Hash functions and recipes

bitcoin-fundamentals-review.asciidoc

@@ -55,6 +55,11 @@ $ echo -n "Mastering the Lightning Network" | shasum -a 256
 ce86e4cd423d80d054b387aca23c02f5fc53b14be4f8d3ef14c089422b2235de  -
 ----
 
+[TIP]
+====
+The input used to calculate a hash is also called a _pre-image_.
+====
+
 The length of the input can be much bigger of course. Let's try the same thing with the PDF file of the Bitcoin whitepaper from Satoshi Nakamoto:
 
 ----
@@ -65,10 +70,36 @@ b1674191a88ec5cdd733e4240a81803105dc412d6c6708d53ab94fc248f4f553  -
 
 While it takes longer than a single sentence, the SHA256 function processes the 9-page PDF, "digesting" it into a 256-bit fingerprint.
 
+Now at this point you might be wondering how it is possible for a function that digests data of unlimited size to produce a unique fingerprint that is a fixed-size number?
+
+In theory, since there an infinite number of possible pre-images (inputs) and only a finite number of fingerprints, there must be many pre-images that produce the same 256-bit fingerprint. when two pre-images produce the same hash, this is known as a _collision_.
+
+In practice, a 256-bit number is so large that you will never find a collision on purpose. Cryptographic hash functions work on the basis that a search for a collision is a brute-force effort that takes so much energy and time that it is not practically possible.
+
 Cryptographic hash functions are broadly used in a variety of applications because they have some useful features. They are:
 
-* Deterministic
+Deterministic:: The same input always produces the same hash.
-// TODO
+
+Irreversible:: It is not possible to compute the pre-image of a hash.
+
+Collission-Proof:: It is computationally infeasible to find two messages that have the same hash.
+
+Uncorrelated:: A small change in the input produces such a big change in the output that the output seems uncorrelated to the input.
+
+Uniform/Random:: A cryptographic hash function produces hashes that are uniformly distributed across the entire 256-bit space of possible outputs. The output of a hash appears to be random, though it is not truly random.
+
+Using these features of cryptographic hashes, we can do build some interesting applications:
+
+Fingerprints:: A hash can be used to fingerprint a file or message so that it can be uniquely identified. Hashes can be used as universal identifiers of any data set.
+
+Integrity Proof:: A fingerprint of a file or message demonstrates its integrity, as the file or message cannot be tampered with or modified in any way without changing the fingeprirnt. This is often use to ensure software has not been tampered with before installing it on your computer.
+
+Commitment/Non-repudiation:: You can commit to a specific preimage (e.g. a number or message) without revealing it, by publishing its hash. Later, you can reveal the secret and everyone can verify that it is the same thing you committed to earlier because it produces the published hash.
+
+Proof-of-Work/Hash Grinding:: You can use a hash to prove you have done computational work, by showing a non-random pattern in the hash which can only be produced by repeated guesses at a pre-image. For example, the hash of a Bitcoin block header starts with a lot of zero bits. The only way to produce it is by changing a part of the header and hashing it trillions of times until it produces that pattern by chance.
+
+Atomicity:: You can make a secret pre-image a condition of spending funds in several linked transactions. If any one of the parties reveals the pre-image in order to spend one of the transactions, all the other parties can now spend their transactions too. All or none become spendable, achieving atomicity across several transactions.
+e to alter the message and still have the same hash.
 
 ==== Digital signatures