Password / Passphrase Entropy Estimator mechanism

Model scope

The core formulas are mathematically standard under explicit uniform-randomness assumptions, but the instrument specification is incomplete for direct human-password analysis, qualitative labels, and crack-time ranges. It must distinguish exhaustive from expected crack time, define attacker-rate tables and units, specify validation constraints, and clearly label results as model-based estimates rather than guarantees.

• H=L·log2(N) is correct only when each character is selected independently and uniformly from a known character set of size N; it is not a valid entropy estimate for typical human-chosen passwords without a separate password-modeling method.
• H=W·log2(wordlist_size) is correct only when words are selected independently and uniformly from the stated wordlist; natural-language phrases, reused phrases, and patterned selections have lower effective entropy.
• 2^H/guesses_per_sec represents exhaustive-search time under the stated model, not expected time to find a randomly selected secret; expected time is approximately 2^(H-1)/guesses_per_sec for an ordered exhaustive search.
• The specification does not define the numeric attacker guess rates needed to produce a crack-time range.
• The specification does not define the qualitative strength-label thresholds.
• For direct password/passphrase analysis, the specification does not define how the effective character set, wordlist, length, patterns, substitutions, repetitions, or dictionary membership are determined.

Units and conventions

• N and wordlist_size are dimensionless counts of possible symbols or words.
• L and W are nonnegative integer counts; L is characters and W is words.
• guesses_per_sec is a positive rate measured in guesses per second.
• Crack-time outputs are in seconds unless explicitly converted.
• Entropy is measured in bits because log2 is used.
• The empty-string edge case uses one possible candidate, so 2^0=1 candidate.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "mode": "charset",
    "charset_size": 26,
    "length": 8,
    "guesses_per_sec": 1000000000
  },
  "expected_outputs": {
    "entropy_bits": 37.6035177451,
    "exhaustive_crack_time_seconds": 208.827064576
  },
  "working": "H = L·log2(N) = 8·log2(26) = 8·4.70043971814 = 37.6035177451 bits. Search space = 2^H = 26^8 = 208,827,064,576 guesses. Time = 208,827,064,576 / 1,000,000,000 = 208.827064576 seconds."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

Invalid zero guess rates can trigger undefined division, and the specification leaves exhaustive-versus-average crack time and rate-unit conventions insufficiently explicit. Zero-length input also requires explicit weak/invalid handling.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json