The initial commit for this code already includes the "80 bits" secret key length. It was not changed afterwards.
Now let's analyze things more critically. HOTP is specified in RFC 4226. Authentication uses a "shared secret", which is the value that we are talking about. What does RFC 4226 says about it ? Essentially, there is a a requirement in section 4:
R6 - The algorithm MUST use a strong shared secret. The length of
the shared secret MUST be at least 128 bits. This document
RECOMMENDs a shared secret length of 160 bits.
And then section 7.5 explains at length various methods for generating the shared secret.
google_authenticator code generates an 80-bit shared secret with
/dev/urandom and then proceeds to encode this secret with Base32: this encoding maps each group of 5 bits to a printable character. The resulting string thus consists of 16 characters, which are written "as is" in a file, with ASCII encoding, meaning that in the file the shared secret has length... 16 bytes, i.e. 128 bits. It is thus possible that the initial confusion comes from that: what is stored has a length which can be seen, in a way, to comply with requirement R6 of RFC 4226.
Of course, the RFC talks about the "shared secret" by calling it "K" in section 5.1 and then proceeds to using it as key for HMAC (section 5.3, step 1). With the shared secret generated with the command-line tool in
google_authenticator, what enters HMAC really is a sequence of 80 bits, not 128 bits, even though these 80 bits happen to be encoded as 128 bits when stored (but they are decoded back to 80 bits upon usage). Thus, this 80-bit secret cannot really, in a legalistic way, comply with requirement R6 of RFC 4226. However, the confusion on "length" (after or before encoding) may explain this feature of
Note, though, that this is just for the command-line tool which can be used to generate the secret as an initial step. The rest of the code supports longer secret values.
(Another theory is that the author wanted to test his code, and, in particular, test the situation in which there is no QR code. In that case, the user must type the code, and an 80-bit secret is easier to type than a 128-bit or 160-bit secret. Possibly, the author first used a short secret to ease development, and subsequently forgot to set it back to its nominal length afterwards. This sort of mishap happens quite often.)
Is it critical ? With my cryptographer's hat, I must answer: no. An 80-bit secret key is still quite strong against brute force, because even with a lot of GPU, 279 evaluations of HMAC/SHA-1 will still take quite some time (with an 80-bit key, average cost of brute force is that of trying half the possible keys, i.e. 279 evaluations). Indeed, HMAC/SHA-1 is deemed "cryptographically strong", meaning that the best known attack is brute force on the key. Let's put figures on it:
HMAC/SHA-1 uses two SHA-1 invocation. So the attack cost is, on average, the cost involved by calling SHA-1 280 times. This page shows benchmarks at 2.5 billions of SHA-1 calls per second for a good GPU. If you are mounting a cracking farm, you will usually use a "middle range" GPU, not a top-notch model, because you will get more power-per-dollar that way. Let's assume that you use 100$ GPU that can do 231 SHA-1 per second (that's a bit more than 2 billions). With a budget of one billion dollars you can have ten millions of such GPU, and they will run the attack in an average of... 652 days.
Of course, 10 millions of GPU take quite some room and, more importantly, use a substantial amount of power. If we suppose that each GPU can run in 50W (a quite optimistic figure), then each attack run will need a bit less than 8 TW.h (terawatt-hours). I live in Canada, province of Québec, where electricity is known to be very cheap due to huge dams and substantial government subventions, resulting in a price of about 0.05$ per kW.h (see the prices). With this price, each attack run will cost around 400 millions of dollars on electricity alone. This does not include cooling prices, because all this energy will become heat and will have to be dissipated (to some extent, a Canadian winter can help). Also, notice that all the GPU will collectively draw 500 MW, a non-discreet amount (that's about half of a nuclear power plant...).
What this amounts to is the following: in practice, an 80-bit key is strong enough. I would be nervous if an 80-bit key protected the launch code for nuclear missiles; however, if the strategic dissuasion was protected by Google's 2FA, I would also be quite nervous for... other reasons.
So we can say that while this 80-bit secret is non-compliant and academically "a bit short", it still is quite strong and does not mandate immediate and drastic actions. It would be cool if the code was fixed; the World won't stop spinning if it is not.