Uses for Cryptographic Hashing

CS 463 Lecture, Dr. Lawlor

The biggest use of hashing in cryptography is to detect changes to things:

To detect changes to software downloads, it's common to include a hash as a checksum. For example, here's the GnuPG download page, with SHA-1 hashes.
To detect changes to a network run requests, I use SHA-1 checksum as a message authentication code for NetRun's backend servers ("sandserv").
To detect changes to an issued https certificate, the certificate ships with SHA-256 and SHA-1 "fingerprints".

But hashing also has lots of other uses:

To "whiten" the output of a pseudorandom noise algorithm (make it more like "white noise"), you can compute a hash of the noise pool. This works because hash algorithms output very random-looking output, by mixing all the entropy in the input message.
To reduce the chance of a data breach revealing user's passwords, it's considered a good idea to only store the hash of the password, not the bare password. To prevent attackers from just looking up the hash in a precomputed table of hashes (a rainbow table), it's common to add an unpredictable salt value.
To assert the existence of something without revealing it, you can publish only the hash. This could be used to publish the terms of a contract, establish priority on an invention, or establish existence for "grandfather exemption" laws. To selectively reveal parts, you can build a tree of hashes, known as a Merkle tree.
BitCoin uses the SHA-256 hash as a "proof of computational work": you win some bitcoins (currently 25BTC, about $300) if you can find a number to add to the current block that hashes to produce enough leading zeros.