Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#141
  1. It is a unique fixed length coded output corresponding to an input.
  2. They are used to write new transactions on the blockchain.
  3. Hash functions need to be collision-resistant (not collision-proof)! Two unique inputs can possibly have the same hash.
#142

• Describe hash functions with your own words.
o A has function is any function that maps data of arbitrary size to a fixed number of bits or value.
• 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).
o Hash functions are used by cryptocurrencies to:
a) Create addresses, public and private.
b) Verify transactions.
c) Determine if a transaction is within a block.
d) Prevent new coins from being minted except through mining.
e) To create security, by linking blocks via hashes.
• What does it mean when we say that hash functions need to be collision resistant?
o We need hash functions to be collision resistant so that the probability of two (or more) inputs produce the same output or hash to be very low so that the cryptographic integrity is not comprised or cracked.

#143

  1. A hash function is a very special pre-set formula for the computation of a digital fingerprint/code that is dependent entirely on the input given to the hash function. While we may be adding a text originally to the function, it is actually automatically converted into binary numbers (1,0) and after this calculation has been made the hash function gives a hash of the output converted into hexa-decimal numbers/digits. Any slightest of change in the input will result in a new output, while it may seem as an almost non existant change in the input text, it is a huge change in the binary number and hexa-decimal translation.

  2. The SHA-256 hashing algorithm is implemented in the Bitcoin network in such a way that the computer nodes holding the network up and running are incentivised to do the work where they need to apply all the most recent inputs (that includes a lot of information about the transactions) and find the correct output hash value for it.

  3. Collision resistant means that up to this day it has not been possible to find two non-identical strings that are giving the exactly identical hash value as the other one.

#144
  1. Hash functions are a mechanism in cryptography that is used to encrypt information.
  2. Hash functions are used to encrypt transactions.
  3. This means that it should be infeasible to get two outputs.
#145

1.) Hash functions give unique set of characters to the original input.
2.) Hash functions are used to give every block it’s unique signatures to insure the security of blockchain.
3.) The public key is derived from the private key. Generating a private key is pretty collision resistant as the space is huge. The fact that an address is in turn a hash of the public key doesn’t change that.

#146
  1. A hash function takes a string of data and converts it into 64 bits. This process is impossible to reverse and provides a unique identifier for your data.
  2. In Bitcoin the hash function is used to hash transaction data. Also mining and finding a nonce requires finding a number that generates a specified hash in combination with data unique to that block.
  3. Collision resistant means two different strings of data not getting the same hash. In theory it’s possible, but extremely improbable.
#147

Hash functions gives a unique output to a unique input and the input cannot be resolved by knowing the output.

Hash functions are part of the block hashing algorithm which is used to write new transactions into the blockchain through the mining process
3)
Collision Resistant means that each input will have its own unique hash. Having two different inputs that resolve in the same hash is known as a collision. No hash function is completly collision free, but the possiblilty of that happening is so small that it’s not a practical problem.

#148
  1. A hash function takes a group of characters and maps it to a value of a certain length
  2. Most common use case is in creating public/private keys and digital signature
  3. it is extremely difficult, if near impossible to generate the same hash for a different input
#149

  1. The hash function is a function that, from non-fixed length input, generates fixed-length output. In hash function is not feasible to guess input by looking at output.

  2. An example of use SHA256 function in bitcoin is a generation of a bitcoin address from a public key.

  3. Ccollision resistance means that it should not be feasible to produce the same output from a different input.

#150
  1. hash functions are one way functions which do not allow output to create input
  2. Hash functions are used to confirm transacions, miners use huge amount of computing power to combine transactions data of the transaction with previos data
  3. it means that there should not be 2 inputs that generate one output, that would cause mess in transaction data.
#151
  1. They are special functions where the uniques input produces a unique output.
    The input cannot be derived from the output.
  2. Bitcoin transactions are hashed, then appended with a random text (nonce) and hashed again. The result is compared to the difficulty level. If it is lower, it is added to the blockchain. If not, the hashing with a new nonce is repeated until the result is lower than the difficulty level.
  3. Collision resistant functions never allow two inputs to produce the same output.
#152

  1. Describe hash functions with your own words
    A mathematical process that has includes the following;
    a) Each input gets its own unique ‘digital fingerprint’ specific to that exact input.
    b)You can go from input to output but never output to input. Going from output to input would in effect defy the purpose of BTC and essentially ‘break Bitcoin’

  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 in BTC to determine Proof of Work as part of the Blockchain hashing algorithm.

  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 refers to the chance of finding any two inputs hashing to the same output being very low, although technically not impossible.

#153

  1. Describe hash functions with your own words.
    It’s a function wherein by computing the input you can get the output, but the reverse is not possible.

  2. How are hash functions used in cryptocurrencies like bitcoin?
    It’s used in mining. Basically block contains the hash and this hash is included to the next block, create chain of blocks, hence called blockchain.

  3. What does it mean when we say that hash functions need to be collision resistant?
    It means it’s near impossible to find another input which will generate the same output.

#154

1.The mathimatical equation that takes input info and hashes it into compressed numerical value.

  1. The miners have to solve the hash of any transaction. This requires extemely long computation which is then agreed upon by varioud nodes.
  2. In order to be collision resistant, the need to not have the same alphanumerics run into each other. Two miners would generate the same hash. Its has to do with the speed at which the miners hash the data. Even tho unlikely to collide, they need to go to e certain speed to make extra sure.
#155

Homework on Hash Functions - Questions

  1. Taking input string however long and giving output of fixed length.

  2. Hash functions used in bitcoin is used to hash data transactions.

  3. To prevent an attempt to find two input strings of a hash function that produce the same hash result.

#156

  1. Describe hash functions with your own words
    Hash functions are functions where given an input, you are returned a consistent, mathematically calculated output. The functions work one way in that the given an input, you can find an output; however, given an output, you cannot find the input without using brute force

  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 in many ways such as hashing transactions, during the mining process to try and add a new block to the chain… new blocks and transactions are run through a hash function like SHA-256 to provide an encrypted key.

  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).
    This means having two different inputs result in the same output. It’s not impossible, but it’s impractical due to the extremely large number of possibilities

#157

1- hashing functions are mathematical functions where you cant find the input based on the output
2- has functions are use to write new transactions into the blockchain through mining
3- it means that you cannot find the input based on the output and extremely hard to have the same output given different inputs

#158

1.Hash function generates a value from string of data using a one way mathematical function.
2. Hash function in Bitcoin is used in mining blocks to verify new transactions.
3. No two inputs produce the same output.

#159
  1. Describe hash functions with your own words
  • Hash functions take input strings of any length and giving an output of a fixed length.
  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).
  • On the blockchain users generate something called a key paid, which is a public & private key using some known algorithm. They are both associated with each other through a mathematical relationship.
  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)
  • It means that each input will have its own unique hash
#160

1 hash functions - functions that transform incoming information into a special code that understand only receiver
2 in Bitcoin hash functions used to generates private and public key, also addresses and transitions
3 it means that hash functions don’t have to lead two different inputs to the same output