HMAC-based one-time password

The HOTP algorithm provides a method of authentication by symmetric generation of human-readable passwords, or values, each used for only one authentication attempt. The one-time property leads directly from the single use of each counter value.

Parties intending to use HOTP must establish some parameters; typically these are specified by the authenticator, and either accepted or not by the authenticated:

• A cryptographic hash method H (default is SHA-1)
• A secret key K, which is an arbitrary byte string and must remain private
• A counter C, which counts the number of iterations
• A HOTP value length d (6–10, default is 6, and 6–8 is recommended)

Both parties compute the HOTP value derived from the secret key K and the counter C. Then the authenticator checks its locally generated value against the value supplied by the authenticated.

The authenticator and the authenticated increment the counter C independently of each other, where the latter may increase ahead of the former, thus a resynchronisation protocol is wise. RFC 4226 does not actually require any such, but does make a recommendation. This simply has the authenticator repeatedly try verification ahead of their counter through a window of size s. The authenticator's counter continues forward of the value at which verification succeeds and requires no actions by the authenticated.

The recommendation is made that persistent throttling of HOTP value verification take place, to address their relatively small size and thus vulnerability to brute-force attacks. It is suggested that verification be locked out after a small number of failed attempts or that each failed attempt attracts an additional (linearly increasing) delay.

6-digit codes are commonly provided by proprietary hardware tokens from a number of vendors informing the default value of d. Truncation extracts 31 bits or ${\textstyle \log _{10}(2^{31})\approx 9.3}$ decimal digits, meaning that d can be at most 10, with the 10th digit adding less variation, taking values of 0, 1, and 2 (i.e., 0.3 digits).

After verification, the authenticator can authenticate itself simply by generating the next HOTP value, returning it, and then the authenticated can generate their own HOTP value to verify it. Note that counters are guaranteed to be synchronised at this point in the process.

The HOTP value is the human-readable design output, a d-digit decimal number (without omission of leading 0s):

HOTP value = HOTP(K, C) mod 10^d.

That is, the value is the d least significant base-10 digits of HOTP.

HOTP is a truncation of the HMAC of the counter C (under the key K and hash function H):

HOTP(K, C) = truncate(HMAC_H(K, C)),

where the counter C must be used big-endian.

Truncation first takes the 4 least significant bits of the MAC and uses them as a byte offset i:

truncate(MAC) = extract31(MAC, MAC[(19 × 8 + 4):(19 × 8 + 7)]),

where ":" is used to extract bits from a starting bit number up to and including an ending bit number, where these bit numbers are 0-origin. The use of "19" in the above formula relates to the size of the output from the hash function. With the default of SHA-1, the output is 20 bytes, and so the last byte is byte 19 (0-origin).

That index i is used to select 31 bits from MAC, starting at bit i × 8 + 1:

extract31(MAC, i) = MAC[(i × 8 + 1):(i × 8 + 4 × 8 − 1)].

31 bits are a single bit short of a 4-byte word. Thus the value can be placed inside such a word without using the sign bit (the most significant bit). This is done to definitely avoid doing modular arithmetic on negative numbers, as this has many differing definitions and implementations.[1]

Both hardware and software tokens are available from various vendors, for some of them see references below. Hardware tokens implementing OATH HOTP tend to be significantly cheaper than their competitors based on proprietary algorithms.[2] As of 2010, OATH HOTP hardware tokens can be purchased for a marginal price.[3] Some products can be used for strong passwords as well as OATH HOTP.[4]

Software tokens are available for (nearly) all major mobile/smartphone platforms (J2ME,[5] Android,[6] iPhone,[7] BlackBerry,[8] Maemo,[9] macOS,[10] and Windows Mobile[8]).

Although the early reception from some of the computer press was negative during 2004 and 2005,[11][12][13] after IETF adopted HOTP as RFC 4226 in December 2005, various vendors started to produce HOTP-compatible tokens and/or whole authentication solutions.

According to the article "Road Map: Replacing Passwords with OTP Authentication"[2] on strong authentication, published by Burton Group (a division of Gartner, Inc.) in 2010, "Gartner's expectation is that the hardware OTP form factor will continue to enjoy modest growth while smartphone OTPs will grow and become the default hardware platform over time."

• Initiative for Open Authentication
• S/KEY
• Time-based one-time password algorithm (TOTP)

• RFC 4226: HOTP: An HMAC-Based One-Time Password Algorithm
• RFC 6238: TOTP: Time-Based One-Time Password Algorithm
• RFC 6287: OCRA: OATH Challenge-Response Algorithm
• Initiative For Open Authentication
• Implementation of RFC 4226 - HOPT Algorithm Step by step Python implementation in a Jupyter Notebook