![]() Authentication fails if the two keys do not match moreover, authentication would equally fail if a key were entered directly as a password, since a different key would be computed for it. When a user enters a password for authentication, a key is computed for it and then compared to the key stored for that user. Thus, no one – including the authentication system – can learn a password merely by looking at stored value. Since a password stored as plaintext may be easily stolen by an actor who gains access to storage, a key corresponding to the password is typically stored instead. įor user authentication, a password is stored either as plaintext or as a key produced from an algorithm that usually involves a hash function. Rainbow tables were invented by Philippe Oechslin as an application of an earlier, simpler algorithm by Martin Hellman. Use of a key derivation function that employs a salt makes rainbow tables infeasible for recovering a secret value from a key. It is a practical example of a space–time tradeoff, requiring less processing but using more storage than a brute-force attack which calculates a key on each iteration, but requiring more processing and less storage than a simple table. Such a table may be used to discover a secret value (password) given its associated key. The first value and last value of each chain are precomputed and stored, making the chain a row in a virtual table where each even-numbered field contains a value and each odd-numbered field contains the corresponding key. Each item in the chain is derived from the previous item so that the chain may be algorithmically reproduced from the first value in the chain: A key derivation function produces a key from a preceding value, and a reduction function produces a value from a preceding key. Rainbow tables partition a function (the hash), whose domain is a set of values and whose codomain is a set of keys derived from those values, into chains such that each chain is an alternating sequence of values and keys, followed by a final value. Undoing the chains takes significant computation time, but overall this tradeoff makes certain classes of attacks practical. Rainbow tables address this problem by storing chains of possible passwords to save space. However, such a dataset can become too big as the range of possible passwords grows. ![]() One line of attack against this protection is to precompute the hashes of likely or possible passwords, and then store them in a dataset. To protect stored passwords from compromise in case of a data breach, organizations avoid storing them directly, instead transforming them using a scrambling function – typically a cryptographic hash. A rainbow table is an efficient way to store data that has been computed in advance to facilitate cracking passwords. ![]()
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