Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#2832

Hash function is the system of turning information into encryption by inputting data no matter how large and getting a set output. The same data gets the same output. Any slight change will get a different output. Outputs cannot be reversed

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#2833
  1. Bitcoin transactions are recorded on ledgers and uses SHA 256 algorithm to protect the information entered on the ledger. A private key is created from the hash and a public key is then created for public trading bitcoin. The private key is protected and is only used once for that specific transaction only. Blocks are confirmed creating a chain that is irreversible
  2. Collision refers to two different inputs getting same outputs which
    is almost impossible
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#2834

  1. Describe hash functions with your own words
    Hash functions are a hexadecimal ‘compression’ of any digitized data – data in this case could be a password, a letter or document, a string of numbers, or sound recording, etc

  2. How are hash functions used in cryptocurrencies like bitcoin?
    Hash functions for cryptocurrencies like bitcoin include condensing transaction data into a unique ‘string’ of digits and letters (hexadecimal) that forms the unique ‘identity’ of a block of transactions without having to store all the information of each individual transaction in the block. It serves the purpose of immutability because even a tiny change to any of the transaction information in the block will generate a completely different hash code for that block

  3. What does it mean when we say that hash functions need to be collision resistant?
    Collision resistant means that two different discrete sets of data / information cannot generate the same hash code. If this were to happen ‘false’ data could be used to generate the same hash code as genuine / original data and open the system for corruption as well as render traceability useless

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#2835

Hash function is to produce a code to lock in information, giving the information a digital signature for verification.
Hash function has I understand for Bitcoin is two fold. One is when miners use their machine to solve equations in 0s and 1s and in this a hash is born from the answer. From the solving of these mathematical riddles a block is created has a reward, which also hashed. Bitcoin uses SHA-256 encryption to create hash.
Collision resistant means Attack Resistant. An attack on the hash would finding two of same hashes, with same data. The collision is meant to trick the system to corrupt or change exiting data has been coded by encryption in bitcoin it is coded by SHA-256 which is also further protected by private and public keys. SHA-256 is extremely difficult to find collisions of the same hash.

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#2836

  1. Describe hash functions with your own words
    A hash function is mathematical algorithm that will convert data (Input) into a bit array (output) with a fixed size. Its also a one way function. The output can not be converted back to the input.

  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 in crypto are used for writing new transactions trough the mining process. The inputs are the most recent not yet confirmed transactions. The output is the hashed data that will be added to the blockchain.

  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)
    If the function is collision resistant it means that its really hard to find two of the same inputs with the same output. The harder it is to find them the better the security.

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#2837

Yes, exactly, if bitcoin wasn’t using Sha256 but an another hashing algorithm with fewer output lenght size, so you can find collisions more easily, you could alter information in a transaction of that block to an addres of yours and still hashed the same and it would be accepted. But luckily Sha256 is such a so huge amount of possible hashes that the the changes of managing this hack is Negligible. But in the future when quantum computing gets more advanced, we might have to switch over to an even bigger hashing algo with more than 256 bits output to prevent this.

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#2838
  • hash functions is a function which convert the input in a string of numbers and letters as output, it can be one or two way function
  • It is used for censor the input and everything connected to it, and for guarantee that data are not changed
  • It means that can’t be two similar inputs which give the same output
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#2839
  1. Describe hash functions with your own words?

hash function is the process of puting in an input and recieve a digital fingerprint and if you change the input even slightly the output in return will change into a completley new finger print or 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).

bitcoin use hash 256 and is used to write new blocks on blokchain together with timestamp and previous block hash.

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 its very difficult to for 2 inputs to produce same outputs

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#2840
  1. Describe hash functions with your own words

Mathematical routine that takes any digital input and creates a unique output specific for that input.

  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).

Insure the integrity and security of the blocks as they are tied together. Also, used as “keys” for individuals to secure their identity associated with transactions.

  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).

The hash function will need to do a well enough job at creating a unique hash value so that it will be nearly impossible for any other input to result in an exact same hash output.

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#2841
  1. Describe hash functions with your own words
    Hash functions are ONE WAY functions that when given any input they create an output that will be unique to that input.

2.Hash functions are used to write/add transactions on the blockchain. The computer power needed to use these hash functions are contributed by mining. The miners get rewarded in bitcoin for hashing. In this way more bitcoin will slowly come into the circulating supply.

  1. Collision resistant means that when you give a hash function two different inputs the chance it creates the same input is (almost) impossibble. If a hash function is not collision resistant it is not secure. Because those collision can be seen and collected, making it easier to crack the code by connected the pieces.
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#2842

1: Hash functions take any input and return a crytographically created hexadecimal code of a specific length. This code acts like a fingerprint for that specific input as any change to the input, no matter how slight, would create a drastically different output.

2: Bitcoin uses hash functions to maintain the integrity of the information stored on its blockchain. Each block created on the blockchain starts with the hash value of the proceeding block, and then its own hash value is used in the following block, hence the term blockchain. Each block in the chain is linked via hash functions such that any change to any information on the chain would cause the hash values from that block on to change.

3: Though hash functions can generate an enormous number of possible outputs, the number of inputs is essentially limitless. That being the case, there is the possibility that two different inputs could generate the same hash output, such an event is called a collision and could defeat the security hash functions provide.

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#2843

  1. A hash function is like an encryption generator for computers. Think like instead of sending a letter in english during ww2; Americans used navajo code. Hash functions work similarly but in the digital era.

  2. Miners verify transactions by inputting data into a hashing function to create a block. Each block then compounds on the previous transactions to form an ever compounding series of hashes. Each layer builds upon the security of the system and helps prevent hackers from translating the code.

  3. Collision resistant means no two inputs have the same output. I’m thinking this comes in handy for the double spend problem and verifying balances in wallets.

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#2844

  1. It is a one way function that produce’s a fingerprint as output, it’s considered impossible to figure out the input from the output, if that happens then Bitcoin is cracked.

  2. It is used in mining for Bitcoin, a large computing power is needed, they work together by combining all the inputs and their own data, until the output start’s with …zeros.

  3. Hash function is collision resistant because that ensures that it is “impossible” for two diffirent inputs to produce the same output.

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#2845

1- Hash functions are functions that compress any binary data into an encrypted output- a series of letters and numbers of specified length.
2- Hash functions are used to encode information about new transactions onto the blockchain and to store the record of previous transactions.
3- Collision-resistant hash functions mean that it must be very difficult to find two inputs that produce the same hash output.

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#2846
  1. A hash function is when a computer takes a specific input of any content and length through a mathematic formula and produce a unique output of a specific lenght.
  2. I think that hash function is used in cryptocurrency to create the public and private keys that are used to sign transactions and receive crypto.
  3. Collision resistant means that there should not be two same output for two different inputs.
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#2847

SHA256 is used to link the blocks in a chain :wink: for deriving public keys the elliptic curve function is used.

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#2848

  1. A hash function is a computation that allows you to enter an input and it will produce a completely unique output, somewhat of a digital fingerprint.

  2. How I understand it in this moment is that in bitcoin, hash function are used in this way: transaction data is sent to all the nodes in the network, this transaction data which is made up of public keys, time stamps, the transaction amount and all that; is hashed. The nodes then hash that transaction data in combination with the previous block on the blockchain. This hash (transaction data + previous block) is hashed with random mathematical proofs until the output produces a hash that begins with a designated number of zeros. Which ever node completes this task first, adds that block (the hash with all the zeros at the beginning) to the blockchain.

  3. When a hash function is collision resistant is means there is a very low probability of finding two inputs that hash to the same output. The chances of this happening is very very unlikely but not impossible. Supposedly there is no such thing as a collision free hash function because a hash function’s output is a fixed length.

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#2849
  1. A hash function is a one-to-one function in which you cannot go back to the input
  2. Data in the first block is recorded as a hash and added also to next block of information
  3. A collision is when two pieces of information get the same hash, so collision resistance is the difficulty for this to happen
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#2850

Homework on Hash Functions - Questions

  1. Describe hash functions with your own words
    Hash function transfers any input into fixed size output; has function is irreversible and needs to have large output space for brute-force attack protection. It is also important that hash functions have non-locality function, which makes it possible for these functions to create very dissimilar outputs from similar inputs.

  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).

In Bitcoin mining hashcash algorithm is used and for it a service string, a nonce and a counter are required. The service string is encoded in the block header data structure and it holds important information. Block header data includes:

  • a version field,
  • the hash of the previous block,
  • the root hash of the merkle tree of all transactions in the block,
  • the current time, and
  • the difficulty.
    The body of the block contains the transactions and a nonce starts at 0 and is incremented for each hash.
  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 resistance means that a hash function is collision resistant and that it is hard to find two inputs that hash to the same output. Meaning two inputs a and b such that H ( a ) = H ( b ).

Every hash function with more inputs than outputs will have collisions.
Collision resistance doesn’t mean that no collisions exist it simply means that they are hard to find.

G.

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#2851

  1. A hash function is a special type of function that takes a unique input of any length and content and provides a unique output based on that based on a mathematical formula. Hashes can be made from nearly any digital content because digital content is ultimately just 1s and 0s at its lowest level.

  2. In the Bitcoin protocol, hash functions are part of the block hashing algorithm, which is used to write new transactions to the blockchain through what is known as the mining process. The inputs for the hash function are all of the most recent, yet-to-be confirmed transactions along with some information related to the previous block. Miners try to combine all of the inputs with an arbitrary piece of data in such a way that the resulting hash starts with a certain number zeros. This requires an extremely large amount of computing power and guarantees that that new coins are mined over long periods of time, not all at once. In order to earn new coins, you have to put in a ton of work to solve a block and by doing so, you’re verifying and locking in all of the new transactions into a block.

  3. Collisions occur when two pieces of data are put through the a hash function both have the same hash as a result. Collision-resistant hash function have a low probability of this occurring.

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