1- A hash function is a function that can take an input of an arbitrary size and get a fixed output.
2-In cryptocurrencies like bitcoin, transactions are used as an input and the output of a fixed length will be obtained using the algorithm: SHA-256.
3-This means that hash function should not have two different input that produce the same output.
Hash functions are algorithms that calculate a uniqie value with a fixed bit lenght. In case of SHA 256 it is 256 Bit long. There is no way to determine the input value backwards. If only a single bit in the input value would be changesd, the reult of the hash function would be completely different.
In cryptocurrencies like Bitcoin hash funktions are used during mining and on transactions in the Blockchain. In mining there is a number to be found that generates a special hash which starts with a certain number of 0 digits combined with the haash of the hash of this block. This is very computing power consuming task.
This means that it is hard to find two inputs that as result would show the same output hash.
1- A hash function is a one-way computational function that takes in a string of text and generates a unique output
2- In cryptocurrencies, Hash functions are used to generate new transactional hashes that added to the chain via the mining process
3- Collision resistance is the property of a cryptographic hash function that makes it infeasible to have 2 separate inputs hashing the same output
Homework on Hash Functions - Questions
A hash function is a tool used to produce a unique hash of a fixed length for any string of data or arbitrary number. A hash is a one way function and cannot be reversed.
Hash functions are used in Bitcoin to hash the transactional data contained in the previous blocks, it is also used to combine the transactional data with the nonce and time stamp.
This means it is hard to find two find two input that hash together to make the same output. Not impossible but hard.
Hash functions are functions that you pass a unique input and it returns a unique output. With hash functions it is not possible to go from output to input.
With bitcoin the transactions are taken as input and run through the hash function/algorithm (SHA 256) which gives an output of a fixed length.
This means that the probability of two different input giving the same output is highly unlikely.
Hash functions are one way functions in the sense that it can be provided with an input that will be converted to an output. It is almost impossible to obtain the input from the output. Hash functions gives data (input) a digital finger print (output) seeing that each unique input the has function is given a unique output is provided.
With Bitcoin, transaction data is stored on what is known as blocks. Each block has a unique hash provided through the SHA-256 hash algorithm. Even a slight change in the data will cause the hash of the block to change. Each block contains the previous blockās hash. If the hash of a block changes it breaks the chain in the block cain rendering the block invalid.
Having two different inputs providing the same output is known as a collision. No hash function can be 100% collision free. For a hash function to be collision resistant there has to be a very low probability for a collision to occur.
Hash function is a security for your network and it is an easy way to check if someone did not change the input.
Hash is a mathematical operation that used for proof of work what is the vital component in consensus. When a miner solves the math true nonce. Then itās send as a block and the other miners check iff the hash is correct and then itās added to the chain of blocks(blockchain).
When itās not colusion resistant it means that 2 inputs can get the same out put. Iff that happens You kind off destroy the concept. Thats why it is important that the hash function needs to be collision resistant
It makes Unique fingerprints
It is infeasible for a hash function with one input to be equal with a different input
Hash functions are one way functions that delivers an unique output for every input, also called unique digital fingerprint.
In the bitcoin protocol, hash functions are part of the block hashing algorithm which is used to write new transactions into the blockchain through the mining process.
Hash functions are collision resistant when it is hard to find two inputs that hash to the same output.
Homework on Hash Functions - Questions
Hash function is unique code which you get as output from input.
In simple terms, hashing means taking an input string of any length and giving out an output of a fixed length. In the context of cryptocurrencies like bitcoin , the transactions are taken as input and run through a hashing algorithm ( bitcoin uses SHA-256) which gives an output of a fixed length
Collision resistance is a property of cryptographic hash functions : a hash function H is collision - resistant if it is hard to find two inputs that hash to the same output; that i , two inputs a and b where a ā b but H(a) = H(b).
What about its usecase in Bitcoin? 
Hash functions are mathematical computations that take any input and convert it to a singularly unique string of numbers like a digital fingerprintā¦ No two inputs will have the same output. And also hash functions are a one way street meaning you should not be able to determine an input from an output.
Hash functions are used in bitcoin to secure the transactions and wallets and also mining the transactions and new bitcoin miners need to add there own data to the new transaction inputs and time stamp data etc plus pick a nonce out of thin air. Then hash all this and compare to the mining difficulty hash.
Collision resistance means the unlikelyhood of two hashes being identical. It is so rare in this case that if it were to happen one could assume the two inputs by chance happened to be the same.
Hash functions are a special, one-way functions that for any input value will produce a unique output value at a fixed length.
Hashing is central to cryptocurrencies like Bitcoin. Blocks are hashed and linked together, and thatās what makes blockchain a secure chain of blocks. Also when miners try to produce a block, it is hashed along with a nonce, and that value must meet the difficulty threshold. They keep trying until they get it, and the electricity that they spend is the proof of work that secures the network.
Collision resistant means that the hash function should produce unique outputs, by and large. If the parameters are set to produce an astronomical number of possibilities, it will take a virtual eternity to produce a duplicate output based on differing input.
Describe hash functions with your own words
Hash function is like a one-way street. A course of action that cannot be undone or does not lead to reciprocation.
How are hash functions used in cryptocurrencies like bitcoin?
Bitcoinās proof of work algorithm is based on SHA-256. Using this, Bitcoin miners solve computationally difficult math problems to add blocks into the blockchain.
Bitcoin blocks are added by verifying the hashes on a lottery basis. Yes, a lottery!! Let see how a miner wins the lotteryā¦
To successfully mine a block, a miner needs to hash the blockās header in such a way that it is less than or equal to the ātargetā.
The target is that the SHA-256 hash of a blockās header must be a 256-bit alphanumeric string, and must start with 18 zeros. The target changes as the difficulty change every 2016 blocks.
And the miners arrive at this particular hash (or target) by varying a small portion of the blockās headers, which is called a ānonce.ā A nonce always starts with ā0ā and is incremented every time for obtaining the required hash (or target).
Since the varying of the nonce is hit and miss, the chances of getting this particular hash (or target), which starts with these many zeros, is very low. Therefore, many attempts must be made by a miner by varying the nonce.
And this requires an enormous amount of computational power and hardware resources which proves that a large amount of work is carried out before mining any individual block. Thatās why this is called āproof-of-work ā.
And in this way, whichever miner first obtains the correct Bitcoin Hash will win the lottery and get the block reward of 6.25 BTC
What does it mean when we say that hash functions need to be collision resistant?
In practice, hash functions are used for ādigestingā large data. For example, if you want to check the validity of a large file (potentially much larger than a few megabytes), you can check the hash value of that file with the expected hash. Therefore, it is desirable (especially for cryptographic hash functions) that the function is collision resistant. That is, it should be āhardā to find two inputs m1 and m2 for hash function h such that h(m1) = h(m2). Most modern hash functions hope to achieve security level of 264 or better, which means that the attacker needs to test more than 264 different inputs to find a collision. Unfortunately, MD4 and MD5 aimed to provide 264 security, but has been shown to be broken using 26 and 237 inputs respectively. SHA-1 aimed to provide 280 security, but has been shown (at least theoretically) to be no more than 261 security.
Describe hash functions with your own words
the function if the program to get an input it will give you an unique out for it .it is also known as digital print.
How are hash functions used in cryptocurrencies like bitcoin?
Hash function is used by miner for all new transactions,it also help to keep the whole process secure.
What does it mean when we say that hash functions need to be collision resistant?
it means that two different different input cant have the same hash it is impossible mathematically those to be the same.
Describe hash functions with your own words
Functions that are able to transform an input into a specific output. But not the other way around.
How are hash functions used in cryptocurrencies like bitcoin? (Try to research this on your own, we will cover this later in the course but challenge yourself and see if you can find information on this already now).
It is used for transactions taken as input and we get a specific output.
What does it mean when we say that hash functions need to be collision resistant? (We didnāt use the term ācollision resistantā in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, thatās how you learn best).
it means that 2 wont give the same resutls at the same time.
1.A hash function is a function that always produces a unique output from a unique input without any collision. A slight change in the input can cause a massive change in the output.
2.A hash function in Bitcoin is basically use for encrypting data transaction(hashing transaction data). It is also used in mining and finding a nonce.
3.Collision resistant means that in a hash function, the encrypted data will be nearly possible to be duplicate (it is still possible but the percentage is astronomically low). In lay mans terms, it is very hard to produce 2 same output from different inputs.