Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#2852

Hash functions: in your own words. Here we go :confused:
Specific systems of coding which enable information to be resumed into a set of finite numbers and/or letters:/
In bit coin hash functions are used to guarantee privacy and efficiency in running its system compressing information. Hash functions convert information without leaving trace of initial information added.
Collision resistant means the possibility for to hashes to match at almost null.

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#2853

  1. A hash function is a one-way function, meaning it is easy to calculate the output from the input but impossible to calculate the input from the output.

  2. The most prominent use of hash functions in Bitcoin occurs in the mining process. Each block contains the hash of the previous block in its header. This is how blocks are linked in the blockchain. Mining a new block means repeatedly hashing the block header of a candidate block while changing a random number (the nonce) until the hash results in a number that is lower than the difficulty target. Then you have a valid block that is propagated to the network. The more computer power (hashing power) you have the greater the chances are that you will find a hash within the target first and win the race and add the next block to the block chain.

  3. A collision means that two different inputs of a hash function generate the same output. This is undesirable since two different sets of data will have the same fingerprint. In a collision resistent hash function it is rare with such collisions.

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#2854

  1. Hash functions take a given input and ‘‘hash’’ (encrypt) it and give you a completely different output. Unlike normal functions, it is practically impossible to figure out the input based on an output when we have a hash function. (Exception is MD5 where vulnerabilities have been found because duplications or collisions are possible).

  2. Hash functions prevent the creation of new Bitcoins out of thin air, leaving the mining process the only possibility to create more of the coin. They also give the block it’s chain. So far I understood each block is chained to the previous one via this hashing function. So should anyone change any data, even a single digit, that would change the hash output entirely making the block invalid.

  3. Collision resistant means a hash function must not generate the same output based on two different inputs. That means that it has to be long enough.

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#2855

Describe hash functions with your own words
Hash functions are mathematical algorithms that produce a digital fingerprint for any data or file through a one-way input to output operation.

How are hash functions used in cryptocurrencies like bitcoin?
SHA-256, part of the SHA-2 standard designed by the NSA and published in 2001, is used for Bitcoin’s Proof of Work cryptographic algorithm and its wallet address generation.

What does it mean when we say that hash functions need to be collision resistant?
Collision resistant means preventing a situation in which two different inputs produce the same output. An example of a type of collision is the “Birthday Problem” which was featured in a previous reading assignment.

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#2856
  1. Describe hash functions with your own words

A hash function is a function that produces a unique output (hash) from an input. This input can be almost any digital content, which is translated into binary code and presented as a series of hexadecimal digits by a hashing algorithm. Another key feature of a hash function is the impossibility of reverse-engineering outputs to deduce inputs.

  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 in bitcoin’s block hashing algorithm, which miners use to write novel transactions into blocks. In mining the hash function’s inputs are unconfirmed transactions, which are transformed into hashes which can be recorded (e.g. in public or private ledgers).

  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).

We mean that there should be (practically) no chance of two identical outputs being produced by different inputs. Less secure hash functions such as MD5 produce a 32-character hash, which is much less collision resistant than e.g. SHA3-512, which presents 128 characters (as there are significantly more combinations, making it less likely a mathematical “birthday problem” could occur, resulting in duplication by chance). These safer algorithms producing longer hashes also protect against purposefully malicious and covert coding, e.g. matching the binary code of two documents (which would appear different in a document viewer).

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#2857

Homework Assignment: Hash Functions (Answer)

  1. Allows an input to produce a unique output every time.
  2. In the creation of Private keys and addresses.
  3. The more cryptographically secure the hash function is.
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#2858

1.input resulting in an output or a digital fingerprint that cant be reversed

2.sha 256 is used by a function in bitcoin called proof of work where new transactions are hashed and inserted into the block and require multiple conformations

  1. collision resistance, the possibility of 2 inputs producing the same output in a hash is technicly impossible
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#2859

  1. A Hash Function is a mathematical process capable of receiving any type and size of data and converting it into a string of numbers and letters. This string of numbers and letters is known as output and it is only possible to get to it if the exact same input with which it was created is placed.

  2. They are used to add transactions to the blockchain through the mining process.

  3. It means that it has to be difficult to find two inputs that give the same output, because otherwise it would be very easy to hack it.

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#2860

  1. Hash Functions are functions that take data like numbers or words for input and generate a unique output depending on the algorithm used. From the output however you can not reverse engineer the function to find the input

  2. Hash functions are used in cryptocurrencies like bitcoin to build each block. Bitcoin being a proof of work it uses hash functions as it’s work to mine each new coin

  3. When you say collision resistant you mean that it is almost impossible to have to different inputs have a matching output to each other

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#2861

Hash function are functions that when given an input produce a unique alphanumerical output " digital finger print" unique to this input. the same input will always produce the same hash but there is no way of calculating the raw input through the alphanumerical output.
2-by creating addresses , as well as, public and private keys
3- that it is impossible for two different inputs to produce the same output when put into a hash function

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#2862

Homework on Hash Functions - Questions

  1. Describe hash functions with your own words
  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).
  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).

1- Hash Functions are the digital fingerprint of an Input, since they produce a unique Output for any given Input.

2- Hash functions takes the transactions and turn them into a fixed 256 bits length, thus ensuring that a huge amount of data can be traced with that fixed number. Also, the hashing turns the date immutable and impossible to be tampered, since any change will change the hash.

3- Collison resistance is the difficulty grade by which given two Inputs, the Outputs may be equal. The higher the Collision Resistance, the more cryptographically secure the hash function is.

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#2863

  1. One way functions where the used input produces an output or digital fingerprint.

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

  3. Hash functions must be collision resistant otherwise it is easy to reproduce the same hash with 2 any 2 messages. If this can be done with ease then a hash collision is replicated and you could make it appear that someone had digitally signed a document that they did not sign, as an example.

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#2864
  1. Its a one-way hashing (digital signment) of data to a digital fingerprint. Can’t be reversed.
  2. For listing and signing all the transactions in a block.
  3. Difficulty of finding 2 inputs that give the same output.
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#2865
  1. one way function input > output
  2. for security - fingerprint for the data set.
  3. no 2 inputs can create the same output.
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#2866
  1. Hash functions is use unique input and code unique output with no way back
  2. Miners using it to code transaction and protecting network
  3. Cryptographic hash functions are usually designed to be collision resistant. hash function with more inputs than outputs will necessarily have such collisions ; the harder they are to find, the more cryptographically secure the hash function is.
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#2867
  1. Describe hash functions with your own words
  • The hash function is an algorithm that, when given an input gives you a unique output totally specific to that input. if anything, no matter how large or small, is different in the input, then you will get a totally different output. and the algorithm works unidirectionally, so you can only go from inputs to outputs, never from outputs to inputs.
  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).
  • I believe hash functions are used in Bitcoin in order to provide a digital fingerprint confirming a particular transaction occurred. so the specific transaction is the input and a unique output is given in the form of the hash. and you are unable to tell what specific transaction occurred between 2 parties because you can’t work from output to input.
  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).
    -the term collision resistant means that you can’t get the same output from 2 different inputs.
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#2868
  1. hash functions are one way functions that create a finger print or unique identifier. It can go from input to output but it cannot go from output to input
  2. public/private keys, wallet addresses
  3. It means you cannot get the same output with different inputs
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#2869
  1. Hash functions create a unique output for every input and make it computationally impossible to reverse said output. Essentially generating a digital fingerprint for an input.
  2. In cryptocurrencies like Bitcoin, the input for the particular hash function (SHA-256) is a combination of transactions grouped in blocks that will be pushed to the chain and previous, already hashed blocks. Such a design creates a strong link between all the blocks - a change of any data in a block would heavily alter the hash of it’s block and all the blocks that follow.
  3. Collision resistance is an important property of effective hash functions. The term means that it is very difficult to find two inputs that generate one hash output.
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#2870

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

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#2871
  1. Hash functions are one-way functions where each unique input gives a unique output. Due to the complexity of the function, it is not feasible to take outputs and find the original inputs.
  2. Hash functions are used in cryptocurrencies like bitcoin to act as proof of work in the consensus mechanism. Miners must use their computational power to solve increasingly difficult hash functions looking for an output answer that begins with many zeroes.
  3. Saying that hash functions need to be collision resistant refers to the security of the network. For a hash function to be collision resistant it must be difficult to find two inputs that result in the same output. If the hash function is not collision resistant, the security of the network could be compromised.
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