Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#2752

  1. Hash functions take a data set and converts it to a unique digital fingerprint that can not be read from output to input.

  2. Bitcoin uses hash functions to encrypt the transaction data in order to make sure the data has not changed when new blocks are formed.

  3. Collision resistant means the hash function is very unlikely to be read from output to input.

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#2753

Collision resistance is the property of hash functions that describe the probability of two inputs resulting in the same output. :slight_smile:

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#2754

  1. it is a mathematical algorithm that maps data of a certain size to a hash value of a fixed size. it is impossible to reverse, and makes your data entry unique.

  2. they can be used to create things like addresses, private and public keys. it also serves to secure and encrypt data inputs, to outputs that only the receiver can decrypt.

  3. collision resistance means itā€™s hard to find 2 inputs that end up hashing to the same output. the harder they are to find, the more secure the encryption of the hash function.

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#2755

A. Hash functions take an input and create a unique hash directly tied to that input. Any changes to the input and the output completely changes.
B. Bitcoin transactions are hashed using SHA-256 and when a new block is need to be added the hashing of the old block is added to the new block.
C. Collision resistant means it is unlikely to generate the same hash for a different input.

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#2756

  1. Hash function is a function that generates output (hash) by entering input. However it is not possible to do it visa versa (entering output and getting input).

  2. Hash function is used to create a block in blockchain together with data entered into this block (new transactions + additional data like timestamp) through mining.

  3. Hash function needs to be collision resistant, which means that it is almost impossible for two inputs to collide (=two inputs having the same output).

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#2757

Hash functions like sha256 are not used to derive public keys, for that the elliptic curve is used, but the public key is hashed to get the address. :slight_smile:

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#2758

  • Describe hash functions with your own words
    A one way function that consistently creates the same 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).
    Hash functions are used on cryptographic signed keys to generate bitcoin address and also to build the linked blockchain ledger

  • What does it mean when we say that hash functions need to be collision resistant? (We didnā€™t use the term ā€œcollision resistantā€ in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, thatā€™s how you learn best).
    Given to different inputs: A & B, it is infeasible for their hashes to be identical.

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#2759
  1. Hash functions are an input with a unique finger print. They are used to encrypt data being stored or transferred.
  2. They are used to give each transaction their own unique fingerprint/encryption. It is used on the input of information entered into the blockchain.
  3. It means that it has to be created to not be easily hacked or tampered with. It means that it is has a high min entropy when the hash function is done properly. Using the SHA256 hash function is the most secure bitcoin could be arguably.
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#2760

  1. Hash functions are a one way algorithm where each input produces a unique output.

  2. Hash functions are used in cryptocurrency by making it a requirement of the chain to have each block be mined by solving the algorithm in such a way that the hash of the output is less than the hash difficulty level. The difficulty level is increased by adding zeros to the start of the hash of the difficulty level.

  3. Hash functions being collision resistant means that with having two inputs a and b where H(a) and H(b) are their hashes, it is nearly impossible for the two hashes to be the same. Each input ought to have a different output.

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#2761

thank you for the clarification.

#2762

  1. A hash function is a complex one-way function, for each unique input it produces a unique output.

  2. 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 resistance means that it needs to be highly unlikely to produce the same output from 2 different inputs.

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#2763

  1. In the essence of hash functions. Hash functions is by means a mathematical operational protocol used to convert an input with an output data result. In an example like bitcoin using SHA-256 bit. It will result in a long text of data. Using letters and number in various sequences called a hash. In essence this is done for overall protection within the blockchain. It makes it difficult to be tampered within.

  2. Hash functions is used to encrypt the data from being tampered with. Itā€™s methods are used to secure information intended for the recipient for example. Also, they create digital signatures hashed through a block within.

  3. Two inputs messages cannot result with the same output. Which in this case it is unlikely to happen.

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#2764
  1. A hash function is a function which takes a certain input, and generates an output which is unique, based on that input. The input cannot be found using the generated output.
  2. For the mining process and for verifying the integrity of the data structure.
  3. It means that even if you take two inputs with a lot of data that need to be reduced to a single hash, the probability that the hash function will be the same even if the inputs are different is very low.
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#2765

1. Describe hash functions with your own words
Each unique input produces a unique output and a unique input also always produces ā€œThe Sameā€ unique output. A hash function is a One Way Function meaning it is unfeasible to guess the value of the input.

Input --> Output - YES
Output --> Input - NO

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 a part of the Proof of Work concept. Miners need to solve a hash function the gives an output that starts with 17 zeros to complete a Proof of Work.

3. What does it mean when we say that hash functions need to be collision resistant? (We didnā€™t use the term ā€œcollision resistantā€ in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, thatā€™s how you learn best).
Consider two different Inputs x and y where h(x) and h(y) are their hash outputs, it is infeasible for h(x) to be equal to h(y) because the probability of ā€˜collisionā€™ is very small.

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#2766
  1. Describe hash functions with your own words

Hash functions are functions where you get a unique fingerprint for an input. And there is no way to figure out when given the fingerprint or hash what the input is.

  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 functions are used:

  • to write new transactions into the blockchain.
  • to successfully ā€œsolveā€ a block, miners try to combine input data in such a way that the resulting hash starts with a certain number of zeroes.
  • in adresses; private and public keys.
  1. What does it mean when we say that hash functions need to be collision resistant? (We didnā€™t use the term ā€œcollision resistantā€ in the lecture, but you will easily find this on Google, we add this question intentionally to make you research information on your own, thatā€™s how you learn best).

Collision resistant means that it is infeasible for different inputs to get the same hash.

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#2767

  1. Hash functions are a unique type of alphanumerical functions where a unique fingerprint output is created for every individually different input. For instance, the slightest change in an input would result in entirely different output being generated.

  2. Hash functions are used in cryptocurrencies to create immutability and security in the blockchain. Specifically in regards to bitcoin, the hashing function SHA-256 is used to create security and consensus when confirming transactions and mining new blocks.

3.Hash functions must be collision resistant in order to maintain the integrity of the blockchain. Essentially, this means that two different inputs must not equal the same output.

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#2768
  1. It turns an input into a long output that is almost impossible to guess creating a very secure environment
    2)they are used in every block that is created to secure the transaction and make it impossible to change
    3)mean when two input creates the same output, this is almost impossible.
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#2769

Answer#1 : Hash functions are used in cryptocurrencies like bitcoin by taking the bitcoin transactions as input and outputting these transactions as a unique digital output.

Answer#2: Collision in regards to hash functions means given two different inputs m and n implies H(m) = H(n). Hash functions need to be collision resistant because hackers can possibly locate inputs m, n and switch the hash values H(m), H(n) to their advantage. To illustrate, lets assume two different transactions on a blockchain with data inputs m = Trx.data1 and n = Trx.data2 (where Trx = transaction) where both hash values are equal to one another, H(Trx.data1) = H(Trx.data2). Therefore if H(Trx.data1) = H(Trx.data2) and if inputs m, n are is easily located, then itā€™s possible a hacker can substitute H(Trx.data1) for H(Trx.data2) or vice versa.

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#2770

  1. A hash function is a function where you are not able to find out the imput if you have the output of the function. This is diffrent from a regular function where you are able to find out the imput if you posess the output.

  2. Hash functions are used in for example bitcoin (sha-256) to protect the unconfirmed transactions that are sent through the medium (ex Internet). After these transactions are confirmed by the miners this data is added to the newest block. The hash function is crucial to have proof of work in BTC.

  3. It means that it is very difficult to find 2 inputs that procuce the same output in a hash function.

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#2771
  1. When you designate an input using a hash function, it will convert binary data into a string of numbers and letters (i.e. output)
  2. Bitcoin utilizes SHA-256 as a hashing algorithm and implements hashing as a way for miners to mine blocks. Depending on the hash rate, the difficulty of the computation will increase or decrease.
  3. It is extremely hard to find two hash functions that result in the same output.
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