Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#1748

I apologize for the delay, but do you mean one of its specific uses?

is the use not its any length input, and provides a return output of a fixed length?

#1749

Yes, but in blockchain hash functions are also used by miners to cryptographically link blocks in a chain, thus the name :wink:

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#1750

1-Hash function means that those functions which an unique input would give a unique output every time ( in a highly 256 bit value which safeguards data integrity).
2- Hash functions are used in bitcoin mainly during mining process which requires high computing power and intense data content to produce an unique output. hence a specific transaction is highly encrypted
3- When one say collision resistant means , there is no two inputs of similar value to get a specific output. every unique input has a unique digital footprint of its own

#1751
  1. Describe hash functions with your own words.

Hash functions are one way functions used to input whatever data or info to get back a “fingerprint” or a numerical assignment as an output.

  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).

With BTC, hash functions are part of the block hashing algorithm which is used to write new transactions into the blockchain through the mining process. It’s the need for this large amount of processing power that makes it so new bitcoins get mined over a long period of time, not all at once.

  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).

This means that it is hard to find more than 1 input that hash to the same output.

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#1752

  1. Hash function is a mathematical operation on an input of any length that outputs it as a fixed length string. The output will always be the same for any given input.

  2. Hash functions are used in crypto currencies to encrypt data that applies to the transaction.

  3. Collision resistant means that the chances of getting the same output for two different inputs is a very small likelihood. Hash functions need this feature so that errors are not made.

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#1753

hash functions are one way function that converts an input into a unique fingerprint .the fingerprint will always be equal in length no matter the input.There is no way to deduce the input just by looking at the output.
The hash function is used in the mining process of cryptos as well as for verify new transactions
collision resistant ; every output is unique and has only one input( like a fingerprint).

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#1754

1 Hash function is a complicated mathematical function that assigns an output of equal size to an input of any size.It s impossible to deduct the input by just having the output.
2 Hash function is used in cryptocurrencies like Bitcoin in order to encrypt (that is to secure)certain information such as private keys or info regarding the previous block
3 collision resistant means that it is extremely unlikely to have 2 different inputs with the same output

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#1755
  1. Hashing is the making of a string of characters into shorter fixed-length value or key that represents the original string. Hashing is index and retrieve items in a ledger because it is way faster to find the item using the shorter hashed key than to find it using the original value. used in many encryption algorithms
  2. Bitcoin protocol hash functions are part of the block hashing algorithm which is used to write new accounts/transactions into the blockchain through the mining process.
    3 Hash function with more inputs than outputs will necessarily have collisions. A hash function such as SHA-256 that produces 256 bits of output from a large input, must generate one of two 256 outputs for each member of a much larger set of inputs, ( pigeonhole principle) does guarantee that some inputs will hash to the same output. Collision resistance doesn’t mean that no collisions exist; simply that they are hard to find.
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#1756

1- It’s is 1 way, any input gives u an unique output & it’s not possible to get the same input if u put the output

2- transactions are taken as input threw SHA-256 (like bit coin) & gives you a unique output

3-Every input gives you a unique output so there is no collisions

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#1757

1.)
Each unique input (random length) always gives a unique output (fixed length)
Only the owner of the input (24 word seed phrase on a Leder Nano S as an an example) is able to generate this one unique output (Hash).

2.)
SHA-256 in Bitcoin:

  • Creating wallets (private keys, public keys, public bitcoin addresses)
  • Signing a massage (Digital Signatures)
  • Every bitcoin transaction has its own hash
  • Every block in the network has its own hash
  • Miners try to solve a hash puzzle to mine new blocks

3.)
Every unique input must have its own unique output.
If two (or more) different inputs have the same output, then one speaks of a collision.
No hash function is completely collision-free, but SHA-256 is still reliable to this day.

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#1758

  1. Mathematical process that take an input of any size and and generate an output or fingerprint of fixed size, this process is one-way and its what makes the blockchain secure.

  2. by taking any input and creating a fixed output, this process can create a unique BTC address for example, they are also a part of mining, the mine the subsequent hashes to form new blocks.

  3. It means that it has to be unfeasible to find 2 inputs that hash to the same output, making it really unlikely for you to “stumble” upon it even by trying mercilessly

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#1759

Was that covered in the video or the past content? because I’ve been jotting down my notes, and I don’t remember covering miners in detail.

But thank you for giving me a better explanation.

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#1760

  1. Hash functions are a one way function where each unique input gives a unique output.

  2. The hash function is used on each transaction and is then combined with the previous block’s hash as well as other data (nonce). Once the transaction is approved by concensus (ie many other nodes have confirmed the math verification) it will be added as part of the new block. As the hash of the previous block is in the calculation, concensus approval will have indicated that it has not been changed. It works like a tree concept (Merkle tree), with the new transactions being the lowest levels (leaves). By using the hash of the data to be stored in the blockchain it is an efficient way of storing vasts amounts of data with the unique input (which could be huge document etc) creating a unique output of 256 bits.

  3. Collison resistant is where you want the hash to be such that it is very, very unlikely that you will get two inputs where their hashes produce the same output This is the unique input gives unique output. You can’t say it definately will because of something called the Birthday Paradox, based on probability rules. So for example a 256 bit hash has 2^256 possibilities, to get to the point where you could have a clash you would need to go through sqrt(2^256) possibilities. It is a vast number of potentials and would take a huge amount of time to find a collision.

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#1761

  1. A hash functions transforms a string input through a complex mathematical formula and creates a unique output. It is infeasible/ impossible to find out the input given the output.

  2. New blocks are mined by combining the input data with a random own intput which will result in the hash of that combined input starting with a certain number of 0s depending on the difficulty.

  3. Collicion resistant means that it is infeasible to find two inputs which lead to the same hash output.

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#1762

  • Describe hash functions with your own words: when you input date, the output becomes a unqiue only to the date input. Any change to the input would change the output.

  • 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 data from bitcoin transactions are inputted into SHA 256 so that a unique hash is created. This hash number can only represent the date inputted, any small change to the transactions (input data) would produce a different hash. This is how the transactions are verified to be correct.

  • 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 means that the the hashing function sha 256 has high min-entropy which makes the hashing function collision resistant.

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#1763
  1. Describe hash functions with your own words

input of data will generate a unique output (sha 256) and is a one way function

  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).

hash creates the unique fingerprint that is tied to the blockchain and the hash of a previous block in a sequence is a tamper-proof sequence that can be easily verified. Bitcoin’s algorithm has applied hashing and blockchain by relying on the participation of autonomous networks. All these networks take part in the production and confirmation of hash transactions . Hash transactions reach approval by way of proof-of-work. Additionally there are checks against the mutual consensus of the participating networks. Once a transaction reaches approval, it joins the public ledger along with other approved transactions. One important application of blockchain technology is that currencies can be decentralized and peer-to-peer. To be sure, blockchain is not always a decentralized entity, as third parties such as banks and credit card companies utilize this technology as well.

  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 means data input cannot output same hash. 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 is, two inputs a and b such that H(a)=H(b) - A cannot = B. Birthday method makes collision more feasible to happen and disputed arguments exist that quantum computing can create birthday attacks thus breaking collision resistance.

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#1764

A hash function is a conversion from text to cryptographics such as 64 bit 128 bit 256 bit where each unique input has a unique output. The hash is infeasible to be broken to find the input based on the output. This is what makes it immutable.

Bitcoin uses SHA- 256 secure hashing algorithm, to hash transactions on the blockchain. Each transaction is unique and secure and can be verified by miners using collision resistance and solving a puzzle such that the time to create a blockchain is 10 min. This solutions become easier or harder depending on the time it takes to solve the puzzle Given the function H( kIx ) = Y and knowing Y(difficulty), select a “k” from min-entropy(large distribution) and find “x” and perform concatenated hash. This is the problem that mining must solve for a block to be added to the chain.

Collision resistance means that if I have two hash functions f(A) =f(B) then A must equal to B for the most part. When you apply this to Bitcoin mining it is based on solving a problem and breaking the collision resistance. Bitcoin miners are then rewarded for solving the puzzle and a new block is added to the blockchain and the result is shared with all miners and can be verified.

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#1765

  1. Describe hash functions with your own words
    Hash functions are a secure way to create a unique output fingerprint of any given input data. The most important aspect of a hash function is that there is no way to take the output and figure out what the input was.

  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).
    Hash functions are used to secure the contents of each of the blocks in the blockchain which makes it impossible to alter the contents of an existing block without being detected. Because the difficulty level of the hash function can be adjusted, the keeps the rate of new block production and hence new bitcoin production at a somewhat controllable rate of 1 block every 10 minutes. This keeps the inflation rate of bitcoin under control and helps to set the value of bitcoin as a function of the amount of energy that was used in the mining process.

  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).
    Collision resistance means that every input into the hash should produce a distinctly unique output. If two different inputs can produce the same hash output then it degrades the integrity of the hash. Collision resistance is critical since every block in the blockchain is hashed and the hash value is use to trace the lineage of the blockchain. Duplicate hash values across more than one block in the blockchain would destroy the integrity of the blockchain.

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#1766

  1. A Hash function take any data input, applies a random number to it, and the result is another long number which can be linked to the first data as a mesuare of verification. The trick is that is only one-way road, the original data cannot be created from the hash using the mathematical way backwards.

  2. The Hash function is used in crypto to create the blockchain. The transactions of one block would be the input data, then the hash is applied to the block and the output is a “long number” which will be used in the next block. That increases de security of the chain, because every block unique “hash” number can be traced to the previous blocks and if one piece of the chain gets corrupted, then the hash of ALL the following blocks change so it can be detected that “someone put his hand in the honeypot”.

  3. Collision resistant means in plain words that the Hash resulted is it extremely difficult to calculate or guess. The only way to find the lucky number (or hash) would take ballizion years of computational effort, which it is not cost effective due that the blockchain is growing and everytime a block is added to the chain… the process of “guessing” had to start again.

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#1767

  1. So, hash functions are a specific type of functions. They take an input and output a fixed length. Its input can be any size. They use certain types of algorithms to perform output. So for instance, with SHA-256 algorithm, output will always be a string with a fixed size of 256 bits. Being hash function also means that it is almost impossible to revert it, i mean, one can not use output to find input.

  2. These kind functions are used in bitcoin to hash transactions and their outputs are used to create a block, although a block have other elements.

  3. Collision resistant refers to the ability to avoid that two different inputs produce the same output value.

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