Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#4079
  1. The hash function converts any input of data in a specific output, this function can not be reverted.
  2. miners need to find a hash that meets the target difficulty. Each block contains a blockheader with the number of the block, the hash of the previous block and a nonce, which includes a timestamp.
  3. it has to be impossible for two different inputs to produce the same output.
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#4080
  1. A function transfers an input to output, in this case, a hash.
  2. To generate a unique fingerprint of the underlying transaction.
  3. ā€œuniqueā€ fingerprint means that there is not another hash function with the same digits. Two different transactions (=input) should not generate the same output.
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#4081

  1. A Hash Function describes going from an input to an output. The process cannot be reverse engineered. Any input can be used, as I understand it even photos and and large files can be used as inputs. The outputs, like fingerprints are unique.

  2. In cryptocurrencies hash functions are used by miners as a proof of work system to secure the blockchain. Miners need to find the hash that meets the target difficulty of the block header to confirm the block, before moving onto the next block.

  3. Collision resistant refers to the fact that no 2 outputs can be the same. All outputs in hash functions are unique and irreversible.

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#4082

1. Describe hash functions with your own words
A: An hash functions acts as the exact fingerprint of a given input since a change in single bit of the input would return a different hash. It is non-reversible as one cannot infer the input from its hash.

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: The transactions into each of the blocks are hashed and the hash is then used to link the blocks. This means that the hash of the previous block is brought into the current block. This ensures that the data is not corruptible

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).
A: Being collision resistant means that no different inputs can produce the very same output (hash). The harder these collision are to find, the robust the hash function is to a brute-force attack

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#4083

Describe hash functions with your own words

Hash function is like a one-way function/relation which produces for each specific/unique input a one uniqe output. I like a simple analogy to a food blender with ingredients. After getting an input (specific ingredients), wich ist still identifiable, hash function produces (blending) a unique output. But the output is like a blended mixture, so itā€™s really impossible to reconstruct the initial data (ingredients) from the hash value. Therefore we can call hash functions ā€œa one-way functionsā€.

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 is used for security purposes and constitutes the backbone of crypto security. 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 (along with some additional inputs relating to the timestamp and a reference to the previous block).
The hash of a transaction makes it easy to identify transactions on the blockchain

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 is when two messages are with the same hash value. So speaking for example of the sha-256 hash function is collision resistant, because having two messages with the same hash value is extremely unlikely. With 2^256 possible hash values (more than the number of atoms in the known universe), the likelihood of two being the same is infinitesimally, unimaginably small.

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#4084

  1. Hash function is a special function based on SHA256 algorithm that takes unique input and produces unique alphanumeric output, which is almost impossible to reverse to the original input.

  2. Hash functions in Cryptocurrencies are used to pass transaction information anonymously.

  3. Collision resistant or collision-free means no two input should result in one same output.

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#4085
  1. Hash functions are one-way functions that take a unique input and generate a unique output. You cannot determine the input just from looking at the output. They use SHA256 to encrypt the input which outputs an alphanumeric string.
  2. Hash functions are used in mining cryptocurrencies such as Bitcoin. Miners need to hash the blockā€™s header in order to get it less than or equal to a target. The target is a is a 256-bit alphanumeric code that all bitcoin clients share. If your hash is below the target you are awarded bitcoin as a reward, but if its higher you need to increment the nonce and hash it again.
  3. Collision resistant hash functions are functions where it is hard to find two inputs that hash to the same output. If there are techniques to find collisions that are more efficient than brute force, then there is a flaw in the hash function and probably shouldnā€™t be used.
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#4086
  1. A hash function maps a data input to a value of a fixed size.
  2. A hash function is used for cryptocurrencies to generate a verifiable random ā€œnumberā€ value (alphanumeric using base 64 etc) which is less than a target to solve a block and generate a block reward.
  3. When collision-resistant, a hash function does not generate the same value from two different input values.
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#4087

  1. Hash Functions are unidirectional functions which take some input, and produce and alphanumeric output that cannot be reversed to find the original input.

  2. Hash functions are used in the cryptocurrencies like Bitcoin as part of the block hashing algorithm. The block hashing algorithm is used to write new transactions into the blockchain. In order to solve a block, miners must produce an output with the required number of leading zeros using all the unconfirmed transactions as input, and the minerā€™s own arbitrary data. Solving the block rewards the miner with the unconfirmed transactions that will go into that block.

  3. It would be difficult to find two inputs that hash to the same output.

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#4088

  1. Hash function takes input in the forms of letters, numbers, special characters, or media files and gives an output of 16-256 bits; no one should reverse it and find out the inputs.

  2. In bitcoin, blockchain and hash functions are used by peer-to-peer networks, each node of the network generates a hash function, and once they reach a consensus, it gets generated as a block on the blockchain and linked o the previous hash block.

  3. Collision-resistant hash means that no two different inputs should give the same hash output.

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#4089

  • A hash function is when an input is processed into a unique fingerprint specific to the data known as a hash. If the data is modified, then the hash completely changes. Bitcoin uses the SHA-256 hashing algorithm designed by the NSA. SHA-256 stands for Secure Hashing Algorithm 256 bits.

  • Hashing functions create a unique ID for each block on the blockchain. Blocks store the previous unique block hash to validate the chain. If the chain detects a non-valid hash, then the entire chain is de-validated and removed from the blockchain.

    Input > SHA-256 > Hashed Output.

  • If you could reverse that process, it would give you access to the input data, which would cripple the integrity of Bitcoin. However, it is currently impossible and computationally infeasible to try. Bitcoin will likely evolve past SHA-256 long before anyone can break it.

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#4090
  1. Hash function is a digital fingerprint. Hash function takes data and converts it into 256 bits
  2. Hash functions in Bitcoin are used in transactions, mining.
  3. It needs to be collision resistant because if it produces same output/s that it makes the system easy to hack and not reliable.
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#4091
  1. Describe hash functions with your own words

each unique input will produce a unique output

  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 convert an input to binary, and then binary to SHA256 results.

  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).

When output equal input

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#4092
  1. Describe hash functions with your own words
    hash functions mean each unique input will produce a unique output. It is a one-way function where you cannot derive the input based on the output.
  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).
    SHA256 is being used in bitcoin as a way to implement 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).
    It means that it should be hard to find two inputs that hash to the same output.
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#4093
  1. Encrypt certain information or data
  2. Create and encrypt unique wallet addresses
  3. A hash function is collision resistant if it is hard to find two inputs that hash to the same output. Collision resistance doesnā€™t mean that no collisions exist; simply that they are hard to find.
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#4094

Its when two inputs result in the same output. :slight_smile:

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#4095

  1. Describe hash functions with your own words
    Hash functions protocol uses calculations to change any size and kind of INPUT into a crypted OUTPUT of a fixed size. It is a one-way function that can not be reversed therefore it is secure.

  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).
    Based on the consensus mechanism of Bitcoin, PoW, I chose Ethereum to make a comparison. Ethereum uses KECCAK 256-bit hash function. The function has a function to make a hash out of a large or small amount of data. It has a property, that a change of a single input pice causes the output to change in an unpredictable way, similar to SHA ā€“ 256. It has an infinite input space.

  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).
    The term collision-resistant means, that it is impossible to find 2 different inputs for a hash function, that would produce the same output. Hash (a) = Hash (b)

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#4096

  1. Describe hash functions with your own words
    Hash functions produce an digital fingerprint of the input data. Cryptography is used to ensure that this function is a one way function, meaning, it is not possible to guess the input from the output. I guess we should say, that with our given knowledge and technology it is not possible to break that function and reverse the outputā€¦

  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 the mining process for adding a new block and also for verifying the existing blocks.
    What I understand form my research is, that multiple transactions are being hashed into something called a merkle tree. This merkle tree has a hash root, which is the digital fingerprint of the input data, in this case the transactions. Each block contains the hash root of the merkle tree, the hash of the previous block, a timestamp and something that is called ā€œnonceā€ (no idea what that is, yetā€¦)

  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).
    What I found regarding this topic is the ā€œbirthday paradoxā€, saying that in statistic, if you have N different possibilities of an event to happen, you need square root (N) different items for a 50 % chance of collision. A collision is defined as an event where two different inputs give the same output. In the birthday example it would be two different person having the same birthday.
    Since we want our crypto money to be safe, we want a collision resistant hash function to verify the blocks and transactions. Collision resistant in this case means, it is highly unlikely for two inputs to generate the same outcome. For a 256 bit hash that would mean that there would be a 50% chance of two inputs out of sqrt(2^256) = 3.4e38 to have the same outcome. And on top of everything this needs to happen within the time one block is created? If I understood it correctly it sounds pretty safeā€¦

My questions are:
Does the merkle tree only contain transactions or is other data stored in it?
Do I get it correctly, that as long as the time frame to create a block is smaller than the time it takes to brute force the hash function, everything is good?

Sources:
https://blockgeeks.com/guides/what-is-hashing/

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#4097

  1. Describe hash functions with your own words
    Hash functions are a unique code, of a specific length, that represents a set of data. If anything is changed in that set of data, the resulting hash function will be different.

  2. How are hash functions used in cryptocurrencies like bitcoin?
    Transforming transactions with all its information and previous transaction information into a unique identifier. Creating public keys to represent a personā€™s wallet address.

  3. What does it mean when we say that hash functions need to be collision resistant?
    Meaning that no two different inputs can result in the same output hash.

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#4098

1 - Hash functions are a Base-16 representation of an input. It only goes from input --> output and can not be reverse engineered
2 - Hash functions in BitCoin are the POW puzzle that the miners need to solve
3 - ā€œCollision resistanceā€ means that two different inputs canā€™t produce the same hash

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