/**
* Calculate the minimum entropy for a password and its matches.
*
* @param string $password
* Password.
* @param array $matches
* Array of Match objects on the password.
*
* @return float
* Minimum entropy for non-overlapping best matches of a password.
*/
public function getMinimumEntropy($password, $matches)
{
$passwordLength = strlen($password);
$entropyStack = array();
// for the optimal sequence of matches up to k, holds the final match (match.end == k).
// null means the sequence ends without a brute-force character.
$backpointers = array();
$bruteforceMatch = new Bruteforce($password, 0, $passwordLength - 1, $password);
$charEntropy = log($bruteforceMatch->getCardinality(), 2);
foreach (range(0, $passwordLength - 1) as $k) {
// starting scenario to try and beat: adding a brute-force character to the minimum entropy sequence at k-1.
$entropyStack[$k] = $this->prevValue($entropyStack, $k) + $charEntropy;
$backpointers[$k] = null;
foreach ($matches as $match) {
if (!isset($match->begin) || $match->end != $k) {
continue;
}
// See if entropy prior to match + entropy of this match is less than
// the current minimum top of the stack.
$candidateEntropy = $this->prevValue($entropyStack, $match->begin) + $match->getEntropy();
if ($candidateEntropy <= $entropyStack[$k]) {
$entropyStack[$k] = $candidateEntropy;
$backpointers[$k] = $match;
}
}
}
// Walk backwards and decode the best sequence
$matchSequence = array();
$k = $passwordLength - 1;
while ($k >= 0) {
$match = $backpointers[$k];
if ($match) {
$matchSequence[] = $match;
$k = $match->begin - 1;
} else {
$k -= 1;
}
}
$matchSequence = array_reverse($matchSequence);
$s = 0;
$matchSequenceCopy = array();
// Handle subtrings that weren't matched as bruteforce match.
foreach ($matchSequence as $match) {
if ($match->begin - $s > 0) {
$matchSequenceCopy[] = $this->makeBruteforceMatch($password, $s, $match->begin - 1, $bruteforceMatch->getCardinality());
}
$s = $match->end + 1;
$matchSequenceCopy[] = $match;
}
if ($s < $passwordLength) {
$matchSequenceCopy[] = $this->makeBruteforceMatch($password, $s, $passwordLength - 1, $bruteforceMatch->getCardinality());
}
$this->matchSequence = $matchSequenceCopy;
$minEntropy = $entropyStack[$passwordLength - 1];
return $minEntropy;
}
public function testEntropy()
{
$match = new Bruteforce('99', 0, 1, '99');
$this->assertSame(log(pow(10, 2), 2), $match->getEntropy());
$password = '******';
$match = new Bruteforce($password, 0, 3, $password);
$this->assertSame(95, $match->getCardinality());
$this->assertSame(log(pow(95, 4), 2), $match->getEntropy());
}
