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Given the hash:

491c290affbf5436f0fc0584ccefb2

how do I construct a rainbow table to crack this password?

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It makes no sense to construct a rainbow table to crack a single password. –  Null Oct 25 '12 at 1:28
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For those wondering, it looks like this is really AES and not a hashing function. Here's where I suspect this is coming from. –  Null Oct 25 '12 at 1:30
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A rainbow table is brute force, just done ahead of time. –  Stephen Touset Oct 25 '12 at 3:49
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Also, Stack Exchange is not an appropriate place to ask people to do your homework for you. –  Stephen Touset Oct 25 '12 at 3:51
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@user1068636 - You do understand that rainbow tables are create by using a brute force approach right? In that you start at the very first possible password and run every single possible password through the algorithm, and simply store the output. –  Ramhound Oct 25 '12 at 13:13
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closed as too localized by Rook, Scott Pack, Iszi, Hendrik Brummermann Oct 25 '12 at 20:34

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2 Answers

One doesn't construct a rainbow table to crack a specific password. If you want to crack a specific password it is more efficient to simply brute force it then to generate a rainbow table. One constructs a rainbow table to be able to crack a lot of passwords that share certain characteristics such as the password hash function and the password dictionary from which the passwords are taken.

If someone has already built a rainbow table for passwords with the same characteristics as the password you're trying to crack then you can use it. But I'd be surprised if anyone has ever built a rainbow table for a password dictionary of any six hex bytes and a "hash function" in which the password is padded with zeroes and AES encrypted with a key of zeroes.

BTW, I wrote hash function in quotation marks because this isn't a hash function - it's an encryption function. If instead the (padded) password was used as a key to AES encrypt a block of zeroes - that would have been a hash function.

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To build the table as is described in the article, well, you just follow the description which is in the article. That's the point of the exercise: to learn how to read a scientific article and implement it. With a 24-bit space of possible passwords, you will just need about 256 tables, each with 256 chains, which is totally within range of a non-optimized implementation. Just like what a student can be reasonably expected to produce as part of homework.

Of course, it makes little sense to build such tables for cracking a single password; precomputed tables, including the special kind which Hellman describes, are worth the effort only when you want to crack at least two passwords. Also, a 24-bit space is a piece of cake and could be cracked with brute force in less than one second on average, if implemented properly (and substantially less if implemented properly with the AES-NI instructions).

Note that Hellman's time-memory trade-off is not a rainbow table, but its immediate predecessor. Rainbow tables are an optimization designed by Oechslin in 2003. I invite you to read the first parts of this article, which recalls Hellman's trade-off and might help you reach enlightenment (which is why you do the homework in the first place).

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