Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#5121

hash functions are one way functions where each input produces an output or digital fingerprint
2.Hash functions bitcoins using in mining for new transactions on the blockchain. the inputs for hash function are unconfirmed transaction plus additional data related to time and the previous transaction. to solve the block miners try to combine all the inputs along data of their own so the outputs start with a bunch of 0s it takes a lot of computing power and guessing
3. collision resistance means that is very difficult to find 2 inputs that produce the same output in a has function. this is an important property in cryptographic hash functions

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#5122
  1. A hash function takes any string of data, uses very complex functions and converts it into 256 bits. This process is impossible to reverse and provides a unique output.
  2. In Bitcoin the Hash function is used to hash transaction data, private, public keys and Bitcoin addresses. Inputing a nonce to the data to be hashed will result in a unique specified hash to that content and the source cannot be deciphered from the output but if its correct through its hashing it will be added to the block and recorded in a ledger.
  3. Collision resistant means: given two different inputs A and B where H (A) and H (B) are their respective hashes, it is infeasible for H (A) to be equal to H (B).

For cryptocurrencies, hash functions have to follow this property. Otherwise the output can’t be unique.

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#5123

  1. Hash Functions are essentially computer translators. They translate digits, letters, and large media files into ALPHANUMERIC strings of a certain size. Standard sizes are 64-bit, 128-bit, and 256-bit.

  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. A hash function that is collision resistant means that two different data inputs will not produce the same data output.

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#5124
  1. A hash function is a computation that takes a unique input and produces a unique output or digital fingerprint called a hash. This hash is a one way function. If the input is altered, the result will also be different.

2.Using SHA-256, miners receive unconfirmed transactions and produce a result when the hash of the block is less than or equal to the target (a 256 bit number that all BTC clients use) of the network.

3.The Pigeonhole Principle details that any hash with more inputs than outputs will have collisions. If these collisions are found, attackers can substitute inputs of the hash without being found out. Collision resistance is needed because it makes it difficult to find two inputs that produce the same digest. This makes the hash function cryptographically secure.

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#5125

1 - Hash functions change a given input into a list of numbers / letters
2 - Hash functions are used to encrypt and decrypt a user’s keys and ensure the transfer of bitcoin is made without a need for a 3rd party
3 - a hash is collision resistant if it’s hard to find twice the same output with different inputs

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#5126

  1. A hash function is a mathematical algorithm in which each unique input will produce a unique output. The same input will always produce the same output but you cannot figure out an input solely on the output first. A hash function is therefore always a one way function.

  2. Bitcoins Hash Algorithm SHA-256 is used in bitcoin mining. Miners use software to hash the blocks header in order to get it equal or less than the target (a number between 0-256). There is a trial and error process requiring high amounts of computational capacity. Blocks are added following successful verification of the hashes and new bitcoin are created and given to the successful miner.

  3. Making a hash function collision resistant means it will be hard to find two inputs that will hash to the same output. This will prevent attackers from being able to brute force a hash function.

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#5127
  1. A hash functions provides a unique output for each unique input, and it’s almost impossible to know the input given the output.
  2. It’s used for mining and each block has the hash of the previous block.
  3. If it is hard to find two inputs that hash to the same output; that is, two inputs a and b where a ≠ b but H ( a ) = H ( b ). When more difficult is to find it, more secure it is.
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#5128

A hash function is a mathematical equation that takes input data of any form or size, and returns output data in the form a unique fixed size alphanumeric string. Changing just a small part of the input for a hash function results in a completely different output. These functions are “one-way,” they cannot be reversed to calculate the input data. Hash functions must be deterministic, meaning that the same input data always results in the same hash.

In Bitcoin, hash functions are used to write new transactions into the blockchain through the mining process. Bitcoin mining uses the hashcash proof of work function which acts as a vote in the blockchain evolution and validate the blockchain transactions. In order to successfully mine a block, miners try to combine all of the inputs with their own random piece of input data in such a way that the resulting hash starts with an x-amount of zeroes. Varying the block’s header is trial and error and the chances of success is very low. Often times you will get a value above the target which is a 256-bit alphanumeric code which all bitcoin clients share. The software will will increment a nonce which involves changing the hash and trying again. To mine the block and receive the reward you must get it equal or less than the target. The lower the target value the harder the it is to generate the new block. This process requires a high level of computational capacity hence, Proof-of-Work.

Any hash function with more inputs than outputs will necessarily have “collisions.” No two inputs should result in the same output. The harder they are to find, the more cryptographically secure the hash function is.

" Given an input m 1, it should be difficult to find a different input m 2 such that hash( m 1) = hash( m 2). "

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#5129
  1. one-way function: every input provides - unique digital fingerprint output
  2. a hash function in Bitcoin is used to hash transactions in each block. Since each transaction has a unique output the blockchain now becomes very secure.
  3. hard to find two inputs that hash to the same output
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#5130

  1. Hash functions are functions that turn any-size of information and turn it into fixed-size values.

  2. They are used to hash transactions in the blockchain. In bitcoin, the current block contains hashes of previous blocks, which are used to validate the current block. You need to brute-force your way to achieve the F(X) value to solve said hash.

  3. It means that we cannot have two inputs that produce the same output. In theory, this can happen, but it’s considered unfeasible, for it would take so much time that the heat death of the universe would happen before that actually happens. Probably.

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#5131

  1. Hash functions are uni-directional in nature, which means that you can use the input to obtain an output but the reversed is extremely difficult almost impossible to compute.

  2. Hash functions are used in cryptocurrencies like bitcoin by assigning each wallet and transaction with a unique hash such that it can’t be replicated or mutable.

  3. A hash function has to be collision-resistant such that there is a very minuscule chance where two of the same input can produce the same output hash.

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#5132

A hash function takes characters and uses algorithms to map and encrypt the data, with only the intended recipient able to decrypt. It is one directional meaning the encryption cannot be deciphered and returned with its original input
Has functions can be used in cryptocurrencies to develop and action smart contracts. It is used for security and to easily identify transactions within the blockchain
Collision resistant refers to the difficulty and therefore extreme unlikelihood that where two inputs would hash and give the same output

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#5133

  1. A linear function that uses an input of words, letters, or symbols to create an output that is unique to that input in an alphanumeric form.

  2. Hash functions are used in the mining process to guess the nonce.

  3. For every input there is a unique output and no duplicates.

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#5134

  1. Describe hash functions with your own words
    Hash functions are inputs that have there one unique output, and you can not go from output to input

  2. How are hash functions used in cryptocurrencies like bitcoin?
    They are used as a way to be unbreakable, so even if you try to guess what the input is, it is next to impossible. and it’s not worth trying

3.What does it mean when we say that hash functions need to be collision resistant?
It means that is hard to have the same output, for diferents inputs

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#5135

  1. A hash is a one-way, irreversible function that maps unique inputs onto unique outputs.

  2. Bitcoin miners run hash functions on the headers of a potential block in order to attempt to find a specific value that can be added to the header such that the hash it produces begins with a certain number of zeros.

  3. A collision occurs when two distinct inputs to a has function produce the same output. This should be extremely difficult.

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#5136

1: Describe hash functions with your own words
A hash function is a one way cryptographic function that generates a fixed number of unique bits for each and every unique byte buffer of any size. SHA-256 generates a 256 fixed number of unique bits for any buffer of any size. A change to the input buffer, no matter how slight, will completely change 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).
In the bitcoin block chain, a series of transactions cannot be tampered with because of the use of hash functions. Each transaction has the owner’s public key and the contents of the last transaction hashed as one buffer of data using SHA-256. This shows how each transaction acts as a confirmation to the previous. Should one transaction be altered in whichever means possible, the following transaction’s hashsum would not match up as the contents would have changed; exposing the error. To rectify the error, one would have to traverse the block chain from that point, re hashing each and every transaction with the previous transaction and current owner’s public key until the end of the chain. That would be a massive waste of computing (financial) resources and therefore makes it impractical to follow through.

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).
A unique input needs to produce a unique output. If two unique inputs, which ever two, produce a common output, then this would mean a collision happened. This would not be good for the block chain because if an attack is known such that an alteration to a transaction is made in such a way that a collision is preempted, then the attacker would not need to re-generate the hash on each of the subsequent transactions. Hence collision resistance is really something that one cannot avoid in the use of crypto currencies!

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#5137
  • Describe hash functions with your own words

A hash is a function that you can give an input that creates a unique outpout, digital fingerprint. When the input is changed the fingerprint changes completly. There is no way to go back from output to input.

  • 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 hash functoin is ued to pass transaction information anonymously across the blockchain. The data gets ‘hashed’in other words the ‘block’ gets hashed. A block of unconfirmed transactions is fed to a hsah function and this creates a hash.

  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).

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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#5138

Describe hash functions with your own words

Hash functions receive particular numbers as inputs, and, with exact mathematical actions, change these numbers to new numbers, which are output. An output result of a hash function actions is called a “hash”. In computer technology, hash outputs are often shorter than the original input. Also, they often have a fixed amount of characters which represent the hash number. Hashes are often used for indexes and for search functions in databases. The shorter length of the hash makes it easier to find it in a database. For example, a large text file, with very many bits, can be converted into a hash which is smaller. This hash can then be used to find the original text file in a database. Because the smaller hash is used instead of the larger original file, search requirements in the database are decreased.

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).

This answer is based on an article on thesslstore.com website. Crypto transactions are verified by multiple nodes on a network. Once verified, each transaction is added to a block that gets hashed. Blocks are groups of transaction records, and each one is unique. Each block has a hash, which both uniquely identifies it and shows where it is in the blockchain. The hash also ensures the correctness of the data to show that it hasn’t been modified since it was recorded in the block. This is because a change in the original input item will cause a change in the hash output. With the SHA256 hash function, even a slight change, like deleting a space between 2 words in a text file, gives a very different hash output. Also, blockchains are databases, and hashes can be used to find records in a database.

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)

Hash functions can sometimes make a hash output which is the same as an earlier one. When this happens, it is called a collision. In computer systems, hash functions can have the role of providing unique outputs. A hash function is not supposed to make the same hash for 2 items, since each hash should be unique. A collision resistant algorithm make this situation less likely.

#5139

  1. Hash functions are a one way mathematical equation. If you put in sth you get an output with digits and letters. These ones are a derivtion of many numbers and letters.

  2. By creating public and private keys and doing transactions.

  3. Becasue every input has exactly one output. Its not possble to have two inputs for one output or the other way round.

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#5140

1 - oneway function with fixed length output. Output is unique helpful in data integrity checks.

2 - Data from all previous blocks will be hashed into current block making it impossible to tamper with

3 - No two outputs of hash will be similar

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