func DateEntropy(dateMatch match.DateMatch) float64 {
var entropy float64
if dateMatch.Year < 100 {
entropy = math.Log2(NUM_DAYS * NUM_MONTHS * 100)
} else {
entropy = math.Log2(NUM_DAYS * NUM_MONTHS * NUM_YEARS)
}
if dateMatch.Separator != "" {
entropy += 2 //add two bits for separator selection [/,-,.,etc]
}
return entropy
}
func SequenceEntropy(match match.Match, dictionaryLength int, ascending bool) float64 {
firstChar := match.Token[0]
baseEntropy := float64(0)
if string(firstChar) == "a" || string(firstChar) == "1" {
baseEntropy = float64(0)
} else {
baseEntropy = math.Log2(float64(dictionaryLength))
//TODO: should this be just the first or any char
if unicode.IsUpper(rune(firstChar)) {
baseEntropy++
}
}
if !ascending {
baseEntropy++
}
return baseEntropy + math.Log2(float64(len(match.Token)))
}
func SpatialEntropy(match match.Match, turns int, shiftCount int) float64 {
var s, d float64
if match.DictionaryName == "qwerty" || match.DictionaryName == "dvorak" {
//todo: verify qwerty and dvorak have the same length and degree
s = float64(len(adjacency.BuildQwerty().Graph))
d = adjacency.BuildQwerty().CalculateAvgDegree()
} else {
s = float64(KEYPAD_STARTING_POSITIONS)
d = KEYPAD_AVG_DEGREE
}
possibilities := float64(0)
length := float64(len(match.Token))
//TODO: Should this be <= or just < ?
//Estimate the number of possible patterns w/ length L or less with t turns or less
for i := float64(2); i <= length+1; i++ {
possibleTurns := math.Min(float64(turns), i-1)
for j := float64(1); j <= possibleTurns+1; j++ {
x := zxcvbn_math.NChoseK(i-1, j-1) * s * math.Pow(d, j)
possibilities += x
}
}
entropy := math.Log2(possibilities)
//add extra entropu for shifted keys. ( % instead of 5 A instead of a)
//Math is similar to extra entropy for uppercase letters in dictionary matches.
if S := float64(shiftCount); S > float64(0) {
possibilities = float64(0)
U := length - S
for i := float64(0); i < math.Min(S, U)+1; i++ {
possibilities += zxcvbn_math.NChoseK(S+U, i)
}
entropy += math.Log2(possibilities)
}
return entropy
}
func extraUpperCaseEntropy(match match.Match) float64 {
word := match.Token
allLower := true
for _, char := range word {
if unicode.IsUpper(char) {
allLower = false
break
}
}
if allLower {
return float64(0)
}
//a capitalized word is the most common capitalization scheme,
//so it only doubles the search space (uncapitalized + capitalized): 1 extra bit of entropy.
//allcaps and end-capitalized are common enough too, underestimate as 1 extra bit to be safe.
for _, regex := range []string{START_UPPER, END_UPPER, ALL_UPPER} {
matcher := regexp.MustCompile(regex)
if matcher.MatchString(word) {
return float64(1)
}
}
//Otherwise calculate the number of ways to capitalize U+L uppercase+lowercase letters with U uppercase letters or
//less. Or, if there's more uppercase than lower (for e.g. PASSwORD), the number of ways to lowercase U+L letters
//with L lowercase letters or less.
countUpper, countLower := float64(0), float64(0)
for _, char := range word {
if unicode.IsUpper(char) {
countUpper++
} else if unicode.IsLower(char) {
countLower++
}
}
totalLenght := countLower + countUpper
var possibililities float64
for i := float64(0); i <= math.Min(countUpper, countLower); i++ {
possibililities += float64(zxcvbn_math.NChoseK(totalLenght, i))
}
if possibililities < 1 {
return float64(1)
}
return float64(math.Log2(possibililities))
}
func ExtraLeetEntropy(match match.Match, password string) float64 {
var subsitutions float64
var unsub float64
subPassword := password[match.I:match.J]
for index, char := range subPassword {
if string(char) != string(match.Token[index]) {
subsitutions++
} else {
//TODO: Make this only true for 1337 chars that are not subs?
unsub++
}
}
var possibilities float64
for i := float64(0); i <= math.Min(subsitutions, unsub)+1; i++ {
possibilities += zxcvbn_math.NChoseK(subsitutions+unsub, i)
}
if possibilities <= 1 {
return float64(1)
}
return math.Log2(possibilities)
}
/*
Returns minimum entropy
Takes a list of overlapping matches, returns the non-overlapping sublist with
minimum entropy. O(nm) dp alg for length-n password with m candidate matches.
*/
func MinimumEntropyMatchSequence(password string, matches []match.Match) MinEntropyMatch {
bruteforceCardinality := float64(entropy.CalcBruteForceCardinality(password))
upToK := make([]float64, len(password))
backPointers := make([]match.Match, len(password))
for k := 0; k < len(password); k++ {
upToK[k] = get(upToK, k-1) + math.Log2(bruteforceCardinality)
for _, match := range matches {
if match.J != k {
continue
}
i, j := match.I, match.J
// see if best entropy up to i-1 + entropy of match is less that current min at j
upTo := get(upToK, i-1)
calculatedEntropy := match.Entropy
match.Entropy = calculatedEntropy
candidateEntropy := upTo + calculatedEntropy
if candidateEntropy < upToK[j] {
upToK[j] = candidateEntropy
match.Entropy = candidateEntropy
backPointers[j] = match
}
}
}
//walk backwards and decode the best sequence
var matchSequence []match.Match
passwordLen := len(password)
passwordLen--
for k := passwordLen; k >= 0; {
match := backPointers[k]
if match.Pattern != "" {
matchSequence = append(matchSequence, match)
k = match.I - 1
} else {
k--
}
}
sort.Sort(match.Matches(matchSequence))
makeBruteForceMatch := func(i, j int) match.Match {
return match.Match{Pattern: "bruteforce",
I: i,
J: j,
Token: password[i : j+1],
Entropy: math.Log2(math.Pow(bruteforceCardinality, float64(j-i)))}
}
k := 0
var matchSequenceCopy []match.Match
for _, match := range matchSequence {
i, j := match.I, match.J
if i-k > 0 {
matchSequenceCopy = append(matchSequenceCopy, makeBruteForceMatch(k, i-1))
}
k = j + 1
matchSequenceCopy = append(matchSequenceCopy, match)
}
if k < len(password) {
matchSequenceCopy = append(matchSequenceCopy, makeBruteForceMatch(k, len(password)-1))
}
var minEntropy float64
if len(password) == 0 {
minEntropy = float64(0)
} else {
minEntropy = upToK[len(password)-1]
}
crackTime := roundToXDigits(entropyToCrackTime(minEntropy), 3)
return MinEntropyMatch{Password: password,
Entropy: roundToXDigits(minEntropy, 3),
MatchSequence: matchSequenceCopy,
CrackTime: crackTime,
CrackTimeDisplay: displayTime(crackTime),
Score: crackTimeToScore(crackTime)}
}
func DictionaryEntropy(match match.Match, rank float64) float64 {
baseEntropy := math.Log2(rank)
upperCaseEntropy := extraUpperCaseEntropy(match)
//TODO: L33t
return baseEntropy + upperCaseEntropy
}
func RepeatEntropy(match match.Match) float64 {
cardinality := CalcBruteForceCardinality(match.Token)
entropy := math.Log2(cardinality * float64(len(match.Token)))
return entropy
}
func YearEntropy(dateMatch match.DateMatch) float64 {
return math.Log2(NUM_YEARS)
}