WEBVTT

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In this lecture we'll talk about the properties and the use cases of hash algorithms. Though all cryptographic

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hash functions have different mathematical foundations

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they do have the same properties.

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Let's consider a cryptographic hash function and see what are its properties.

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The first property is called determinism.

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This means that the output of a hash function doesn't change between executions if it runs on the same

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input.

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It doesn't matter when or on what machine you calculate the hash, it will be the same

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if you use the same algorithm and input. In these examples I've calculated the hash of word Linux into

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different ways: using the sha512 some command and using the Openssl command; is the

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same hash. If I calculate the hash using an online tool we get the same result.

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Another important property of hash functions is that two different inputs always have different hashes

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or we can say that if two inputs like two files have the same hash they must be equal.

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If a single beat changes across inputs it will produce an entirely different hash. Let's calculated the

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hash of the word computer using sha256

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computer and the algorithm is sha256.

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This is the hash; now let's calculated the hash of the word computer1 using the same algorithm.

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We notice that two different words have two different hashes.

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Each input has its own unique hash.

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Keep this in mind! Now, theoretically speaking, it's possible to have collisions and that means different

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inputs with the same hash; but with a good cryptographic hash function

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there isn't a known way of finding a collision with all the computing resources in the world.

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We'll discuss hash collisions in a dedicated lecture later in the course. A hash function is one-way,

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meaning that it’s computationally infeasible to determine the original message from its hash value. Hashes

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work based on an irreversible mathematical transformation.

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In other words, given a hash, it would be impossible or extremely difficult to determine the deterministic

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steps taken to reproduce the input of that hash. Look at this hash.

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There is no way, no matter how much computational power you possess, to find the file or the text that

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has produced this hash.

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Hash functions always produce a fixed length output regardless of size of the input.

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For example SHA256 always produces a hash of 256 bits and sha-512 a hash of 512 bits.

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In fact the number after the Sha word means the length of the output hash. Let's see some examples. I'll

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calculate the hash of two characters, a and b, using SHA256.

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This is the hash which has a length of 256 bits or 64 hexadecimal characters.

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Now I calculated the hash of a phrase!

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And the output hash has the same length 64 symbols in base 16. Let's

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see now the hash of a file. I'm not interested in how big the file is; it's hate will have a length of

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256 bits or 64 hexadecimal characters.

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Sorry the command is SHA256sum.

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Okay.

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Permission denied.

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Okay let's choose another file etc/password

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or

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etc group/password.

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Or 

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/bin/ls

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and so on.

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We see the hash it's the same length.

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If I had the file of one gigabyte its hash would be of the same length. Another property of hash algorithms

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is that the avalanche effect. Changing one bit in the input should create an avalanche effect and its

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result is an entirely different hash. Let's an example!

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Let's take a bigger file, for example a dictionary file that comes with Kali Linux. Let's see how many

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characters and the words are in that file.

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usr/share/dict and american-english; there are almost 1 million characters. Let's calculate the hash

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of that file.

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This is the hash and I'll change a single character.

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I am opening the file using vim

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and at the end of the file I'll add a whitespace ; okay.

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And I'm saving the file.

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Okay I must be root in order to be able to edit the file.

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No problem.

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It's very easy.

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So at the end I'm adding a white space and I'm saving the file.

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Let' see its hash!

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And we noticed that

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its hash is entirely different.

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It's in fact a new hash.

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This is the avalanche effect. These five properties we've just discussed are the most important ones

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of any hash function.

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A good cryptographic hash function must also provide compression, efficiency and collision and preimage

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resistance. Compression means that the length of the output should be small enough.

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Efficiency means that the output hash should be computed easily enough in terms of time and hardware

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resources and collision and preimage resistance means to be secure enough.

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I'll go deeper into these two properties in a dedicated lecture where we'll talk about the attacks on

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hash algorithms.