Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#561

  1. Hash functions take an input to mathematically create a unique output. Changing one letter or number in the input drastically change the output.

  2. Hash function in Bitcoin is used to hash the transactions on the chain. Each transaction has it’s own unique output.

  3. Collision resistance means it is almost impossible to find two inputs that create the same output.

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#562
  1. A Hash function is a one-way function where a given input but is impossible to find the input even if the output is known. So going back isn’t possible.
    2.hash functions are part of the block hashing algorithm which is used to write new transactions into the blockchain through the mining process.
  2. Collision resistant means that it is very hard to find two inputs that generates the same output.
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#563

#1 - A hash function creates a digital fingerprint of a unique input

#2 - SHA256 is used to generate unique wallet- and block addresses

#3 - Collision resistant means, that there is no input hashed in the same way. The hashed output is always unique

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#564

Describe hash functions with your own words

Hash functions is a digital fingerprint, which also is a one way function

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 hash transaction data.

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 resistant means two objects don’t get the same hash value.

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#565

  1. A secure and relevant Hash function takes unique inputs and gives them a unique finger print based on the chosen algorithm, with no option to figure out the input itself through the output. Shall anyone figure out how to retrieve the input through the output string then this whole algorithm becomes insecure and irrelevant.

  2. In Bitcoin any transaction is treated as an input, and it runs through the hash function to get it’s unique transaction string.

  3. It means that the possibility of 2 different inputs having an identical output should be nearly nonexistent.

#566

  1. Hash functions are complex functions that cannot be “reversed” in an algebraic manner used in cryptography.

  2. Bitcoin and cryptocurrencies like bitcoin use ‘miners’ to solver, or ‘confirm’ transactions by decoding or solving the function.

  3. Since a hash has finite number of possibilities or combinations, it is slightly possible for 2 different values to share the same hash value. To be collision resistant means to reduce the likelihood of duplicating a hash value with 2 different inputs as greatly as possible.

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#567

1.Hash functions are mathematical formulars which creates a unique output for any given input.

2.Bitoin uses hash functions for the transactions. Each Transaction is taken as input and run trough a hashing algorithm.

3.Each input has his own unique output. You will never find 2 different inputs which have the same unique output. (mathematicaly its not impossible but very, very hard to find.)

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#568

  1. Hash functions are functions where you can only use an input to get an output and can’t use the output to figure out the input.

  2. They are used to encrypt the data stored in each block. So once the block has been mined the new block uses the hash output to start the new block so if anything in a previous block is changed the whole chain is broken. ( please correct me if I got his incorrect)

  3. Collision resistant means how resistant is the hashing algorithm from producing the same output twice.

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#569

  1. Hash functions are functions that give you a unique, unrelated output that is completely dissimilar from an input.

  2. Hash functions are used to reduce the size of and secure the list of transactions that take place on the bitcoin network. Hashing from block to block creates a secure blockchain that, when combined with decentralized mining, is nearly impossible to hack.

  3. This means that the function needs to create specifically unique outputs across all inputs. When two separate inputs create a singular output, it could create problems for any program that is utilizing the hashing function.

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#570
  1. Each unique input produces it’s own unique output.
  2. For bitcoin hash-functions are part of the block hashing algorithm which is used to write new transactions into the blockchain through the process of mining.
  3. A hash-function is collision resistant if it is basically infeasible to find 2 inputs that hash to the same output.
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#571
1. Describe hash functions with your own words

A hash function takes an input and transforms it in a deterministic way into a fixed length output. This transformation should be done in a way that makes it practically impossible to reverse the output back into the input, but producing the output should be fast.

2. How are hash functions used in cryptocurrencies like bitcoin?

One use of hash functions in crypto currencies is for public/private keys. The public key is derived from the private key via hashes and elliptic curve prime number space transforms.

If I remember the Mastering Bitcoin book correctly, hashes are also used in creating the signature by hashing the private key together with all the transaction data (from, to, value, UTXO, etc). Because this is done in a deterministic way, the signature can be verified mathematically. You can verify that the signature is related to the public key, that receiver and amount is related to the signature, etc. This is why a bad actor who’s taken over the BTC network can only double spend their own transactions- because they would need access to the private key for any given transaction in order to modify it with a valid signature.

3. What does it mean when we say that hash functions need to be collision resistant?

A Collision occurs when 2 unique inputs produce the same hash output. The hash function needs to designed such that the probability of this happening is extremely rare. Otherwise you cannot assume that if 2 hash outputs are equal then their inputs are equal and the function is largely useless for authentication.

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#572
  1. A hash function is a special method that receives an input and produces a unique fingerprint of the data as output. This method must be one way; so that you can never recreate the input from the output fingerprint.
  2. In Bitcoin the SHA-256 hashing function is used in a few places. Inside the block header block contains a hash pointer, which is a pointer to the previous block plus a hash of the the previous block’s data. The blockchain is organized in a merkle tree of hashed blocks all linked together.
  3. Collision resistant hashing means even the smallest change, 1 bit will result in a completely different output. Hence h(a) will ‘mostly[0.27%]’ never equal h(b), except if its your birthday and you meet someone with your exact birthday. Which is 0.27%. This actually happened to me once, no joke. March 4th, XXXX :slight_smile:
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#573
  1. Describe hash functions with your own words

A hash function takes any size input and converts it to a specific size output. The output value is unique for each unique input, or to be precise the output’s likelihood of being unique has a very high probability.

  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 ensure that all data within a specific block are correct, because each block has a hash ‘signature’ which will be different if even one bit of data within the block is changed.

  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).

This means that it is very difficult to find two inputs with a matching output. For a blockchain system to be secure, the amount of work required to randomly find these collisions (matching outputs) must be totally impractical.

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#574
  1. Hash functions are the transferring of information input through a SHA 256 code giving a unique output
    2.Each hash function in crypto currencies takes the transaction of digital money, date, time, amount and public key location, uses a SHA256 code to encrypt the information, giving all the information inputted a fixed length output and adds it to the blockchain showing the link to the previous block in the chain.
  2. Hash functions are not collision resistant but very rare, so difficult to find. As all inputs of large messages have a limited size output the output SHA256 code can collide but the number of output possibilities are also very large.
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#575
  1. The Hash function is a way of converting an input into a 256 bits long output and it is not reversible.
  2. To make the contents of the blocks unchangeable, each block is “sealed” with a hash calculated with the S.H.A. 256 which takes as argument all the data of the block, that is all the operations contained in it.
    In this case, the hash is performed by a control code: modifying even a single comma the content of a block that is known to conflict with its Hash thus highlighting the counterfeiting. In order for a counterfeit attempt to be successful, that is, accepted by the Bitcoin Protocol, the “attacker” must be able to modify 50% + 1 of the copies of the network’s Blockchain. The hash functions therefore make Bitcoin extremely secure from a possible hacker attack.
  3. Collision resistance is a property of the Hash functions. It indicates that for each input entered, it is very difficult for one output to be the same as the other. If I enter A and B (with A other than B), the chances that, with the Hash function, I get the same number are extremely low.
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#576

  1. A hash function is a function that uses an algorithm to output a unique string.

  2. Hash functions are used to solve a block, and write new transactions to the blockchain.

  3. When a hash function is collusion resistant it means that it is unlikely that two unique inputs would result in the same output.

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#577
  1. Describe hash functions with your own words
    You input data of any length in the hash function and it outputs a fixed length of data. If you only change a single bit of the input data the output is completely different. It is infeasible to deduce the input from 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).
    The hash function used is AES-256. The output is always 256 bits. It takes transactions and some additional data as input and outputs a fixed 256-bit length of data. To solve a block the hash should start with a specific amount of 0s. The number of 0s required depends on the computing power trying to solve this and is called difficulty. It should take about 10 minutes to find such a hash. The difficulty gets lower/higher when the computing power gets lower/higher.
  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 collision happens when different inputs result in the same output. No hashing function is completely collision free. If it takes too long to find a collision it is considered secure.
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#578

  1. Hash functions take an input, whether it be a file, a string of text, etc…; and create a mathematical snapshot of the input. If anything in the input is changed, then the hash function output completely changes. Also, generally, hash functions are one way, so the input can’t be deduced from the output.

  2. Hash functions are used in Bitcoin for many things, but one of the main uses is to maintain data integrity by hashing each block with the hash of the previous block, and so any changes made to any of the previous blocks is instantly detectable in the current block because the hash in the current block would also have to change.
    Also, it is used in mining, where the value of the hash of the block needs to be below a certain number, which is determined by the difficulty.

  3. Collision resistance is a desirable property of hash functions that says that for two distinct inputs the outputs will not be the same. If the outputs of two different inputs are the same, that means a collision has occurred.

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#579
  1. A hash function turns information into a string of characters giving that information/data a unique digital fingerprint.
  2. Hash functions are used to give a unique hash (digital fingerprint) to each block of data.
  3. Collision resistant is a term in cryptography that does not allow two different inputs to have the same output.
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#580
  1. One way function, no way to guess input given output
  2. Next block contains the hash of the previous block data
  3. It is virtually impossible to have two different strings that have the same hash function (it’s possible, but very highly unlikely, random sample of 2^128 will have 0.5 probability of two having the same hash).
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