|Password Recovery Solutions
If protection system is safe enough the only way to find password is search all of the password variants. This way of cracking is usually called a 'brute force attack'. It takes a great amount of resources to crack even a not very long password. Brute force attack will not help you to break a 9-character password even if all the letters of the password are in the same case. But why must smart guys use brute force? For the most part there are combinations like jkqmzwd which are totally senseless among billions and trillions of passwords being searched. I attended this problem some time ago. My purpose was creation of a search algorithm which would only try "reasonable" passwords. I named this algorithm "smart force attack" as opposed to "brute force attack" methods. I was proceeding with the following assumptions:
it is important that the "smart force" engine was fast enough, 'cause the time taken to generate a password is added to the time taken by the verification itself.
linguistics is to be considered. English language has its own rules. If, while reading a text, you engage an unfamiliar word you nevertheless can feel that it's a word, not an abracadabra of random characters. A person identifies validity of a word intuitively, although some rules can be written expressly. Some of them are evident - for example, a password starting with "p" is much more probable than a password with "k".
psychology is to be considered. The following fact is known: when making up a random number a person clearly prefers some digits to others (the preference is mainly defined by the last digit in a number). By the way, some pretty curious mathematical laws regarding gambling and guessing numbers could be deduced from this rule, but this is to be discussed separately. The same preferences work with letters, too. I have analyzed the distribution of probabilities of actual passwords' distribution depending on the first letter. It can be stated that the obtained distribution greatly differs from a usual words' distribution. The phrase greatly differs should be understood in such a way that 'I know the basics of math statistics well, I know how to count probabilities and what criteria to use but I'm too lazy to actually employ this in practice and I prefer to assess them roughly :-). Thus, we should add psychological rules to the linguistic ones, and the former are even hardly to formalize than the latter.
the "extraneous force" is to be considered. With all considerations accepted, a sequence of characters which goes like "qwerty" should be quite random, yet anyone who has seen a keyboard knows it's not true. I take a chance and make a suggestion that there's a whole lot of other factors that can hardly all be taken into consideration and correctly formulated. With all the aforementioned, a very curious idea comes to existence: to tackle the problem one should use artificial intelligence methods. Neuron networks are the best way to solve poorly determined problems. Neuron networks is an interesting field, yet it's completely new to me. (There is, however, a functioning model, created by me. There is no way to state its practical value, because it's performance is sluggish; moreover, the passwords it generates often look like an outright abracadabra :-).
Let us now discuss a more traditional method. It is evident that some letters are encountered more frequently than others. Therefore the search can be more reasonably started with the most probable letters. The probability of encountering a letter very much depends on its position within a word. For example, for a "Y" letter a probability to be found in the beginning of a word equals to 0.003. Yet it can be found forty times more frequently at the last position (a chance of 0.120). It can be a second letter in a word with a probability of 0.030, and a last but one letter with a probability of 0.004.
It is evident that the probability of encountering a letter not only depends on its position within a word, it also depends on preceding letters. For example, for an "H" to appear after a "C" is four hundred times more probable (sic!) than after an "E". Of the greatest significance is the fact that many combinations are not encountered at all and they can be excluded from the search altogether. Clearly the probability of a double letter occurrence also greatly depends on its position within a word. For example, the "SS" combination as an ending occupies the fifth position in a list of the most popular endings, meanwhile it cannot be used as a beginning at all. Moreover, there exists a connection with all of preceding letters, not just the immediate one. I decided to simplify the task, for starters. By means of statistical analysis I have created a table of values of a function P(a,p,i,n) - a Probability to encounter an "a" letter after a "p" letter at a position of "i" in a word of "n" letters. Knowing these values one could get something that to an extent could be called a probability of a given sequence of characters making sense for a human being - this being obtained for any array of characters by multiplying respective probabilities. Further, one should search character sequences in order of decreasing probability. This task is not that simple. Unfortunately, this is about where my desire to publish the results of my research ends :-). I will only mention that the problem of an optimal password search is not unlike an iceberg - only its tip is marked here. The obtained results indicate that the time of a search of all variants with a non-zero probability for a 10-character password will total about 8 days instead of 45 years (as is in the case of a "brute force attack") with a search speed of 100,000 passwords per second. Notice any difference? If we limit ourselves to passwords of a significant probability, we can cut the waiting time to about 10 hours. If, furthermore, we take advantages of improving the algorithm, we can see that even twelve-characters-long passwords can be cracked in a reasonable time. Of course, the "smart force attack" won"t work with a password like "I"m$smarter!"
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