Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#14
  1. Describe hash functions with your own words

You have an input and run it thru a ‘hash generator’ (e.g. sha-256) and it will create a unique fingerprint wich cannot be reversed.

  1. 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).

Every transaction (ledger) will be hashed together with the hash of the previous block to create a new block. And so on. This way, when a previous block has been altered, the chain will be invalid.

  1. What does it mean when we say that hash functions need to be collision resistant? (We didn’t use the term “collision resistant” in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, that’s how you learn best).

You need to be sure there is no chance to have 2 different inputs generating the same output hash. When this happens it is called a collision.

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#15
  1. An Hash function processes strings of any size and return an output string of a fixed size. its needs to be infeasible to discover the input based on the output. For the hashing algorithm to be considered secure.
  2. Hash function are used to create digital signature, the id of the block, based on the hash of all transaction and data contain in this block and also with a nonce. Hash merkle trees more lighter and easier to navigate then have a giant transaction database and having to parce trough it every time you need to refer to it.
  3. That It must never or almost never produce the same output from 2 different input. this would mean that the hash function is less reliable. Hence judged insecure.
#16

  1. Hash function is a mathematical function which takes an input of variable length and gives an output of a fixed lanegth. It has important properties of being cillision resistant and the pre-image resistance is negligible.

  2. Hash functions are used in bitcoin to perform chaining. Once the transactions in the block are stored, the hash is calculated using the hash function. This hash will be stored in the upcoming block, which results in chaining. This also will provide data integrity because if someone tries to manipulate the data, the hash of that block will change and this will breake the chain making the block invalid.

  3. It means that if two different input are provided, the Y must be different. No two different input will lead to same output.

#17
  • Describe hash functions with your own words

Hash function is a set of data. For every input that is given, it will give an unique output for it (digital fingerprint)

  • 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).

Hash function is used for every transaction and the output data is stored in a blockchain

  • What does it mean when we say that hash functions need to be collision resistant? (We didn’t use the term “collision resistant” in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, that’s how you learn best

Each input will have it’s own unique hash output so 2 inputs should never have the same output

#18

1. Describe hash functions with your own words
It is a function that gets an input, does some calculations and gives you a fixed lenght output (that is allways the same for the same input) that you cannot reverse to get the input again. But you still can verify if the input has been changed or not by hashing the input again and check if the output is still the same.

2. 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).
The info in the blocks are hashed and the hash is used to link the blocks together. So the hash of the previous block is inside the current block. So if you want to change some info in a certain block, you must recalculate all hashed of all previous blocks too.

3. What does it mean when we say that hash functions need to be collision resistant? (We didn’t use the term “collision resistant” in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, that’s how you learn best).
when a collision happens it means that you suddenly have 2 different inputs with the same hashed output. This makes the algorithm unusable.

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#19

  1. Hash functions are unique digital imprints that are produced from input to output. And always one way - input to output.

  2. Hash functions are used in cryptocurrencies like bitcoin by being part of the block hashing algorithms. To successfully ‘solve’ a block, miners try to combine all of the inputs with their own input data in a way where the resulting hash starts with a certain number of zeroes.

  3. Collision resistant means that for the most part each input will have its own unique hash.

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#20

  1. Hash functions work by taking an input no matter how big or small into the hash and getting a fixed 256bit output.

  2. A hash function in Bitcoin is used to hash transactions in each block. Since each transaction has a unique output the blockchain now becomes very secure.

  3. Collision resistant means not 2 different inputs cant have the same output.

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#21
  1. Describe hash functions with your own words

a Hash function is a cryptographic function that creates a unique output for a given input. That output may not be reversed to reveal the original input unless authorised.

  1. 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).

The hash function is used in bitcoin to codify the inputs of the transactions that comprise each block on the blockchain which in turn become an integral part of subsequent blocks. Because each hash is unique to the relevant input a change in data will in turn result in a different hash output which will in turn travel up through the subsequent blocks making them null and void.

  1. What does it mean when we say that hash functions need to be collision resistant? (We didn’t use the term “collision resistant” in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, that’s how you learn best).

Collision Resistant Hash is where the probability of a hash function outputting the same hash for two different inputs is extremely unlikely.

#22
  • Describe hash functions with your own words

A mathematical function that gives a unique fingerprint to any piece of information

  • How are hash functions used in cryptocurrencies like bitcoin?

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.

  • What does it mean when we say that hash functions need to be collision resistant?

a hash function is collision resistant if it is hard to find two inputs that hash to the same output

#23
  1. A hash funtion its a kind of resume funtion of a set of elements input into another subset of elements outputs.
  2. They have certain properties:
    - deterministic: Same input result in same output.
    - quick computation: Its fast to obtain H(x) of a given input x.
    - pre-image resistant: given a H(x) is not feasible to obtain x.
    - small changes in the input changes alot the result of the output
    - colision resistant: given two inputs x and y its infeasible that H(x) = H(y)
    - puzzle frendly: for every output “Y”, if k is chosen from a distribution with high min-entropy it is
    infeasible to find an input x such that H(k|x) = Y.
  3. is in 2.
#24
  1. Hash functions is basically taking an input and hashing/ applying mathematical/ operations to produce and output so that it becomes proctically impossible to find the input given the output.
  2. Hash functions are used to calculate public addressed from private keys and seed phrases, to find nonces and to calculate unique identifiers for every block.
  3. It means no 2 inputs should have the same output.
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#25

1- Hash Function: Is a one way function that gives a unique output for each input.

2- Bitcoin transactions are hashed using SHA-256 and when a new block is need to be added, then the hashing of the old block is added to the new blocked and all hashed together

3- There must be no two different inputs that give the same output

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#26

Homework on Hash Functions - Questions

  1. Describe hash functions with your own words

Hash function is a crypthographic hash which gives unique output for every unique input. No matter of the size of the input you will always get the fixed output made of 16^16 (consist of 0-9 & a-f).

  1. 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).

In the context of cryptocurrencies like Bitcoin, the transactions are taken as an input and run through a hashing algorithm (Bitcoin uses SHA-256) which gives an output of a fixed length.

Every newly added block consist the hash of the previous one and creates new for the subsequent block. It all together creates harmony, if you change anything in the history, it will change the hash of that particular block and the chain will collapse.

  1. What does it mean when we say that hash functions need to be collision resistant? (We didn’t use the term “collision resistant” in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, that’s how you learn best).

A hash function is collision resistant if it is hard to find two inputs that hash to the same output.
Collision resistance does not mean that no collisions exist; simply that they are hard to find.

#27 
Describe hash functions with your own words

Hashing functions operate on the input you give them and complete unique outputs.

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).

The SHA-256 hashing algorithm is to hash a bitcoin transaction and produce a unique 256 character hash. No matter the size of the original input.

What does it mean when we say that hash functions need to be collision resistant? (We didn’t use the term “collision resistant” in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, that’s how you learn best).

It should be hard to find 2 inputs that produce the same output

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#28

1- A hash function is a unique collection of numbers and letters that are used as a digital fingerprint for the data that is hashed.

2- Hash function in bitcoin are the unconfirmed transactions.

3- it means that every output should be unique.

#29

  1. Hash functions take any input of data, and maps the data to an output of fixed length. In SHA256, the output is a hexadecimal number. Any change in the data input, causes a massive change in the mapped hash.

  2. In bitcoin, hash functions (specifically SHA256) are used to cryptographically secure transaction data. It allows the blockchain to be open, transparent, and yet also secure. Each block on the blockchain is turned into a hash, which is then stored as the block header in the next block. This makes it so that any attempt to change the data in a block (reverse or steal a transaction for instance) results in a complete change to the hash connecting the previous blocks, and shows a break in the chain.

  3. Collision resistance is a property of cryptographic hash functions. It means that it is hard to find two functions that map to the same output. In SHA256, it means that every hash has 2 to the 256th power amount of combinations, an amount so astronomically large it makes the odds minuscule that a hash will have the same output twice.

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#30
  1. Hash function is to cryptographically generate a unique output with a unique input, through a mathematical algorithm to specific function parameters which is extremely difficult to regenerate in the inverted form.
  2. The unique transactional input is encrypted with a hash function to generate a fixed length unique output.
  3. The Bitcoin Hash function is collision resistant if, it is difficult to find two exact inputs that hash to the exact output in a period of the estimated 10min per new Bitcoin block generated in the Bitcoin blockchain. An extremely low probability of occurrence.
#31
  1. A hash function is a one-way function in witch a unique input gives a unique output.The output can only be derived from the input.You can not derive the input from the output.
  2. They are used in a data structure called the Merkel Tree
  3. It means that the hash function has been made in such a way that it is really difficult to find two different inputs that give the same unique output.
#32
  • Describe hash functions with your own words
    A hash function is a “trap-door” function, which means it computes in on direction and is mathematically hard to reverse engineer the input from the output. The hash value characterizes the input in a unique way; it is a digital signature.
  • 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).
    Hash functions are used to generate digital signatures of the data in the blocks of the blockchain, and are used in mining puzzles to provide challenges of increasing difficulty as the blockchain is built.
  • What does it mean when we say that hash functions need to be collision resistant? (We didn’t use the term “collision resistant” in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, that’s how you learn best).
    Different inputs to a hash function should infeasibly produce the same output. That is, it is possible for the output to be the same (a collision) but highly unlikely, in proportion to the amount of entropy of the hash function.
#33
  1. A hash function is generating an output with a fixed-length from any input, using a mathematical function.
  2. Bitcoin hashing uses SHA-256 to convert any input to a 256-bit output.
  3. A hash function is said to be collision-resistant because is infeasible to find two different inputs to hash to the same output.