/// <summary>
/// Perform the password matching on the given password and user inputs.
/// </summary>
/// <param name="password">The password to assess.</param>
/// <param name="userInputs">Optionally, an enumarable of user data.</param>
/// <returns>Result for the password.</returns>
public static Result EvaluatePassword(string password, IEnumerable <string> userInputs = null)
{
password = password ?? string.Empty;
userInputs = userInputs ?? Enumerable.Empty <string>();
var timer = System.Diagnostics.Stopwatch.StartNew();
var matches = GetAllMatches(password, userInputs);
var result = PasswordScoring.MostGuessableMatchSequence(password, matches);
timer.Stop();
var attackTimes = TimeEstimates.EstimateAttackTimes(result.Guesses);
var feedback = Feedback.GetFeedback(result.Score, result.Sequence);
var finalResult = new Result
{
CalcTime = timer.ElapsedMilliseconds,
CrackTime = attackTimes.CrackTimesSeconds,
CrackTimeDisplay = attackTimes.CrackTimesDisplay,
Score = attackTimes.Score,
MatchSequence = result.Sequence,
Guesses = result.Guesses,
Password = result.Password,
Feedback = feedback,
};
return(finalResult);
}
/// <summary>
/// Returns a new result structure initialised with data for the lowest entropy result of all of the matches passed in, adding brute-force
/// matches where there are no lesser entropy found pattern matches.
/// </summary>
/// <param name="matches">Password being evaluated</param>
/// <param name="password">List of matches found against the password</param>
/// <returns>A result object for the lowest entropy match sequence</returns>
private PasswordMetricResult FindMinimumEntropyMatch(string password, IEnumerable <Match> matches)
{
var bruteforce_cardinality = PasswordScoring.PasswordCardinality(password);
// Minimum entropy up to position k in the password
var minimumEntropyToIndex = new double[password.Length];
var bestMatchForIndex = new Match[password.Length];
for (var k = 0; k < password.Length; k++)
{
// Start with bruteforce scenario added to previous sequence to beat
minimumEntropyToIndex[k] = (k == 0 ? 0 : minimumEntropyToIndex[k - 1]) + Math.Log(bruteforce_cardinality, 2);
// All matches that end at the current character, test to see if the entropy is less
foreach (var match in matches.Where(m => m.End == k))
{
var candidate_entropy = (match.Begin <= 0 ? 0 : minimumEntropyToIndex[match.Begin - 1]) + match.Entropy;
if (candidate_entropy < minimumEntropyToIndex[k])
{
minimumEntropyToIndex[k] = candidate_entropy;
bestMatchForIndex[k] = match;
}
}
}
// Walk backwards through lowest entropy matches, to build the best password sequence
var matchSequence = new List <Match>();
for (var k = password.Length - 1; k >= 0; k--)
{
if (bestMatchForIndex[k] != null)
{
matchSequence.Add(bestMatchForIndex[k]);
k = bestMatchForIndex[k].Begin; // Jump back to start of match
}
}
matchSequence.Reverse();
// The match sequence might have gaps, fill in with bruteforce matching
// After this the matches in matchSequence must cover the whole string (i.e. match[k].j == match[k + 1].i - 1)
if (matchSequence.Count == 0)
{
// To make things easy, we'll separate out the case where there are no matches so everything is bruteforced
matchSequence.Add(new Match()
{
Begin = 0,
End = password.Length,
Token = password,
Cardinality = bruteforce_cardinality,
Pattern = BruteforcePattern,
Entropy = Math.Log(Math.Pow(bruteforce_cardinality, password.Length), 2)
});
}
else
{
// There are matches, so find the gaps and fill them in
var matchSequenceCopy = new List <Match>();
for (var k = 0; k < matchSequence.Count; k++)
{
var m1 = matchSequence[k];
var m2 = (k < matchSequence.Count - 1 ? matchSequence[k + 1] : new Match()
{
Begin = password.Length
}); // Next match, or a match past the end of the password
matchSequenceCopy.Add(m1);
if (m1.End < m2.Begin - 1)
{
// Fill in gap
var ns = m1.End + 1;
var ne = m2.Begin - 1;
matchSequenceCopy.Add(new Match()
{
Begin = ns,
End = ne,
Token = password.Substring(ns, ne - ns + 1),
Cardinality = bruteforce_cardinality,
Pattern = BruteforcePattern,
Entropy = Math.Log(Math.Pow(bruteforce_cardinality, ne - ns + 1), 2)
});
}
}
matchSequence = matchSequenceCopy;
}
var minEntropy = (password.Length == 0 ? 0 : minimumEntropyToIndex[password.Length - 1]);
var crackTime = PasswordScoring.EntropyToCrackTime(minEntropy);
var result = new PasswordMetricResult();
result.Password = password;
result.Entropy = Math.Round(minEntropy, 3);
result.MatchSequence = matchSequence;
result.CrackTime = Math.Round(crackTime, 3);
result.CrackTimeDisplay = Utility.DisplayTime(crackTime, this.translation);
result.Score = PasswordScoring.CrackTimeToScore(crackTime);
//starting feedback
if ((matchSequence == null) || (matchSequence.Count() == 0))
{
result.warning = Warning.Default;
result.suggestions.Clear();
result.suggestions.Add(Suggestion.Default);
}
else
{
//no Feedback if score is good or great
if (result.Score > 2)
{
result.warning = Warning.Empty;
result.suggestions.Clear();
result.suggestions.Add(Suggestion.Empty);
}
else
{
//tie feedback to the longest match for longer sequences
Match longestMatch = GetLongestMatch(matchSequence);
GetMatchFeedback(longestMatch, matchSequence.Count() == 1, result);
result.suggestions.Insert(0, Suggestion.AddAnotherWordOrTwo);
}
}
return(result);
}
private void GetDictionaryMatchFeedback(DictionaryMatch match, bool isSoleMatch, PasswordMetricResult result)
{
if (match.DictionaryName.Equals("passwords"))
{
//todo: add support for reversed words
if (isSoleMatch == true && !(match is L33tDictionaryMatch))
{
if (match.Rank <= 10)
{
result.warning = Warning.Top10Passwords;
}
else if (match.Rank <= 100)
{
result.warning = Warning.Top100Passwords;
}
else
{
result.warning = Warning.CommonPasswords;
}
}
else if (PasswordScoring.CrackTimeToScore(PasswordScoring.EntropyToCrackTime(match.Entropy)) <= 1)
{
result.warning = Warning.SimilarCommonPasswords;
}
}
else if (match.DictionaryName.Equals("english"))
{
if (isSoleMatch == true)
{
result.warning = Warning.WordEasy;
}
}
else if (match.DictionaryName.Equals("surnames") ||
match.DictionaryName.Equals("male_names") ||
match.DictionaryName.Equals("female_names"))
{
if (isSoleMatch == true)
{
result.warning = Warning.NameSurnamesEasy;
}
else
{
result.warning = Warning.CommonNameSurnamesEasy;
}
}
else
{
result.warning = Warning.Empty;
}
string word = match.Token;
if (Regex.IsMatch(word, PasswordScoring.StartUpper))
{
result.suggestions.Add(Suggestion.CapsDontHelp);
}
else if (Regex.IsMatch(word, PasswordScoring.AllUpper) && !word.Equals(word.ToLowerInvariant()))
{
result.suggestions.Add(Suggestion.AllCapsEasy);
}
//todo: add support for reversed words
//if match.reversed and match.token.length >= 4
// suggestions.push "Reversed words aren't much harder to guess"
if (match is L33tDictionaryMatch)
{
result.suggestions.Add(Suggestion.PredictableSubstitutionsEasy);
}
}
/// <summary>
/// Estimate the extra entropy in a token that comes from mixing upper and lowercase letters.
/// This has been moved to a static function so that it can be used in multiple entropy calculations.
/// </summary>
/// <param name="word">The word to calculate uppercase entropy for</param>
/// <returns>An estimation of the entropy gained from casing in <paramref name="word"/></returns>
public static double CalculateUppercaseEntropy(string word)
{
const string StartUpper = "^[A-Z][^A-Z]+$";
const string EndUpper = "^[^A-Z]+[A-Z]$";
const string AllUpper = "^[^a-z]+$";
const string AllLower = "^[^A-Z]+$";
if (Regex.IsMatch(word, AllLower))
{
return(0);
}
// If the word is all uppercase add's only one bit of entropy, add only one bit for initial/end single cap only
if (new[] { StartUpper, EndUpper, AllUpper }.Any(re => Regex.IsMatch(word, re)))
{
return(1);
}
var lowers = word.Where(c => 'a' <= c && c <= 'z').Count();
var uppers = word.Where(c => 'A' <= c && c <= 'Z').Count();
// Calculate numer of ways to capitalise (or inverse if there are fewer lowercase chars) and return lg for entropy
return(Math.Log(Enumerable.Range(0, Math.Min(uppers, lowers) + 1).Sum(i => PasswordScoring.Binomial(uppers + lowers, i)), 2));
}
/// <summary>
/// Returns a new result structure initialised with data for the lowest entropy result of all of the matches passed in, adding brute-force
/// matches where there are no lesser entropy found pattern matches.
/// </summary>
/// <param name="matches">Password being evaluated</param>
/// <param name="password">List of matches found against the password</param>
/// <returns>A result object for the lowest entropy match sequence</returns>
private Result FindMinimumEntropyMatch(string password, IEnumerable <Match> matches)
{
var bruteforce_cardinality = PasswordScoring.PasswordCardinality(password);
// Minimum entropy up to position k in the password
var minimumEntropyToIndex = new double[password.Length];
var bestMatchForIndex = new Match[password.Length];
for (var k = 0; k < password.Length; k++)
{
// Start with bruteforce scenario added to previous sequence to beat
minimumEntropyToIndex[k] = (k == 0 ? 0 : minimumEntropyToIndex[k - 1]) + Math.Log(bruteforce_cardinality, 2);
// All matches that end at the current character, test to see if the entropy is less
foreach (var match in matches.Where(m => m.j == k))
{
var candidate_entropy = (match.i <= 0 ? 0 : minimumEntropyToIndex[match.i - 1]) + match.Entropy;
if (candidate_entropy < minimumEntropyToIndex[k])
{
minimumEntropyToIndex[k] = candidate_entropy;
bestMatchForIndex[k] = match;
}
}
}
// Walk backwards through lowest entropy matches, to build the best password sequence
var matchSequence = new List <Match>();
for (var k = password.Length - 1; k >= 0; k--)
{
if (bestMatchForIndex[k] != null)
{
matchSequence.Add(bestMatchForIndex[k]);
k = bestMatchForIndex[k].i; // Jump back to start of match
}
}
matchSequence.Reverse();
// The match sequence might have gaps, fill in with bruteforce matching
// After this the matches in matchSequence must cover the whole string (i.e. match[k].j == match[k + 1].i - 1)
if (matchSequence.Count == 0)
{
// To make things easy, we'll separate out the case where there are no matches so everything is bruteforced
matchSequence.Add(new Match()
{
i = 0,
j = password.Length,
Token = password,
Cardinality = bruteforce_cardinality,
Pattern = BruteforcePattern,
Entropy = Math.Log(Math.Pow(bruteforce_cardinality, password.Length), 2)
});
}
else
{
// There are matches, so find the gaps and fill them in
var matchSequenceCopy = new List <Match>();
for (var k = 0; k < matchSequence.Count; k++)
{
var m1 = matchSequence[k];
var m2 = (k < matchSequence.Count - 1 ? matchSequence[k + 1] : new Match()
{
i = password.Length
}); // Next match, or a match past the end of the password
matchSequenceCopy.Add(m1);
if (m1.j < m2.i - 1)
{
// Fill in gap
var ns = m1.j + 1;
var ne = m2.i - 1;
matchSequenceCopy.Add(new Match()
{
i = ns,
j = ne,
Token = password.Substring(ns, ne - ns + 1),
Cardinality = bruteforce_cardinality,
Pattern = BruteforcePattern,
Entropy = Math.Log(Math.Pow(bruteforce_cardinality, ne - ns + 1), 2)
});
}
}
matchSequence = matchSequenceCopy;
}
var minEntropy = (password.Length == 0 ? 0 : minimumEntropyToIndex[password.Length - 1]);
var crackTime = PasswordScoring.EntropyToCrackTime(minEntropy);
var result = new Result()
{
Password = password,
Entropy = Math.Round(minEntropy, 3),
MatchSequence = matchSequence,
CrackTime = Math.Round(crackTime, 3),
CrackTimeDisplay = Utility.DisplayTime(crackTime, translation),
Score = PasswordScoring.CrackTimeToScore(crackTime)
};
return(result);
}
public static Result MostGuessableMatchSequence(string password, IEnumerable <Match> matches, bool _exclude_additive = false)
{
int n = password.Length;
List <List <Match> > matchesByJ = new List <List <Match> >();
foreach (int i in EnumerableUtility.Range(0, n))
{
matchesByJ.Add(new List <Match>());
}
foreach (Match m in matches)
{
matchesByJ[m.j].Add(m);
}
foreach (List <Match> lst in matchesByJ)
{
lst.Sort(delegate(Match m1, Match m2)
{
return(m1.i - m2.i);
});
}
Optimal optimal = new Optimal(n);
/*
# helper: considers whether a length-l sequence ending at match m is better (fewer guesses)
# than previously encountered sequences, updating state if so.
*/
void update(Match m, int l)
{
// helper: considers whether a length-l sequence ending at match m is better (fewer guesses)
// than previously encountered sequences, updating state if so.
int k = m.j;
double pi = EstimateGuesses(m, password);
if (l > 1)
{
/*
# we're considering a length-l sequence ending with match m:
# obtain the product term in the minimization function by multiplying m's guesses
# by the product of the length-(l-1) sequence ending just before m, at m.i - 1.
*/
pi *= optimal.pi[m.i - 1][l - 1];
}
// calculate the minimization func
double g = factorial(l) * pi;
if (!_exclude_additive)
{
g += Math.Pow(MIN_GUESSES_BEFORE_GROWING_SEQUENCE, l - 1);
}
// update state if new best
// first see if any competing sequences covering this prefix, with l or fewer matches,
// fare better than this sequence. if so, skip it and return
foreach (KeyValuePair <int, double> val in optimal.g[k])
{
int competingL = val.Key;
double competingG = val.Value;
if (competingL > l)
{
continue;
}
if (competingG <= g)
{
return;
}
}
optimal.g[k][l] = g;
optimal.m[k][l] = m;
optimal.pi[k][l] = pi;
}
// helper: make bruteforce match objects spanning i to j, inclusive.
Match makeBruteForceMatch(int i, int j)
{
Match m = new Match();
m.Token = password.Substring(i, j - i + 1);
m.Pattern = "bruteforce";
m.i = i;
m.j = j;
return(m);
}
// helper: evaluate bruteforce matches ending at k.
void bruteForceUpdate(int k)
{
// see eif a single bruteforce match spanning the k-prefix is optimal
Match m = makeBruteForceMatch(0, k);
update(m, 1);
foreach (int i in EnumerableUtility.Range(1, k + 1))
{
// generate k bruteforce matches, spanning from (i=1, j=k) up to (i=k, j=k)
// see if adding these new matches to any of the sequences in optimal[i-1]
// leads to new bests
m = makeBruteForceMatch(i, k);
foreach (KeyValuePair <int, Match> val in optimal.m[i - 1])
{
int l = val.Key;
// corner: an optimal sequence will never have two adjacent bruteforce matches
// it is strictly better to have a single bruteforce match spanning the same region:
// same contribution to the guess product with a lower length
// --> safe to skip those cases
if (val.Value.Pattern != null && val.Value.Pattern.Equals("bruteforce"))
{
continue;
}
// try adding m to this length-l sequence
update(m, l + 1);
}
}
}
// helper: step backwards through optimal.m starting at the end,
// constructing the final optimal match sequence
List <Match> unwind(int nN)
{
List <Match> optimalMatchSequenceList = new List <Match>();
int k = nN - 1;
// find the final best seqence length and score
int l = 1;
double g = Double.MaxValue;
foreach (KeyValuePair <int, double> val in optimal.g[k])
{
int candidateL = val.Key;
double candidateG = val.Value;
if (candidateG < g)
{
l = candidateL;
g = candidateG;
}
}
while (k >= 0)
{
Match m = optimal.m[k][l];
optimalMatchSequenceList.Insert(0, m);
k = m.i - 1;
l--;
}
return(optimalMatchSequenceList);
}
foreach (int k in EnumerableUtility.Range(0, n))
{
foreach (Match m in matchesByJ[k])
{
if (m.i > 0)
{
foreach (int l in optimal.m[m.i - 1].Keys)
{
update(m, l + 1);
}
}
else
{
update(m, 1);
}
}
bruteForceUpdate(k);
}
List <Match> optimalMatchSequence = unwind(n);
int optimalL = optimalMatchSequence.Count;
double guesses = (password.Length == 0) ? 1 : optimal.g[n - 1][optimalL];
double seconds = guesses / Math.Pow(10, 4);
double crackTime = PasswordScoring.GuessesToCrackTime(guesses);
// UnityEngine.Debug.Log($"Seconds: {seconds}");
// Debug.Log($"Score: {PasswordScoring.GuessesToScore(guesses)}");
int score = PasswordScoring.GuessesToScore(guesses);
return(new Result
{
Password = password,
Guesses = guesses,
GuessesLog10 = Math.Log10(guesses),
MatchSequence = optimalMatchSequence,
CrackTime = Math.Round(crackTime, 3),
CrackTimeDisplay = Utility.DisplayTime(crackTime),
Score = score
});
}