factor codes in a constant time way is convert to ints first. Google does it.

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