func crackTimeToScore(seconds float64) int {
if seconds < math.Pow(10, 2) {
return 0
} else if seconds < math.Pow(10, 4) {
return 1
} else if seconds < math.Pow(10, 6) {
return 2
} else if seconds < math.Pow(10, 8) {
return 3
}
return 4
}
func getWordsEntropy(numWords int, guessesPerSec float64) Entropy {
entropy := Entropy{}
var (
avgHumanLifespanInYears float64 = 67.2 // https://en.wikipedia.org/wiki/Life_expectancy
ageOfUniverseInYears float64 = 13798000000. // https://en.wikipedia.org/wiki/Age_of_the_universe
)
entropy.Entropy = 12.92 * float64(numWords)
// https://xkcd.com/936/
// https://security.stackexchange.com/questions/62832/is-the-oft-cited-xkcd-scheme-no-longer-good-advice/62881#62881
// https://hashcat.net/forum/thread-2580.html
entropy.KeySpace = math.Pow(7776., float64(numWords))
// Divide the keySpace in half. On average it is expected that an
// exhaustive search of only half the keySpace will result in success.
entropy.HalfKeySpace = entropy.KeySpace / 2
// // "Assume that your adversary is capable of a trillion guesses per second" - Snowden
// // http://www.nytimes.com/2013/08/18/magazine/laura-poitras-snowden.html?pagewanted=all&_r=0
// guessesPerSec = 1000000000000.
entropy.Seconds = entropy.HalfKeySpace / guessesPerSec
entropy.Minutes = entropy.Seconds / 60
entropy.Hours = entropy.Minutes / 60
entropy.Days = entropy.Hours / 24
entropy.Years = entropy.Days / 365
entropy.Millenia = entropy.Years / 1000
entropy.HumanLifetimes = entropy.Years / avgHumanLifespanInYears
entropy.UniverseLifetimes = entropy.Years / ageOfUniverseInYears
return entropy
}
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
}
/*
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 entropyToCrackTime(entropy float64) float64 {
crackTime := (0.5 * math.Pow(float64(2), entropy)) * SECONDS_PER_GUESS
return crackTime
}