Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#3438
  1. one way function repeatable with same input only goes from input to output not the reverse.
  2. function is to write new transactions into the blockchain through the miners calculations.
  3. It means it is not impossible to have collisions as going from large data to smaller data may sometimes result in collisions and two seperate inputs with matching outputs.
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#3439
  1. Hash function is a one way function where for each unique input gives you a unique output. This cannot be reversed.
  2. Hash function is used to hash transaction data into the Bitcoin public ledger, and this cannot be altered.
  3. To be sure no two different inputs can hash the same output.
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#3440

  1. Describe hash functions with your own words
    A useable hash function is a complex mathematical operation that takes data input and encrypts it into a unique and unrepeatable output, which cannot be used to identify the input data and cannot be hacked or traced backwards.

  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 cryptocurrencies like bitcoin to encrypt blocks of transaction details and create a unique transaction identifier or ā€œhashā€ output for each block, which prevents double-spending and block-data manipulation, providing for unbreakable data integrity. Without ASH-256 and itā€™s perfect integrity, cryptocurrencies would not be a viable store of value.

  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).
    Hash functions need to be ā€œcollision resistantā€ in order to ensure two distinct or different inputs cannot create an identical hash output. This would render the hash function useless in terms of protecting the integrity of the blockchain inputs. For example, if ā€œAiā€ and ā€œBiā€ are both unique inputs unto themselves, and they both output an identical hash of ā€œCoā€, there has been a collision and the hash function is unusable, such as happened with the ASH-1 algorithm.

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#3441

Its SHA256 :slight_smile:

#3442
  1. A hash function changes any digital input into a unique base 16 code. If any part of the input is changed, the output of the function changes. It is not possible to reverse the process to obtain the input from the output code.
#3443

Opps, forgot to do 2 and 3ā€¦
2) In cryptocurrency, any transaction gets hashed to preserve the integrity of the transaction. That way if someone tries to change the transaction, the changed hash alerts the rest of the blockchain to the change and the attempted change is ignored.
3) A function is collision resistant when no two different input can produce the same hash code. A collision would be if x is not = to y but f(x) = f(y). Using SHA-256, collisions are not possible.

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#3444
  1. Describe hash functions with your own word

A hash function is a secure oneway algorithm that outputs data into alphanumeric form essentially providing a digital fingerprint for that data.

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

Hash functions are used to secure information within the bitcoin blockchain and provide a digital fingerprint for each transaction that has occurred on the blockchain.

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

This means that a hash function should not have the same output for 2 different inputs. This is ofcourse to avoid duplicate data

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#3445
  1. Describe hash functions with your own words
    A hash function has 2 properties: 1, any input has a unique output, and 2, it is not possible to know how to get from the output back to the input.

Really, if the output is confined to a certain number of digits, then every input cannot have a unique output. The SHA256 algorithm puts out a 64 digit hexadecimal number. That means there can only be 16^64 unique outputs. So if I get a computer and increment the numbers from 0 to 16^64 as inputs, at least one of those outputs must be repeated.

Here is a calculation for how many unique values can be expressed using base 10:
16^64 = (101.6)^64 = 10^641.664 ~ 10^641.15810^13 = **1.15810^77** possible unique outputs
I suppose that is practically infinite as far as most human endeavors are concerned.

  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).

The article we read says that the hash function is used in the proof of work algorithm. Miners try to get a new hash lower than a certain target number. Because of the nature of the hash function, this is essentially a process of random guessing. I understand how this causes mining rewards to be allocated randomly roughly in proportion to the computing power in the mining network, but I donā€™t understand yet how solving these hashes helps to maintain the bitcoin network.

  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).

Collision resistance means that it is hard to find cases where two inputs produce the same output. I guess this is the same topic as the one I wrote about in the first question about how SHA256 has a finite number of unique outputs.

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#3446
  1. Describe hash functions with your own words: Hash functions are one-way functions where you can know the output, but not the input. They cannot be reversed.
  2. How are hash functions used in cryptocurrencies like bitcoin? When bitcoin is mined, the miner uses their own unique piece of code to feed the function in an attempt to solve the proof of work algorithm in a way that the result begins with 18 zeros.
  3. What does it mean when we say that hash functions need to be collision resistant? It means that every output has one unique input. No two inputs can create an identical output. One unique input equals one unique output.
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#3447

  1. Hash functions are mathematical algorithms that map data of an arbitrary size and produce a fixed-size array. For each unique input, they generate a unique output. Furthermore, they are one-way functions, since the input cannot be decrypted from the output.

  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. It means that they should avoid generating the same output from different inputs.

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#3448

Hash functions are matematical equations that allow to have an unique output based on your input.

The Hash functions are part of the block hashing algorithm which is used to write new transactions into the blockchain through the mining process.

Collision-resistance is a property of cryptographic hash functions which means that a hash function H is collision-resistant if it is hard to find two imputs that have the same hash output.

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#3449

1 Hash function creates a fingerprint of the data you provide and cannot be decrypted. The hash isnā€™t the representation of the data.
2. Transactions in bitcoin are hashed
3 The hash function produce always different hash for different input

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#3450

Describe hash functions with your own words

A hash function is code that will produce a unique output for every unique input. The same input will always create the same output. It is not possible to use the output to re-create the input. Hash functions are one way.

How are hash functions used in cryptocurrencies like bitcoin?

Bitcoin is one big hash factory. The power of the network is measured in Tetra Hash per second (TH/s) and the current value at blockchain.com is 144.3m. That aside, blockchains are essentially linked list of hashes that use hashes to verify hashes and it goes on and on.

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

Apparently it is possible for two inputs to produce nearly identical (fixed length) outputs, and this quality can be used (possibly) to guess the input. To prevent this, there are algorithmic techniques built into hash functions that are referred to ā€˜collision resistant propertiesā€™. There doesnā€™t seem to be universal agreement on this requirement.

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#3451

  1. Describe hash functions with your own words
    A hash function will take data and convert it into a fixed length string of alphanumerical data that is always the same for that same input. That output cannot be reversed to get the original input data, it is a unique digital fingerprint.

  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).
    Each transaction is ran through a hash function and when a new block is created the hash of the old block is added to that new block to create a new hash. So in order to change any block you would have to change every block prior to that one.

  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 is much more difficult for two inputs to give the same output, while that may still occur it is extremely rare.

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#3452
  1. Hash functions are functions that generate a unique fixed-length output for each unique input value. Reconstructing the input from the output should not be possible.
  2. In Bitcoin SHA-256 is used:
  • In the process of generating the shareable addresses while keeping the private key secret
  • To link the blocks of the chain, making tampering of previous blocks extremely hard.
  • In the mining puzzle: only the miner that finds the nonce that makes the hash value of the current block lower than the difficulty target, gets to mine that block and earns the reward in form of new BItcoins.
  1. Collision resistance means that it is infeasible to find two inputs that generate the same output.
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#3453
  1. Hash function is converting input to output that is looking like noreverseble today.
  2. A cryptographic hash function is an algorithm that takes an arbitrary amount of data inputā€”a credentialā€”and produces a fixed-size output of enciphered text called a hash value, or just ā€œ hash .ā€ That enciphered text can then be stored instead of the password itself, and later used to verify the user.
  3. Collision resistance is a property of cryptographic hash functions: 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 2^256 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 doesnā€™t mean that no collisions exist; simply that they are hard to find.

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#3454

SHA256 is not used to generate public keys, for that the Elliptic curve function is used. :slight_smile:

#3455

This is how hash functions are traditionally used. But how are they used in Bitcoin? :wink:

#3456

Thanks for your input AleÅ”! But SHA 256 is used to generate the Address from the Public Key, right?

#3457

lolā€¦ oops. Typo :slight_smile: