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    Introduction to Rainbow Tables

    By Martin Westergaard Jørgensen on October 19, 2012
    Rainbow tables are a tool used to reverse one-way cryptographic hashes such as MD5, NTLM and SHA1. Using complex mathematical formulas, it can cover large password key spaces in a short time

    Why should you use rainbow tables?
    The common way to try and reverse a cryptographic hash is to either use brute-force or use a dictionary.

    Brute force is done by hashing every single possible password, or key, in the keyspace and comparing the result to the target hash. This can be computationally infeasible as the passwords gets more complex. For example a password with a length of 7 characters based on uppercase, lowercase, numbers and symbols can take up to 65.5 trillion tries. Even with many computers and a way to distribute the work, it will take a long time to cover the full keyspace.
    Dictionary attacks takes another approach to the problem. It doesn’t try the full keyspace, but restricts it to the words that seems most likely. With the above example of a 7 character password, it is not likely the user used a password like xVdg#12 but instead simple words like ‘Article’ that are easy to remember. By only testing for passwords that are most likely, it is possible to quickly test for long passwords.
    Rainbow tables are a middle ground between brute force and dictionary attack. Rainbow tables cover most of the keyspace (usually > 99.9% of the keyspace) and does it in a time that is much faster than brute force attacks. The key to doing this is by using precomputed files, rainbow tables, with complex mathematical formulas to reverse the cryptographic hashes. The reasoning behind rainbow tables is most of the work is done once upfront, so you don’t have to do very much work when you need to reverse a hash.
    Advantages of rainbow tables

    Time savings
    Rainbow tables usually recovers the hash faster compared to brute force attacks due to the work done upfront.
    Space savings
    To store every single 7 character password possible for the given example, it would require a least 417 TB of space - rainbow tables only need around 80 GB of storage space, depending on your generation options.

    http://www.youtube.com/watch?v=aH0l2GKcLyk by:Carl Sagan

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