Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#721

  1. Hash functions in cryptography are basically an input function that creates a fixed output, or fingerprint. This can be used to verify that a set of data has not been altered, because the resulting output will not have changed.

  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. For a hash function to be collision resistant, it must be hard to find 2 inputs that hash to create the same output.

#722
  1. Describe hash functions with your own words

A hash function is an algorithm that returns a specific number for a given input. On blockchains, the input is the block itself.

  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).

To be a cryptographic hash, it must be pre-image resistant and second pre-image resistant, and collision-resistant.

  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 should be difficult to find two different messages with the same hash result.

#723

  1. Hash function converts data into (e.g. SHA-256) 256 bit word. This function is a one-way function. Only from input to output.

  2. Hash functions in cryptocurrencies like Bitcoin are used for hash transactions and in mining blocks.

  3. Collision resistant means that 2 input hash to the same output, its hard to find.

#724

Hash functions is a function that takes input and produces a unique fingerprint in form of a hash.
This process cannot be reversed.
2.
The SHA 256 is today used in bitcoin and when you transact with bitcoin.
3.
Collison resistance means that it’s not likely or near impossible to get the same output form a hash function.

#725

Each hash should be a unique algorithm of the input data. When two identical hash strings collide together, that is because although they have different inputs, their outputs were the same. The resilience of the SHA is when the likelihood of a collision is highly unlikely.

#726

1)Describe hash functions with your own words

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).

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).

1)Hashing is generating a value or values from a string of text using a mathematical function.

2)In the context of cryptocurrencies like Bitcoin, the transactions are taken as input and run through a hashing algorithm (Bitcoin uses SHA-256) which gives an output of a fixed length.

3)It basically means that the chances of generating the same hash is almost impossible

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#727
  1. Repeatable with same input, but input cannot be discovered by any function against the output value. Output value always fixed length.
  2. Block is hashed so that any attempted change would invalidate the entire chain.
  3. Probability of diff input values generating identical output is less than 1 over the number atoms in the known universe.
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#728

  1. They are modern “cryptographic machines” that by a mathematical function change any given input value of written information into a coded string (output) that is not easily decoded.

  2. By acting as the computational power for guessing the root hash input from only knowing the output related to a single block ( including several transactions) in a specific cryptocurrency’s blockchain, the first miner to solve/guess the problem is rewarded with a predetermined amount of coins.

More specifically, the blockchain of a cryptocurrency requires miners to compare all the hashes of each transaction in a block by pairing and comparing the hashes until he eventually find the root hash input. This process is defined as the Merkle tree as it is visually compared to the branch of a tree which lead to further connecting branches. The miners starting point (the block) is at the very end of the last branch. His job is to compare the hash of each previous branch until he reaches the root branch. A correct root hash can then be mathematically verified by comparing it with all of the far out stretching branches (the individual transaction hashes) to solve the problem.

  1. A collision is the one vulnerability of a blockchains hash function. This is performed by finding two different inputs which become the same output. In other words, you would cross reference these and know/crack the secret mathematical function of the blockchain and be able to overrule any information to your liking. As in the instance of Bitcoins SHA-256 bits hash function, the probability to find such a matching pair is:
    1 to 100000000000000000000000000000000000000000000000000000000000000000000000000000.
    The pure numbers of required guesses makes it highly resistant, specifically as it has not been cracked. In other words, it is highly secure.
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#729

  1. A hash function is a function that takes an input value and from that input creates an output value beyond dispute of the input value.

  2. Bitcoin uses the sha-256 hash algorithm to generate verifiably random numbers in a way that requires a predictable amount of CPU effort.

  3. A hash function h is collision resistant if it is hard to find two inputs a and b and a =b . Every hash function with more inputs than outputs will necessarily have collisions.

#730

Q1: A hash function is simply taking an unique data input of any length and performing some mathematical functions on this to create a unique fixed length data output. Each specific input should generate the same output. Yet is should not be possible to work out data input from the hash output. This is known as a one-way function and makes hash functions secure. In addition any changes in the input (however small) will result in a different hash output.

Any hash function where input can be derived from hash output will render that hashing algorithm not secure.

Q2: Bitcoin is a digital ledger of hashes which use proof of work with SHA-256. This is called Bitcoin mining.

Q3: Collision resistance is a property of cryptographic hash functions. A hash function H is collision resistant if it is hard to find two inputs that hash to the same output.

#731

  1. A hash function is the function which will returns a unique hash for any input you provide which will be original hash. If you make any change the hash will be completely different.

  2. Bitcoin use hash function SHA-256 hashing algorithm. The hash function is used to create the digital signature for each unique block. That changing a small part of the input for a hash function results in a completely different output. This property is crucial to the ‘proof of work’ algorithm involved in mining. This way the miners try to combine all of the inputs with their own piece of input data.

  3. That means that it will be very difficult to find any two messages that the hash will have the same value.

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#732

  1. Describe hash functions with your own words
    A hash function does encrypt values in a one way fashion in that it is impossible to deduce the input from the output. Every unique input will result in a unique output with usually a fixed size or length determined by the chosen hash function type. There is also compression taking place - in regards to the file size, the hash is significantly smaller compared to the initial values.

  2. How are hash functions used in cryptocurrencies like bitcoin?
    They are interwoven in the functional structure in that they link the transactions on the blockchain together via the hash points that are generated. The immutability which underlies to the encryption mechanism further makes it easy to verify the validity and that in turn minimizes computing resources.

  3. What does it mean when we say that hash functions need to be collision resistant?
    2 different data inputs should not result in the same hash.

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#733

  1. Hash functions are functions that can take any input and create a 256 bit hash that is unique to that input, it will always produce the same hash with the same input, and you are unable to determine the input based on the hash output.

  2. hash functions are used to encrypt transaction data so that only the people meant to receive a transaction can open it. Each block on the blockchain also has a unique hash and changing any hash on any block on the chain will break consensus. When that happens the change is rejected so that keeps it from being hacked.

  3. It is collision resistant, meaning highly unlikely that two different transactions will randomly get the identical hashes because the 16 gigit, 256bit hashes are random and there are so many possible combinations that it is highly improbable for two transactions to randomly receive that same hash function.

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#734
  1. Describe hash functions with your own words

Hash functions are specific “one way” cryptographic functions whereby an input will always produce a unique output. These hash functions are bade up base16 alphanumeric properties after the input has been converted from binary code.

  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 in bitcoin to allow for the incentive mechanism that drives the entire network, call mining. Mining is the process for verifying and linking blocks, which leads to the creation of more bitcoin.

  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).

What this means for the most part is that each input will have it’s own unique hash. As a result, the chances are near zero that the same hash could be produced by two different inputs.

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#735

  1. A hash function is a mathematical formula which gives a particular and unique output for a given input. In the case of bitcoin it is called SHA 256. There is no way to guess what the input was from the output.

  2. In bitcoin the hashfunction is used to verify the integrity of the data and linking blocks. The link between the blocks is hashed and each link is linked to the next and previous one, which means that if someone try to change the information in a single block, all the other blocks need to change also, which does not happen.

  3. Collision resistant mean that outputs need to be unique. We have to be certain that for a single input you get a unique output. However, it is never 100% collision resistant, but in theory can happen, although its highly unlikely.

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#736

  1. Describe hash functions with your own words
    -> A hash function is a function that goes from input to output, but not the other way around. They are both unique and if input is slightly changed, output will also completely change.

  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 BTC, it is used like a digital fingerprint or signature of a block that can (basically) not be altered and secures all data inside that block.

  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).
    -> 2 different inputs could create the same binary hash, but the probability is so low that it can be neglected.

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#737

  1. Hash functions are a one way input which gives you a unique fingerprint output or HASH

  2. Hash functions are used in bitcoin mining in someway to run the algos in mining. Also when you do a transaction in bitcoin or another crypto you can take your hash and search on the block explorer to see the confirmations from the miners.

  3. So collision resistance is when it is very difficult for 2 inputs to produce the same output hash. This is very important for crypto for each transaction to have its own unique Hash function.

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#738

Is a function that based on an unique input gives an unique output with fixed lenght. Also has a “one way” property , you can only go from “input” to “output” and cannot go from “output” to “input”.

Hash functions are used in cryptocurrency mainly to guarantee security. Hashing in Cryptocurrency needs to have few property:

  • Deterministic , that means that an unique input will ALWAYS give the exact same unique output.
  • Quick Computation: that means that the has function must be quick to process to be efficient for the system.
  • Pre-Image Resistance : that means that is infeasible to the determine the original input from an output (hash value)
  • Small Changes In The Input Changes the Hash.: even a slight/minimum change in the input will give a totally different output.
  • Collision Resistant , check answer below for the 3rd question.

The hash function must be collusion resistant or the entire system will not work properly, in case of cryptocurrency if a collision would happen you could potentially access to others people funds.

In case of bitcoin as it uses SHA-256 there is one on 2^256 possibility of collision, so is infeasible that this event will happen.

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#739

  1. Hash functions have a specific input and output and if any portion of the input is change the output changes as well.

  2. In the context of cryptocurrencies like Bitcoin , the transactions are taken as input and run through a hashing algorithm, SHA256, which gives an output of a fixed length.

  3. Collision resistance is a property of cryptographic hash functions: a hash function H 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), and a ≠ b. … Cryptographic hash functions are usually designed to be collision resistant .

#740
  1. Hash functions - Every input generates an unic output / 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.
    In bitcoin mining, the inputs for the function are all of the most recent, not-yet-confirmed transactions .
  3. Collision resistance is a property of cryptographic hash functions : a hash function H is collision resistant if it is hard to find two inputs that hash to the same output; Every hash function with more inputs than outputs will necessarily have collisions.