HOTP Counter Calculator
Check RFC 4226 HOTP counter drift against the look-ahead window and price the false-accept risk that window creates.
About HOTP Counter Calculator
HOTP codes come from a counter that only the token increments, so pressing the button without logging in leaves the token ahead of the server. The server compensates by computing the next s codes and accepting any match, then resynchronising its counter. Every code in that window is a valid answer, so the window multiplies the odds of a blind guess by s. Look-ahead is the setting that decides whether users with over-pressed tokens call the helpdesk or silently gain a wider guessing window, and RFC 4226's s = 3 to 5 is the balance point.
Formulas
HOTP Counter
drift = token counter − server counter; the server accepts if 0 ≤ drift ≤ s, where s is the look-ahead window.
- s
- Look-ahead depth the server searches
- drift
- How many counts the token has run ahead of the server
Cost of the look-ahead window
false-accept probability per attempt = s ÷ 10^digits, and s × attempts ÷ 10^digits before lockout.
Worked example
With the default values below, HOTP Counter Calculator returns Counter Drift of 5. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Server counter valueaccepts 0–1,000,000,000 counts
- 42 counts
- Token counter valueaccepts 0–1,000,000,000 counts
- 47 counts
- Look-ahead window (s)accepts 1–100 counts
- 5 counts
- Code lengthaccepts 4–10 digits
- 6 digits
- Attempts allowed before lockoutaccepts 1–100 attempts
- 5 attempts
Results
- Counter Drift
- 5 counts
- Will the Server Accept It
- Yes — the server accepts and resynchronises to the token
- Extra Counts Needed to Resynchronise
- 0 counts
- False-Accept Chance per Attempt
- 0.000500%
- False-Accept Chance Before Lockout
- 0.002500%
Step by step
- 1Values used
- 2HOTP Counter
- 3Cost of the look-ahead window
- 4Counter Drift= 5 counts
- 5Will the Server Accept It= Yes — the server accepts and resynchronises to the token
- 6Extra Counts Needed to Resynchronise= 0 counts
- 7False-Accept Chance per Attempt= 0.000500
- 8False-Accept Chance Before Lockout= 0.002500
Assumptions and limits
- The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How is HOTP Counter calculated?
drift = token counter − server counter; the server accepts if 0 ≤ drift ≤ s, where s is the look-ahead window. HOTP codes come from a counter that only the token increments, so pressing the button without logging in leaves the token ahead of the server. The server compensates by computing the next s codes and accepting any match, then resynchronising its counter. Every code in that window is a valid answer, so the window multiplies the odds of a blind guess by s.
Why does HOTP Counter matter?
Look-ahead is the setting that decides whether users with over-pressed tokens call the helpdesk or silently gain a wider guessing window, and RFC 4226's s = 3 to 5 is the balance point.
What values do I need to enter?
This calculator takes 5 inputs: Server counter value, Token counter value, Look-ahead window (s), Code length, Attempts allowed before lockout. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.
Why can't the server just accept any future code?
Because the acceptance window is also the attacker's guessing window: with s unbounded, every code the token will ever produce is valid and the scheme collapses. RFC 4226 keeps s small and requires throttling on top.
What if the token counter falls behind the server?
It cannot happen through normal use, because only the token increments. A negative drift means the code was already consumed — either a replay attempt or a server-side counter that was restored from an old backup.
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