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Systems that use passwords for authentication must have some way to check any password entered to gain access. If the valid passwords are simply stored in a system file or database, an attacker who gains sufficient access to the system will obtain all user passwords, giving the attacker access to all accounts on the attacked system and possibly other systems where users employ the same or ...
Brute-force attacks work by calculating every possible combination that could make up a password and testing it to see if it is the correct password. As the password's length increases, the amount of time, on average, to find the correct password increases exponentially. [6]
Rainbow tables are a practical example of a space–time tradeoff: they use less computer processing time and more storage than a brute-force attack which calculates a hash on every attempt, but more processing time and less storage than a simple table that stores the hash of every possible password.
Attempt possible combinations of the weaker initial key, potentially commencing with a dictionary attack if the initial key is a password or passphrase, but the attacker's added effort for each trial could render the attack uneconomic should the costlier computation and memory consumption outweigh the expected profit
Lists of common passwords are widely circulated and many passwords are short enough that even all possible combinations may be tested if calculation of the hash does not take too much time. [ 29 ] The use of cryptographic salt prevents some attacks, such as building files of precomputing hash values, e.g. rainbow tables .
However most users choose passwords in predictable ways and many passwords are short enough that all possible combinations can be tested if fast hashes are used, even if the hash is rated secure against preimage attacks. [6] Special hashes called key derivation functions have been created to slow searches. See Password cracking.
Lottery mathematics is used to calculate probabilities of winning or losing a lottery game. It is based primarily on combinatorics, particularly the twelvefold way and combinations without replacement. It can also be used to analyze coincidences that happen in lottery drawings, such as repeated numbers appearing across different draws. [1
The purpose of password cracking might be to help a user recover a forgotten password (due to the fact that installing an entirely new password would involve System Administration privileges), to gain unauthorized access to a system, or to act as a preventive measure whereby system administrators check for easily crackable passwords. On a file ...