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Christian Cook
Christian Cook

X Art Password Cracked !LINK!



At one time or another, we have all been frustrated by trying to set a password, only to have it rejected as too weak. We are also told to change our choices regularly. Obviously such measures add safety, but how exactly?




X Art Password Cracked



I will explain the mathematical rationale for some standard advice, including clarifying why six characters are not enough for a good password and why you should never use only lowercase letters. I will also explain how hackers can uncover passwords even when stolen data sets lack them.


If you are told to select a 12-character password that can include uppercase and lowercase letters, the 10 digits and 10 symbols (say, !, @, #, $, %, ^, &, ?, / and +), you would have 72 possibilities for each of the 12 characters of the password. The size of the possibility space would then be 7212 (19,408,409,961,765,342,806,016, or close to 19 x 1021).


That is more than 62 trillion times the size of the first space. A computer running through all the possibilities for your 12-character password one by one would take 62 trillion times longer. If your computer spent a second visiting the six-character space, it would have to devote two million years to examining each of the passwords in the 12-character space. The multitude of possibilities makes it impractical for a hacker to carry out a plan of attack that might have been feasible for the six-character space.


For a truly strong password as defined by ANSSI, you would need, say, a sequence of 16 characters, each taken from a set of 200 characters. This would make a 123-bit space, which would render the password close to impossible to memorize. Therefore, system designers are generally less demanding and accept low- or medium-strength passwords. They insist on long ones only when the passwords are automatically generated by the system, and users do not have to remember them.


There are other ways to guard against password cracking. The simplest is well known and used by credit cards: after three unsuccessful attempts, access is blocked. Alternative ideas have also been suggested, such as doubling the waiting time after each successive failed attempt but allowing the system to reset after a long period, such as 24 hours. These methods, however, are ineffective when an attacker is able to access the system without being detected or if the system cannot be configured to interrupt and disable failed attempts.


_________________________________If A = 26 and N = 6, then T = 308,915,776D = 0.0000858 computing hourX = 0; it is already possible to crack all passwords in the space in under an hour_________________________________If A = 26 and N = 12, then T = 9.5 1016D = 26,508 computing hoursX = 29 years before passwords can be cracked in under an hour_________________________________


If A = 100 and N = 10, then T = 1020D = 27,777,777 computing hoursX = 49 years before passwords can be cracked in under an hour_________________________________If A = 100 and N = 15, then T = 1030D = 2.7 1017 computing hoursX = 115 years before passwords can be cracked in under an hour________________________________If A = 200 and N = 20, then T = 1.05 1046D = 2.7 1033 computing hoursX = 222 years before passwords can be cracked in under an hour


To understand the subtle processes exploited in such cases, take another look at the possibility space. When I spoke earlier of bit size and password space (or entropy), I implicitly assumed that the user consistently chooses passwords at random. But typically the choice is not random: people tend to select a password they can remember (locomotive) rather than an arbitrary string of characters (xdichqewax).


This practice poses a serious problem for security because it makes passwords vulnerable to so-called dictionary attacks. Lists of commonly used passwords have been collected and classified according to how frequently they are used. Attackers attempt to crack passwords by going through these lists systematically. This method works remarkably well because, in the absence of specific constraints, people naturally choose simple words, surnames, first names and short sentences, which considerably limits the possibilities. In other words, the nonrandom selection of passwords essentially reduces possibility space, which decreases the average number of attempts needed to uncover a password.


Below are the first 25 entries in one of these password dictionaries, listed in order, starting with the most common one. (I took the examples from a database of five million passwords that was leaked in 2017 and analyzed by SplashData.)


1. 1234562. password3. 123456784. qwerty5. 123456. 1234567897. letmein8. 12345679. football10. iloveyou11. admin12. welcome13. monkey14. login15. abc12316. starwars17. 12312318. dragon19. passw0rd20. master21. hello22. freedom23. whatever24. qazwsx25. trustno1


For four-digit passwords (for example, the PIN code of SIM cards on smartphones), the results are even less imaginative. In 2013, based on a collection of 3.4 million passwords each containing four digits, the DataGenetics Web site reported that the most commonly used four-digit sequence (representing 11 percent of choices) was 1234, followed by 1111 (6 percent) and 0000 (2 percent). The least-used four-digit password was 8068. Careful, though, this ranking may no longer be true now that the result has been published. The 8068 choice appeared only 25 times among the 3.4-million four-digit sequences in the database, which is much less than the 340 uses that would have occurred if each four-digit combination had been used with the same frequency. The first 20 series of four digits are: 1234; 1111; 0000; 1212; 7777; 1004; 2000; 4444; 2222; 6969; 9999; 3333; 5555; 6666; 1122; 1313; 8888; 4321; 2001; 1010.


The obvious conclusion for users is that they must choose their passwords randomly. Some software does provide a random password. Be aware, however, that such password-generating software may, deliberately or not, use a poor pseudo-random generator, in which case what it provides may be imperfect.


You can check whether any of your passwords has already been hacked by using a Web tool called Pwned Passwords ( ). Its database includes more than 500 million passwords obtained after various attacks.


Using such hash functions allows passwords to be securely stored on a computer. Instead of storing the list of paired usernames and passwords, the server stores only the list of username/fingerprint pairs.


For added safety, a method known as salting is sometimes used to further impede hackers from exploiting stolen lists of username/fingerprint pairs. Salting is the addition of a unique random string of characters to each password. It ensures that even if two users employ the same password, the stored fingerprints will differ. The list on the server will contain three components for each user: username, fingerprint derived after salt was added to the password, and the salt itself. When the server checks the password entered by a user, it adds the salt, computes the fingerprint and compares the result with its database.


Method 1. You scroll through the entire space of passwords. You calculate the fingerprint, h(P), for each password, checking to see whether it appears in the stolen data. You do not need a lot of memory, because prior results are deleted with each new attempt, although you do, of course, have to keep track of the possibilities that have been tested.


Scrolling through all the possible passwords in this way takes a long time. If your computer runs a billion tests per second, you will need 2612/(109 x 3,600 x 24) days (1,104 days), or about three years to complete the task. The feat is not impossible; if you happen to have a computer network of 1,000 machines, one day will suffice. It is not feasible, however, to repeat such a calculation every time you wish to test additional data, such as if you obtain a new set of username/fingerprint pairs. (Because you have not saved the results of your computations, you would need an additional 1,104 days to process the new information.)


This memory requirement is too large. Method 2 is no more feasible than method 1. Method 1 requires too many computations, and method 2 requires too much memory. Both cases are problematic: either each new password takes too long to compute, or precomputing all possibilities and storing all the results is too large a task.


Here is how it works: First, we need a function R that transforms a fingerprint h(P) into a new password R(h(P)). One might, for instance, consider fingerprints as numbers written in the binary numeral system and consider passwords as numbers written in the K numeral system, where K is the number of allowable symbols for passwords. Then the function R converts data from the binary numeral system to the K numeral system. For every fingerprint h(P), it computes a new password R(h(P)).


To generate a data point in this table, we start from a possible password P0, compute its fingerprint, h(P0) and then compute a new possible password R(h(P0)), which becomes P1. Next, we continue this process from P1. Without storing anything other than P0, we compute the sequence P1, P2,... until the fingerprint starts with 20 zeros; that fingerprint is designated h(Pn). Such a fingerprint occurs only once in about 1,000,000 fingerprints because the result of a hash function is similar to result of a uniform random draw, and 220 is roughly equal to 1,000,000. The password/fingerprint pair [P0, h(Pn)], containing the fingerprint that starts with 20 zeros is then stored in the table.


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