function minimum_entropy_match_sequence($password, $matches)
{
# e.g. 26 for lowercase
$bruteforce_cardinality = calc_bruteforce_cardinality($password);
# minimum entropy up to k.
$up_to_k = array();
# for the optimal sequence of matches up to k, holds the
# final match (match.j == k). null means the sequence ends
# w/ a brute-force character.
$backpointers = array();
$password_len = strlen($password);
for ($k = 0; $k < $password_len; $k++) {
# starting scenario to try and beat:
# adding a brute-force character to the minimum entropy sequence at k-1.
$up_to_k[$k] = _get_index($up_to_k, $k - 1) + logarithm($bruteforce_cardinality);
$backpointers[$k] = NULL;
foreach ($matches as $match) {
if ($match['j'] !== $k) {
continue;
}
$i = $match['i'];
$j = $match['j'];
# see if best entropy up to i-1 + entropy of this match
# is less than the current minimum at j.
$candidate_entropy = _get_index($up_to_k, $i - 1) + calc_entropy($match);
if ($candidate_entropy < $up_to_k[$j]) {
$up_to_k[$j] = $candidate_entropy;
$backpointers[$j] = $match;
}
}
}
# walk backwards and decode the best sequence
$match_sequence = array();
$k = strlen($password) - 1;
while ($k >= 0) {
$match = $backpointers[$k];
if ($match) {
$match_sequence[] = $match;
$k = $match['i'] - 1;
} else {
$k -= 1;
}
}
$match_sequence = array_reverse($match_sequence);
# fill in the blanks between pattern matches with bruteforce "matches"
# that way the match sequence fully covers the password:
# match1.j == match2.i - 1 for every adjacent match1, match2.
$make_bruteforce_match = function ($i, $j) use($password, $bruteforce_cardinality) {
return array('pattern' => 'bruteforce', 'i' => $i, 'j' => $j, 'token' => _slice($password, $i, $j + 1), 'entropy' => logarithm(pow($bruteforce_cardinality, $j - $i + 1)), 'cardinality' => $bruteforce_cardinality);
};
$k = 0;
$match_sequence_copy = array();
foreach ($match_sequence as $match) {
$i = $match['i'];
$j = $match['j'];
if ($i - $k > 0) {
$match_sequence_copy[] = $make_bruteforce_match($k, $i - 1);
}
$k = $j + 1;
$match_sequence_copy[] = $match;
}
if ($k < strlen($password)) {
$match_sequence_copy[] = $make_bruteforce_match($k, strlen($password) - 1);
}
$match_sequence = $match_sequence_copy;
# or 0 corner case is for an empty password ''
if (isset($up_to_k[strlen($password) - 1])) {
$min_entropy = $up_to_k[strlen($password) - 1];
} else {
$min_entropy = 0;
}
$crack_time = entropy_to_crack_time($min_entropy);
# final result object
$result = array('password' => $password, 'entropy' => round_to_x_digits($min_entropy, 3), 'match_sequence' => $match_sequence, 'crack_time_seconds' => round_to_x_digits($crack_time, 3), 'crack_time_display' => display_time($crack_time), 'score' => crack_time_to_score($crack_time));
return $result;
}
function generic_list_siblings(&$app, $c)
{
global $lang;
$db =& $app->db;
$def =& $db->def;
$p =& $app->ui;
$id = $app->arg('id');
$id_last = $db->column($c->table, 'id_last', $id);
$id_next = $db->column($c->table, 'id_next', $id);
list($thisindex, $last) = _get_index($app, $c->table, $def->id_parent($c->table), $c->table, $id);
if ($id_last) {
$e = $app->event()->copy();
$e->set_arg('id', $id_last);
$p->link($lang['previous'], $e);
}
echo ' ' . sprintf($lang['x of y'], $thisindex, $last) . ' ';
if ($id_next) {
$e = $app->event()->copy();
$e->set_arg('id', $id_next);
$p->link($lang['next'], $e);
}
}
