Rainbow Tables (probably) aren’t what you think

Note: To understand this article, you‘ll need to understand password hashing and cracking first. Rainbow Tables are a very interesting but also fairly complex data structure, so if you aren’t interested in CompSci, you probably won’t be into this article.

Rainbow Attack by TheeWeguy
Rainbow Tables != Lookup Tables
Many people use “rainbow table” to refer to “a lookup table of password hashes”, but in reality a rainbow table is a far more complex, and more interesting technology. This article will discuss the problem with lookup tables, and how rainbow tables solve it. We’ll be focusing on a scenario where we want to crack any md5 hash of a 4 digit password, meaning our search space looks like so:
0000
0001
0002
...
9999
Lookup Tables Explained
Lookup tables are probably what you thought rainbow tables are, and are what most people mean when they say “rainbow table”. A lookup table is an extremely simple data structure. All it does is store both the hash and the corresponding password in a massive list. For example, by hashing the candidate list and storing the hash, we arrive at the following list:
4a7d1ed414474e4033ac29ccb8653d9b:0000
25bbdcd06c32d477f7fa1c3e4a91b032:0001
fcd04e26e900e94b9ed6dd604fed2b64:0002
...
fa246d0262c3925617b0c72bb20eeb1d:9999
In reality, you’d sort the file by the hash value, allowing you to use a binary search instead of having to read every line. But that’s not the focus of this article.
Lookup tables are a very simple and elegant solution, and can be searched very quickly, but the storage space quickly becomes infeasible for more complex passwords. For example, if we wanted to create a lookup table for all 8 character passwords with a full upper/lower/digits/symbols character set, we’d need about 160 PetaBytes of storage… Clearly another solution needs to be used at that scale.
Precomputed Hash Chains
The predecessor of rainbow tables, precomputed hash chains allow us to store far less on disk, at the expense of greater computing power requirements at “lookup” time.
To generate a hash chain, we need to first define a reduction function. Whereas a hash function takes a password and converts it into a hex string, our reduction function takes a hex string and converts it into a password within our desired search space. You can think of this as a random password generator that uses the input hash as a seed.
For example, when a hash function behaves like so:
0000 -> 4a7d1ed414474e4033ac29ccb8653d9b
Our reduction function would behave like so:
4a7d1ed414474e4033ac29ccb8653d9b -> 4515
Note that this is not reversing the hash, it’s deriving a new password from the hash. With hash and reduction functions, we can only go forward, never backwards.
We then our hash and reduction functions to generate a bunch of hash chains (in this instance each chain is 3 long):

Here’s the clever part. We never store the full hash chain, we only store the first and last link of each chain. As with the lookup tables, we’d probably sort the hash chains by the hash value for quicker lookup, but we’re ignoring that for the sake of illustration. We also need to store some metadata, like the chain length and the reduction function, so that we can recreate individual chains when needed.
It might seem strange that we’re spending the cycles to calculate the hash results but then not actually storing all the results. But here’s a useful way to think about it: Precomputed hash chains don’t store the solutions, they store hints that allow you to do a more targeted brute force at lookup time. Still confused? Keep reading to see how we use the chains.
Imagine we have the hash bf56a1b37b94243486b2034f8479c475 and we want to reverse it. We can check if we’ve already computed this before, by following the same process we used to generate the chains. By reducing and hashing, comparing with the saved hashes in the precomputed chains every time, we discover that we previously computed this hash in the 0000 chain.

Now that we know we’ve found the chain containing our solution, we can recreate it from the start to find the input of that solution, and therefore crack our hash.

https://parking.wustl.edu/files/formidable/346/Demon-Slayer-Mugen-Train-2020-rrwwrr.pdf
https://parking.wustl.edu/files/formidable/346/demon-slayer-mugen-train-ggwwpp.pdf
https://parking.wustl.edu/files/formidable/346/godzilla-vs-kong-2021-xxbbxx.pdf
https://parking.wustl.edu/files/formidable/346/godzilla-vs-kong-online-zzhhzz.pdf
https://parking.wustl.edu/files/formidable/346/watch-demon-slayer-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-demon-slayer-mugen-train-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-godzilla-vs-kong-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-godzilla-vs-kong-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-mortal-kombat-ccwwcc.pdf
https://parking.wustl.edu/files/formidable/346/watch-mortal-kombat-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-mortal-kombat-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-nobody-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-nobody-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-Raya-and-the-Last-Dragon-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-raya-last-dragon-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-seaspiracy-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-seaspiracy-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-the-unholy-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-the-unholy-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-tom-and-jerry-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-tom-and-jerry-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-voyagers-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-voyagers-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-zack-justice-league-full-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/watch-zack-snyders-justice-league-online-nitflix.pdf
https://parking.wustl.edu/files/formidable/346/zack-snyders-justice-league-mmttmm.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-1.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-2.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-3.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-4.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-5.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-6.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-7.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-8.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-9.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-10.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-11.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-12.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-13.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-14.pdf
https://parking.wustl.edu/files/formidable/346/watch-Godzilla-vs-Kong-fullfree-15.pdf
https://parking.wustl.edu/files/formidable/346/WATCH._-Godzilla-vs.-Kong-2021-F.U.L.L-Movie-ultra-hd.pdf
https://parking.wustl.edu/files/formidable/346/WATCH._-Mortal-Kombat-2021-F.U.L.L-Movie-ultra-hd.pdf
https://parking.wustl.edu/files/formidable/346/WATCH._-The-Unholy-2021-F.U.L.L-Movie-ultra-hd.pdf
https://parking.wustl.edu/files/formidable/346/WATCH._-Voyagers-2021-F.U.L.L-Movie-ultra-hd.pdf
https://parking.wustl.edu/files/formidable/346/Watch-Girl-in-the-Basement-2021-Online-F.R.E.E-full4kmovies.pdf
https://parking.wustl.edu/files/formidable/346/Watch-Godzilla-vs.-Kong-2021-Online-F.R.E.E-full4kmovies.pdf
https://parking.wustl.edu/files/formidable/346/Watch-Mortal-Kombat-2021-Online-F.R.E.E-full4kmovies.pdf
https://parking.wustl.edu/files/formidable/346/Watch-The-Unholy-2021-Online-F.R.E.E-full4kmovies.pdf
https://parking.wustl.edu/files/formidable/346/Watch-Tom-Jerry-2021-Online-F.R.E.E-full4kmovies.pdf
https://parking.wustl.edu/files/formidable/346/Watch-Voyagers-2021-Online-F.R.E.E-full4kmovies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/girl-in-basement-2021-online-free.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Free-watch-godzilla-vs-kong-online-full.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Bad-Trip-2021-free-123movies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Willys-Wonderland-2021-full-free-bluray.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/demon-slayer-kimetsu-no-yaiba-2020-full-hq-online.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Zack-Snyders-Justice-2021-full-bluray-HD.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/chaos-walking-2021-full-bluray-movies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/cherry-2021-full-free-online-hd.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/monsterhunter-2020-full-free-online-bluray.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Coming-2-America-2021-full-free-online-hd.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/wonderwoman-2021-full123movies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/tomand-jerry-full-free-online.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Rayaand-The-last-dragon-2021-full-free-online-tv.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/coming-2-america-2021-full-free-bluray.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/godzilla-vs-kong-2021-full-free-online.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/watch-cherry-2021-movies-online-hd.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Zack-Snyders-Justice-League-2021-movies-bluray-on-tv.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/judasandthe-black-messiah-2021-bluray-movies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/monster-hunter-2020-bluray-movies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/streams-free-watchdemon-slayer-mugen-train-online.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/watch-zack-snyders-justiceleague-online-2021-123movies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/girl-in-the-basement-2021-movies-online-tv.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/Billie-Eilish-2021-full-123movies.pdf
https://police.msu.edu/wp-content/uploads/formidable/37/nobody-2021-bluray-123movies-free.pdf
https://police.msu.edu/wp-content/uploads/formidable/