Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#3498

  1. Hash function is a mathematical process that takes input data of any size and performs an operation on that data and returns output data of a fixed size.

  2. in BTC protocol, hash functions are part of the block hashing algorithm used to write new transactions into the blockchain through the mining process.

  3. a hash function is collision resistant if it’s hard to find two inputs that hash to the same output.

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#3499

  1. Each Unique input gives a Unique output, or digital fingerprint of the input. Hash functions are uni-directional and can only go from input to output.

  2. Has functions ar apart of the block hashing algorithm, tis is used to write transactions onto the blockchain via mining. The inputs for the function are all of the most recent, unconfirmed transactions. Only little added data such as relating to the timestamp and reference to the previous block are added to the input.

  3. This is the property of a Hash function that makes it hard for 2 inputs to hash to the same output. Thus, only being able to go from input to output. If the collision resistance of the hash function breaks then its security is compromised and it no longer works.

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#3500
  1. Hash functions are linear and uni-directional algorithms that provide a unique and specific output for each individual input. The input can be of any length, while the output is always of a fixed length. The process cannot be reversed, so that outputs cannot be used to derive inputs.
  2. Hash functions are used to ensure the integrity of the blockchain, by creating records of transactions that cannot be copied/counterfeited. The hash function has to have 4 characteristics in order for it to be suitable for cryptography, including cryptocurrencies:
    a) Deterministic - the same particular input will give you the exact same output every single time.
    b) Quick - in order to be useful, the process must be fast and efficient
    c) Pre-image resistance - it must be infeasible (vice impossible) to determine the input from analysis of the output, meaning it must be almost statistically impossible to determine an input by picking a random input, running it through the has and comparing it to the output (brute force method).
    d) Any change to the input results in an entirely new output.
    e) Collision resistant - it is infeasible for two different inputs, put through two different hash algorithms, to result in the same output
    f) Puzzle friendly - outputs have a statistical high min-entropy
  3. Collision resistance refers to the extremely low probability that two different inputs, put through two different hash algorithms, will result in the same output.
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#3501

  1. Describe hash functions with your own words - Hash functions are digital fingerprints created from an input that creates the output

  2. How are hash functions used in cryptocurrencies like bitcoin? - Unique Hash Value (for every input, it produces a unique output), High Hashing Speeds (for each input the computation is fast) & Secure Hash Function (its almost computationally infeasible to reverse the function and make it two-way) and all of this is ensured through bitcoin mining. My research and responses for this question came from themoneymongers.com article from Sudhir Khatwani

  3. What does it mean when we say that hash functions need to be collision resistant? Collision resistant means that you can’t have two unique inputs resulting in the same output. If you have two unique inputs resulting in the same output a collision occurs and you have something broken in the algorithm and therefore is insecure. Research and response from thesslstore.com January 25, 2021 article.

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#3502
  1. Describe hash functions with your own words

Hash function is unique input which gives a unique output (digital fingerprint). And main one to use would be SHA-256 as others may not be secure enough.

  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).

Cryptocurrencies like bitcoin uses SHA-256 hash function to pass transaction information on the blockchain anonymously. This exact hash function due to its algorithm is very safe and secure because it can not be reversed / removed or edited…

  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 in cryptography is quality of hash functions which means that different inputs can not be found to have the same output / hash.

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#3503
  1. Hash function changes imput to output in a way to get an unique output. You can’t figure out input from output. SHA-256 is a digital signature of transaction.
  2. Bitcoin uses SHA-256 to generate random unique number using predictable amount of CPU effort.
  3. Collision resistant means that you should never get the same output from different inputs.
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#3504
  1. Describe hash functions with your own words:
  • Hash functions are functions that give a unique output for each unique input, so if the input is manipulated in anyway the output will change.
  • Hash functions are one way functions, so you can only go from inout to output, never back from output to 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):
  • 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.
  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):
  • Within hash functions, a collision happens when an attacker can find two inputs that both map to the same output.
  • Collision resistance is the property of a hash function that it is computationally infeasible to find two colliding inputs.
  • A hash function is said to be a collision resistant hash function if it is a collision resistant one-way hash function.
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#3505
  1. Hash functions take any unique input and return unique output (normally fixed length)
  2. Hash functions are used in cryptocurrencies, to take a unique mix of input that uniquely identifies a transaction and generates a unique hash value. This is a one-way transformation; a unique input will create a unique output, but you can’t take the output and figure out / re-engineer the original input
  3. Hash functions need to be collision resistant, in that two different sets of input musn’t ever create the same output value
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#3506
  1. Converting input in linear and unidirectional manner (one way) to generate output
  2. To add blocks to existing blockchain
  3. When two different inputs cannot hash into the same hash value
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#3507

  1. Hash functions are uni-directional, meaning that they can only go in one direction. Each input will create a uniquie output or digital fingerprint.

  2. 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. A hash function is collision-resistant if it is hard to find two inputs that hash to the same output.

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#3508

  1. Describe hash functions with your own words – it is a function that is impossible or difficult to reverse.

  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). – A cryptographic hash function combines the message-passing capabilities of hash functions with security properties

  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). - Input is transformed to unique output and the probability of two different inputs transforming to the same output is very low.

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#3509

1. Hash functions are basically a function that encrypts it’s input to an output that can not be reversed back into the input, the output of the function consists of alphanumeric text. no matter how long or big is the text input, the output from hash function will always be in a certain length depends on which type of has function was used. changing minor details in the input will drastically change the hash output and many other conditions for hash functions to be qualified for Crypto currencies. Bitcoin uses SHA-256 and Ethereum uses Keccak-256 for both of those hash functions give output hash of a 256 bit, those hash functions currently considered well secured for Crypto currencies usage.

2. Bitcoin is one of the Crypto currencies that was built on Blockchains, so basically Hash functions are used to encrypt the data stored inside each blockchain. hash functions are used to get hash pointers and also to create the Merkle trees. Merkel trees are consists of leaves that are hashed into baby node then hashed again to nodes then hashed to root node, Merkle trees acts are a multiple layer of security and also to help the ease and reduced time of tracking the hash/data instead of tracking them in a series liked in a linked list. hash functions have to have these conditions to be used for blockchains and crypto currencies; Deterministic, Quick computation , Small changes in the input changes the output drastically, Pre-image resistant, Collision resistant and Puzzle friendly.

3. Collision resistant basically means eliminating or reducing the chances of inputs having similar hashes for the most part, suppose having A and B as 2 different inputs so if H(A) and H(B) must be different from each other for the most parts. suppose we have P as number of the population and S is the sample size of the population, when we increase S then the chance of collision will increase as well . Collision resistant is easier to break than pre-image resistant, previous image resistance were broke by using the square root of the population ( in case of SHA-256, 2^256 is the population) so if we write it this was as Sqrt(2^256)=2^128, so at 2^128 hashes will increase the collision by 50%. Previous hash functions were broken before such as; MD5 was broke after 2^21 hashes, SHA-1 was broke after 2^61 hashes. but the current hash function SHA-256 that is used for bitcoin is considered safe and secured so ultimately we can say if H(A)=H(B) only when the inputs A=B.

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#3510

:small_orange_diamond: A hash function is a mathematical function that can take any data and produce an output “hash” for that particular input or so a digital fingerprint.

:small_orange_diamond: They are used as a form of verifying data integrity. Each block in the blockchain contains hashes of previous blocks. It has a unique hash value, high hashing speed, and secure.

:small_orange_diamond: Hash functions need to be collision resistent meaning hard to have two inputs that produces to the same output. It can also go from input to output but not viceversa.

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#3511
  1. Hash Functions are one way functions which transform a certain input into unique output.
  2. They are used to encrypt a transaction so its secure and only the recipient can decrypt it.
  3. When you get the same output for two or more different inputs (which is very hard to achieve).
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#3512

  1. They take any digital input and create a unique alphanumeric string based on the binary representation of the input data. Hashes are a one way function, meaning you cannot take a hashed output and reinterpret the input data.

  2. Transaction data in the defined time period (each 10 mins for BTC) that are to be included in the block are used as the input for the hash function. Miners must combine the transaction data in the correct way to match the hash output of the block “Confirming” the inputs are valid. This uses a lot of computer power to do the guess work

  3. Collision resistance means that a hash function has a statistically insignificant chance of producing the same alphanumeric output from two different input data sets. Meaning that the hash outputs are statistically likely to be unique to the input.

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#3513

Hash Functions are Linear, one directional so the input to output is the only route. Output to input is not possible with SHA-256 for example.

  1. Hash Functions are used to write new transactions into the blockchain through the process of mining. The inputs are yet to be confirmed transactions which will have timestamp date and links to previous block. This requires a large amount of processing power to solve the block.

  2. Collision Resistance is where it is way too difficult to find 2 matching inputs. Whilst Mathematically possible it would require a huge amount of processing power to find just one matching input.

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#3514

  1. A Hash Function is like a digital fingerprint; each unique input creates an equally unique output.

  2. Hash functions are used to keep the blockchain secure, the hash function is like a digital fingerprint that is assigned to each input to the blockchain to verify new transactions.

  3. It means that it is difficult to find two of the same inputs for an output.

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#3515

1.

daaaaaaaaaaaaaadddddddddddd
daaaaaaaaaaaaaadddddddddddd3071×2728 1.97 MB

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#3516

  1. Hash function is a one way function where a unique input gives a unique output

  2. Hash functions in cryptography combine the message passing capabilities with security properties

  3. This means that no two input hashes should map to the same output hash.

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#3517
  1. Hash functions are a 1 way algorithm that turns an input function into an output function, without being able to turn an output function into an input function.
    2.They are used as a consensus mechanism that miners use to verify a transaction. what makes it easy to verify is the hashing algorithm used , which shows public and private keys on the network, which signs the transaction.
  2. it basically means that for every hashing algorithm. One function will always match one output. If two input functions match one output function it would mean your hashing functions have collided.
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