Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#1487

Thanks for the tool boss, I really need to know this things in and out and develop some application for cryptocurrency for couple of project and a blockchain system for them too.Do you think I will be able to achieve this with the course and where should I concentrate on in terms of course to study, there are about 1253 lessons in all and I will like to know as much as I need to be successful.Please point me in the right direction Mauro.

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#1488

No problem. Keep learning the basics of the blockchain for now. After that, you can start to learn about programming in our Javascript course. Eventually, you will be moving to some blockchain programming. The knowledge from this course is essential. Keep up the great work. I see you are very passionate about learning. :muscle:

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#1489

  1. A hash function takes any input and make a 256 bit unique output. Same input sameboutput.

  2. In bitcoin the hash function is used to convert transactions.

  3. Its unlikely that two different inputs gives the same output.

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#1490

It does not have to be SHA256, it can be another hash function as well. They may have a different hash size. :smiley:

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#1491

Ok. Thanks
/michael

lør. 4. jul. 2020 23.36 skrev Mauro Fabijanić via Ivan on Tech Blockchain Academy Forum <[email protected]>:

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#1492
  • Describe hash functions with your own words
    A kind of secret equation which enables someone to input information and produce a unique set of output data which cannot be deduced to the original input as its’ encryption methodological engine is unbreakable
  • 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 sourced from a progression of data inputs in data structures from the inception of time for bitcoin and cryptocurrencies. Because the input will only produce one unique set of results over a period of time at certain time stamps. One can cryptographically duduce the authenticity and genuiness of the Hash.
  • 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 are collision resistant if two or more inputs cannot have the same output. This would defeat the purpose of cryptography as their would be no unique identifier.
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#1493

thanks for taking the time to reply@Mauro

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#1494

  1. Hash functions are like functions which has an input which you work out the output, but not able to construct the input from the output. Bitcoin uses SHA 256 to accomplish this

  2. Hash functions are used in bitcoin for building the blockchain data when hashing the previous block, with the data of the present block and nounce

  3. You don’t want two input providing the same hashed output

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#1495
  1. Hash function allows to to input data to receive unique hash output.

2.the hash function is used for the transaction. The data in the transaction is converted by using the hash function, the data can not be seen but the hash output can. (I think! :grimacing:)

  1. It means hash function can not have the same output from different inputs.
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#1496

I am not sure I understand. I see SHA256 is the encryption algorithm, but what I found about how it works is yet to be understood.

I do not understand the question, the property of prime numbers are well defined as any number p not divisible by any numbers but 1 and p.
You may obtain any positive integer by multiplying primes, the inverse is a bit harder. All positive integers can be written as a product of primes. We all know 3x3x11=99 this is fairly easy to go both ways. But how about 988027= ???. As I made this number I know it is 991x997=988027. It is easy to multiply, but hard to find factors.
This property of numbers and the modulus function are what I believe are two of the most important cornerstones in cryptography. but I am here to find out.

@Mauro Perhaps I read too much into the question, also omitting what I thought obvious? :thinking:

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#1497

Hash functions are a computer program that transforms any kind of data into a number of fixed lengh
Cryptotographic hash function transform any data or block of data into a digital signature which is the basis of the integrity of the bitcoin. Their basic properties are :
Transform the data into a signature rapidly and that any change in the data changes the hash value in an unpredictable way. Another important feature is that hash function are one way functions, which means that it is quasi impossible to recover the original input based on the hash value .They are also collision resistant which means that from two sets of data you can never get the same hash value.

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#1498
  1. A hash function is a (computationally fast) function that is on purpose made hard to invert; i.e. solving the equation: y=HASH (x) for a given y must be computationally hard.

A hash function always gives a “string” output of the same size (i.e. number of bits). Actually, a string can always be interpreted as an integer, so a hash function can be said to for example always give integers in an interval, for example 1…2^256.

  1. In the bitcoin blockchain each block is hashed and the hash is included in the next block. The hashing function is SHA256.

Also, when mining, miners try to solve the equation: SHA256( SHA256(block) | nonce) = y. Here nonce is the unknown number that they try to find and y is a hash that starts with a minimum number of zeroes. The number of zeroes is the difficulty level.

Also, bitcoin addresses are generated by a double-hash of the public key from the ECDSA key pair:
ADDRESS = RIPEMD160 ( SHA256 ( PUBLIC KEY ) )

  1. Being collision resistant means that it is computationally hard to find an X and a Y, where X is not equal to Y such that HASH (X) = HASH (Y). Note that it is easier to find a collision, than it is to find for a given H an X such that HASH(X) = H because you have 2 degrees of freedom (X,Y) instead of just one (X), but collisions are still hard to find for SHA256 for example.
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#1499
  1. Mathematical scramble eggs for a unique code.
  2. They are used for extra protection in public keys with SHA256 and RIPEMD-160.
  3. Collision resistant means two inputs NOT giving the same output.
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#1500

  • Describe hash functions with your own words
    A hash takes an input, applies an encryption to it then produces a fixed length result that is unique and with high variance based on each value of the input.

  • How are hash functions used in cryptocurrencies like bitcoin?
    A block hashing algorithm is used to enter transactions into the ledger of a block

  • What does it mean when we say that hash functions need to be collision resistant?
    In probability theory, the birthday paradox explains how collisions occur with relative high frequency. A collision means that a match has been found between an input and a hash. Therefore another order of complexity is needed to ensure sufficiently low probability of collision for the network.

Feel free to correct me if I am wrong here!

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#1501

They are used for many things :slight_smile: the transaction id is the transaction hash. But the most important one is to cryptographically link the blocks in a chain through PoW :slight_smile:

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#1502

Hash functions are mathematical functions that a computer calculates so we don’t have to do it by hand :slight_smile:

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#1503
  1. Describe hash functions with your own words

A function where an input string of text can be converted to a unique output. Knowing an output we are not able to go back to the 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).

Bitcoin uses the SHA256 hash to take the information from the previous block (maybe the nonce and address, not sure) and any txs that the miner cares to include up to the maximum allowable block size limit (based on the data size associated with each transaction not its bitcoin size) then the miner hashes this data and attempts to find a solution with the necessary number of zeros or greater number of zeros (smaller value output in hexidecimal) then transmits its solution to the network. The closer the miner is to the centre of hash the more likley they are to be accepted in the case where two equally valid answers are found at nearly the same time.

  • 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).

Very low chance that two different inputs with produce the same hash output.

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#1504

Hashing the public key doesn’t really make things more secure. The only reason this is done is to make the address a bit shorter (public key is 65 bytes and address is 20 bytes long) :slight_smile: one of the main reasons hashing is used is for making blocks cryptographically linked to each other in a chain

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#1505

  1. Hash functions take an input of data, such as the word “Hello” and convert that using the hash function into an output. The output is produced in the form of an alphanumeric sequence. The smaller change in the input, such as changing “Hello” to “hello” will give a completely unique sequence.

  2. Hash functions are used in bitcoin to hash transaction data. They are also used in crypto mining to create blocks. They use all of the transactions and use the hash function to create one hash for all transactions. Miners put together transactions and a nonce(this is just a random number) and they brute force the nonce until they get an output with a specific number of zeroes at the beginning of the hash.

  3. They need to be collision resistant for the security of the hash functions so that the same output will be almost impossible to guess from a different input from the original.

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#1506

Great job, it was awesome chatting with you about these answers :fire:

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