Passphrase Word-Count Minimum Check

Check the minimum number of independently uniform word choices needed to meet a supplied ideal entropy target.

Description

A uniformly chosen word from a list of W distinct choices contributes log₂(W) ideal bits.

A uniformly chosen word from a list of W distinct choices contributes log₂(W) ideal bits. A target bit count can therefore be converted to the minimum number of independent choices, subject to the uniform-selection assumption.^[1]

Check the minimum number of independently uniform word choices needed to meet a supplied ideal entropy target.

When to use Passphrase Word-Count Minimum Check

Use this tool to check the minimum number of independently uniform word choices needed to meet a supplied ideal entropy target.

Choose the text, counts, explicit reference time or format parameters requested by this tool. Follow the stated byte, epoch-time and randomness assumptions.

How to use Passphrase Word-Count Minimum Check and understand its results

Choose the text, counts, explicit reference time or format parameters requested by this tool. Follow the stated byte, epoch-time and randomness assumptions.
Enter wordListSize, wordCount, targetBits using the field table and calculation rules, then run the tool.
Read minimumWords, meetsTarget. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
wordListSize	Word list size	integer; minimum: 2; maximum: 9007199254740991	Required
wordCount	Current word count	integer; minimum: 0; maximum: 9007199254740991	Required
targetBits	Required ideal entropy	number; minimum: 0	Required

Enter an integer word-list size of at least two, a nonnegative integer current word count and a nonnegative target bit count. The tool calculates bits per word, takes a ceiling and adjusts adjacent counts against the floating-point target comparison. It returns the minimum and whether the current count meets it. Zero target needs zero words; an unrepresentable safe-integer minimum is an error.

minimumWords = ceil(targetBits / log₂(wordListSize)); meetsTarget = wordCount ≥ minimumWords

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
minimumWords	Minimum word count	integer; minimum: 0; maximum: 9007199254740991
meetsTarget	Meets entropy target	boolean

json

{
  "input": {
    "wordListSize": 4096,
    "wordCount": 4,
    "targetBits": 60
  },
  "output": {
    "minimumWords": 5,
    "meetsTarget": false
  }
}

Limitations and assumptions

It does not evaluate a typed passphrase, remove duplicate word-list entries or supply a recommended target. Human-selected, correlated or biased words do not justify the model. Target comparisons use logarithms rather than exact symbolic arithmetic.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.

Alternative or Complementary methods

Use Diceware Words to Entropy Bits: Calculate ideal word-passphrase entropy from independent uniform choices in a caller-supplied Diceware-style word list. For a complementary task, use Entropy Bits From Charset × Length: Calculate ideal entropy for independent uniform draws from a supplied character-set size.

References

Passphrase Word-Count Minimum Check — tool.io

Similar or alternative tools

Diceware Words to Entropy Bits
Calculate ideal word-passphrase entropy from independent uniform choices in a caller-supplied Diceware-style word list.
Entropy Bits From Charset × Length
Calculate ideal entropy for independent uniform draws from a supplied character-set size.