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One of the technical access controls used by a company consists of entering a 5-digit PIN. When entered, the PIN number is hashed and the hash code is compared to the stored value of the hash code in the system. To produce a rainbow table for the hash codes of all the possible 5-digit PIN configurations, how many hash codes must be generated?

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    No rainbow table needed - you just need 10^5 entries in your table to have all possible hashes. That's tiny. Rainbow tables are only needed when you have so many results that you need reduce memory by adding additional computation. Nov 9 '15 at 21:18
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The total character length is 10 since these are the available digits:

0 1 2 3 4 5 6 7 8 9

10^5 = 100,000

So about 100k hashes. You don't need rainbow tables for this, though, but you should read up on them for a better understanding.

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Concerning the Rainbow Table: the number of hashes in a hash-chain is not fixed. Might be (theoretically) any number; though the number of chains and number of hashes per chain have a great influence on the performance.

In your case generating a Rainbow Table is quite an overkill though. This kind of software is usually applied for way greater sets of passwords. In your case the alphabet is {0,1,2,3,4,5,6,7,8,9} with a fixed wordlength of 5, thus there are 10^5 = 100000 valid words. The small number of valid words allows the generation of a simple lookup-table or derivation of the password via a simple brute-force-attack.

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  • Thanks a lot Paul. However, how the alphabet {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is chosen with the 10 base? if the elements in the set of numbers is an assumption, is this the same technic applied in all the cases? Nov 10 '15 at 14:05
  • @ShanthamurthyHanumantharayapp PINs usually consist of digits, thus the alphabet is [0-9]. Though the content of the alphabet isn't relevant here. The important point is just the number of words that can be used as valid passwords
    – Paul
    Nov 10 '15 at 14:12
  • Thanks Paul now I am clear about Rainbow Table functionality. And why is this named after Rainbow? Nov 10 '15 at 14:26
  • Never mind Paul I figured out, since the Rainbow table is new to me and I was interested in digging deep to understand the concept. Thanks for all your answers. Nov 10 '15 at 14:52

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