# Hash Week!

Over the last two days we've talked about hash functions and their uses in cryptography and elsewhere. Remember that an ideal hash function is basically what cryptographers call a random oracle - given an input, it produces a random number in some range. (In practice this range is always [0,2^(2^n)], with n usually equal to 5 or 6 for non-cryptographic hashes or n equal to 7, 8, or 9 for cryptographic hashes.) This random number is deterministic, in that the same input always produces the same output. But the output is otherwise unpredictable. Given an output, it should not be possible to…

Yesterday we looked at hash functions. As you recall, they're functions which take an input and generate a random-seeming output. As a quick example, here's the output of the SHA-256 hash function for the name of the Scottish physicist James Maxwell and a misspelling thereof:
SHA256("James Clerk Maxwell") = 2667629603913530690117759428994407894024237387971995154086108064226397\
5353322
SHA256("James Clark Maxwell") = 9129664885155451589341762461551711693832872424126676652783015499131718\
4589063
A tiny change in the input generates a wildly different output, so tt looks like SHA256 is a…

Last week NIST anounced the winner of its Cryptographic Hash Function Competition. After five years of review and many rounds of discussion and elimination, the winner is a hash function called Keccak, and its developers deserve many congratulations. It's a shame hash functions aren't better known in the general public, because not only are they a vital part of keeping data safe online, they're one of the most interesting bits of applied math. Better still, their basic concept is not complicated at all.
Hash functions are so cool, in fact, that I want to spend several posts this week…