Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#4640

  • Describe hash functions with your own words
    Hash Functions are functions you can produce an output with input but not vice versa.

  • 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).

  • 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 is the property of a hash function that it is computationally infeasible to find two colliding inputs

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#4641

What happened with the second answer? :wink:

#4642

  1. Hash function takes a unique input and creates a unique output - The output cannot be used to create the original input, making it a one way function

  2. Hash functions are used to reward miners base on certain conditions for the output

  3. Two different inputs don’t produce the same output.

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#4643

A1. Hash function is a mathematical process that takes input data of any size, performs an operation on it, and returns output data of a fixed size such as: “Hello how are you?” can be mapped to

91f97a34f2e0c27bb10d67ffe66811530394d900490b417d1d4437c4a5efc614

by SHA256. In addition, hash function is a one-way function. So it cannot be reverted.

A2. 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. In the bitcoin mining, the inputs for the function are all of the most recent, not -yet-confirmed transactions (along with some additional inputs relating to the timestamp and a reference to the previous block).

A3. Collision resistance is a property of cryptographic hash functions by which any two inputs rarely produce the same hash output; that is, two inputs a and b such that H(a) = H(B) . Every hash function with more inputs than outputs will necessarily have collisions. Therefore, collision resistance doesn’t mean that no collisions exist; simply that they are hard to find.

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#4644
  1. A hash function is a one way function for which an input can create an output but never an output can create an input. The result of this mathematical equation will produce a unique digital signature.
  2. The hash function SHA-256 is used in bitcoin by miners to validate transactions and add new blocks to the blockchain database. The process of obtaining the unique finger print requires lots of random guessing and it does not have a formula.
  3. It means that it is very unlikely that the mathematical computation of an output will have two inputs.
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#4645

Hash functions convert input to a fixed length putput in such a way that a change in any single bit will completely change the output. This enables authentication of input. The function is not reversible ie input cannot be determined by any action on the output.

Hash function is used by miners to complete blocks & in securing wallets.

Collision resistant means that while not mathematically impossible, it is highly unlikely that two different inputs will produce the same output when hashed.

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#4646
  1. Its a one way function in wich an unique input will give an unique output
  2. It is use to identify a transaction. A set of input such as confirmed transaction between 2 public adresses and time data will be hashed to provide a hash number for the block.
  3. It means its hard for two different inputs that hashed the same output
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#4647
  1. A hash function is the process of creating a unique output from any given input. Ie pre-image resistant.
  2. Hash functions are used in crypto because you cannot reverse the decryption which means that the ledger is tamper proof.
  3. Collision résistance prevents the same output from two different inputs.
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#4648
  1. Describe hash functions with your own words.

Hash functions output a unique signature that changes anytime the input changes, allowing you to verify the data input into the hash function has not been altered.

  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).

It verifies the data in the blockchain has not been altered.

  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 less likely an attacker can find an alternate input that produces the same hash output as the original input the better the hash function.

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#4649
  1. Hash functions are a string of numbers and digits which encrypt data and verify its integrity. They are a one way function which means that you can’t calculate the input of the function from the output. The hash is always exactly the same from the same input and if the input even changes slightly - the hash output key will be completely different.
  2. BItcoin miners encrypt the data for a transaction into a hash and this activity produces bitcoins.
  3. Collision resistance = no two inputs create the same output key.
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#4650

  1. Hash function is a one way algorithm that maps an input into a fixed length of bits.

  2. Hash functions are used in mining, verifying new transactions in bitcoin

  3. collision resistant hashing means there is much less chance for there to be two outputs… near impossible

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#4651
  1. Hash functions is a one way function that provides a unique output (a finger print) to any input entered.
  2. Hash functions are used to write transactions into the blockchain through mining.
  3. It means that there is a different output to every input entered.
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#4652
  1. Hash function is a one way mathematical function where each input produces a unique fixed-length output - digital fingerprint.
  2. Bitcoin miners apply the SHA-256 hash function to block header and repeatedly add the ‘nonce‘ in such a way that it is always equal or less than the ‘Target hash’. The target at the time writing should be an alphanumeric number, consist 18 or more zeros and less than the target value which changes every 2016 blocks.
  3. Collision resistance means that it is very difficult to find two inputs that produce the same output in a hash function.
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#4653

  1. Describe hash functions with your own words
    a hash function is an encryption or mathematical process that takes input data of any length and performs an algorithm on it producing a fixed length encrypted hash result. This result can then be used to test validity against other input data for various applications.

  2. How are hash functions in crypto currencies 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.

  3. 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; that is, two inputs a and b such that H(a) = H(b).
    Every hash function with more inputs than outputs will necessarily have collisions. Consider a hash function such as SHA-256 that produces 256 bits of output from an arbitrarily large input. Since it must generate one of 2256 outputs for each member of a much larger set of inputs, the pigeonhole principle guarantees 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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#4654

  1. Hash functions are one way functions where each input produces an output or digital fingerprint.

  2. Hash functions in Bitcoins are using in mining for new transactions on the blockchain. The inputs for the hash function are the unconfirmed transactions plus additional data related to time and the previous transaction. To solve the block miners try to combine all of the inputs along with data of their own so the outputs start with a x number of 0’s.
    3. Collision resistance means that is statistically improbable to find 2 inputs that produce the same output in a hash function.

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#4655
  1. Hash functions are unidirectional functions where a unique input results in the same unique output, but two different inputs cannot generate the same output (technically possible, but hard to find such pairs).
  2. Computers on the bitcoin network are generating hashes based on the transactions but adding arbitrary data to it in order to meet the output requirements (in bitcoin the result hash should begin with x amount of zeroes)
  3. A hash is collision resistant if there are no two inputs producing the same output. (The end result has the same amount of variation as the input)
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#4656

  1. A hash function is a one-way function, where any given input will give you an output that is unique to the input (like a fingerprint for the input). They differ from regular functions because they are non-reversible, meaning you can not see what the input is from the output.

  2. Hash functions are used in Bitcoin as part of the mining process. Miners will use the computational power to try as guess a hash function that is less than the block header in order to win the block reward (Bitcoins). This processes secure the block and validates all transactions that were part of that block

  3. Collision resistance in hash functions means that it is hard to find two inputs that are not equal that give the same hashed output (so where x ≠ y, but H(x) = H(y). In a hashing algorithm where there are more inputs that outputs, you are more likely to find a collision. The higher the collision resistance, the more cryptographically secure the hashing function is said to be.

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#4657

True, But still Sha256 has a very huge field of possible hashes that makes it extremely difficult to have a collision.

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#4658

  1. A hash function is a function where each unique input has one unique output.

  2. Bitcoin uses one way hash function SHA-256 and proof of work throughout the mining process. Most notably a miner wins the right to mint the next block and the block reward by guessing the correct hash target first.

  3. Collision resistance is when a unique hash can be created using multiple inputs which would allow an attacker to replace an authentic hash with a fraudulent hash without the receiver knowing.

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#4659
  1. Hash functions - each input produce different output if something is changed
  2. In bitcoin mining, the inputs for the function are all of the most recent, not-yet-confirmed transactions (along with some additional inputs relating to the timestamp and a reference to the previous block).
  3. Collision resistance is a property of cryptographic hash functions: a hash function 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 ).
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