Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#3959
  1. Hash functions are one-way functions. One unique input means one unique output. There is no possibility to recover input from output.
  2. In BTC the hash function is used when block is being hashed to write new transactions into the blockchain before each new transaction. This happens during the mining process.
  3. Collision resistance of hash functions – is a property of hash functions - when it is extremely hard to find two inputs that hash to the same output.
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#3960
  1. Describe hash functions with your own words

A hash function is a computational function which when given an input data of any size produces a unique output of fixed size which we can think of as a digital fingerprint of the input. It is a one way function meaning that the output (fingerprint) given cannot be used to calculate the input. Any small change to the input will result in a completely different output being given.

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

Hash functions are used in bitcoin to secure and update the network with all of the new transactions. In order to add a new block of data to the blockchain miners have to input this data plus data of their own into a hash function until an output which matches certain criteria (for example beginning with 3 0’s) is met. The miner who finds an appropriate input first receives bitcoin as payment. The rate at which a new block is added to the blockchain is roughly ten minutes and this ratio is maintained by making the problems harder or easier to solve on a roughly bi monthly basis.

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

Collision resistance is a property of a cryptographic hash function that is necessary if a hash function is to be considered to be unflawed. As a hash function can compute an input of any size into an output with a set size such as 126bit or 256bit naturally some inputs will have to produce the same output as the possible pool of inputs is larger than the pool of possible outputs. A hash function were it is very difficult to find two inputs that produce the same output is know as being collision resistant.

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#3961

1 Hash functions are a not reversable output fingerprint of a input data.

  1. The blockchain is a chain of hash functions. It is used to verify that no data has been altered in the former block.

3 Being collision resistant means that it is hard to reverse the output to the input. Its basically one way function.

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#3962

Hash functions give unique outputs to unique inputs. You can not solve them backward.

They are used to mine BTCs or confirm the transaction. Actually, they are the foundation of PoW.

Collision Resistance, it is computationally difficult to find two distinct numbers that gives the same output.

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#3963

  1. a hash functions are unidirectional inputs of any size that results in a mathematical algorithm of the same amount of digits.

  2. Hash functions are used in cryptocurrencies to avoid counterfeiting of transactions, creation of addresses, and mining: proof of work

  3. The property of a hash function that is computationally impossible to find two colliding inputs.

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#3964

  1. Hash functions are a unique fingerprint for any data input.

  2. Miners must solve a hash that inputs the transaction data to output a hash that starts meets a specific requirement.

  3. Collision resistant means that finding 2 inputs that hash to the same output of a hash function is extremely difficult.

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#3965

1.Hash functions rewrite the digital information into a hash. This information is irreversible and continuously linear
2. Block hashing algorithms are used to write recent transactions into the block chain. Bitcoin miners use a “proof of work” algorithm to solve the block resulting in a bitcoin.
3. Once a hash is produced the output is always completely different in it’s result. The difference is always exclusively from point A to point B. Every characteristic translates to something new, never the same. This is collision resistance.

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#3966

  1. Hash function is a function requiring an input that creates a unique output (digital fingerprint that changes if the input is changed) that cannot be reversed to determine the input/raw data.

  2. To write new transactions into the blockchain through the mining process that cannot be manipulated/changed to determine the input.

  3. It means we need to ensure that two different inputs being hashed aren’t creating the same output.

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#3967

  1. Describe hash functions with your own words
    Very complex, one-way functions taking any type and amount of data and turning it into an alphanumeric string of a certain size (64-, 128- or 256-bit, etc.)

  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).
    Being an irreversible scrambling function converting input information (many different kinds/lengths) to a unique pre-determined length of a bit string (digital fingerprint).

  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).
    No two input hashes should map to the same output hash.

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#3968

  1. hash functions produces unique output (digital fingerprint) from every unique input. It can only go from input to output but not the other way around.

  2. It is used in cryptocurrencies like bitcoin to “write new transactions into the blockchain through the mining process.”

  3. Hash functions need to be collision resistant to avoid having same output from two different inputs.

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#3969

  1. Hash functions are a one way function. You can go from input to output but you can never go from output to input

  2. hash functions in btc are part of the block hashing algorithm which is used to write new transaction into the blockchain using the mining process. the positives are also the speed time from the message input to the hash function output.

  3. hard to find two inputs identical. If collisions are easy to find, they allow an attacker to take an authentic digitally signed message, find a different message that produces the same digest (the collision), then substitute the fake message for the real one while keeping the same signature value. Someone trying to validate the signature won’t be able to tell the difference. This destroys the value of digital signatures.

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#3970

  1. A hash algorithm is used to facilitate the creation of a digital finger print. This is done through using an input in what ever special hashing algorithm decided on. Once the algo. is chosen and input entered the function is put to work and produces a unique alphanumeric output that can only be procured in one way. Meaning, the output can not be reversed to find what was originally used as an input.

  2. Hash functions are used in every bitcoin transaction. A users private key and message are the inputs of the hash, the output is then the public key. Then through the mining of a block, there is verification that the sender indeed has a public key, therefor also a private key.

  3. Collision resistance means the probability of having a hash output duplicated is extremely, extremely unlikely.

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#3971
  1. A hash function is a unique data input to create a certain data output.
  2. In crptocurrencies hash functions are part of the hash algorithm which write the transactions in a block through the mining process.
  3. that means that no 2 inputs will ever give the same output
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#3972

  1. Hash functions are computations of unique inputs into unique outputs. As the outputs are uniquely transformed from the input. Any slight change to input would complete change the output value. Also, the output value cannot be reversed back into input form.

  2. The miner has to generate a hash that is less than or equal to the target in order to get awarded with bitcoin. Also, the hashes are all begin with zeros (now at least 19 zeros).

  3. It means the function has to make it impossible to let two inputs be hashed to the same output. This goes with the security and finality aspects of blockchain.

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#3973

1. Describe hash functions with your own words.

A hash function is a unique identifier for any given input. It can that take plain text data and converts it into a unique ciphertext. Hash functions are secure and one small change in the original input translates into a different hash functions.

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

Hash functions are part of the SHA-256 which is used to write new transactions on the blockchain via mining. The SHA-256 transforms a given input into a 32-byte hash value consisting of alphanumeric strings.

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

Hash functions are collision resistant when it is nearly impossible for two inputs to hash to the same output.

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#3974

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

#3975

  1. It takes an input and give an output, however function cannot be reversed to take the output and get the input. Each output is unique.

  2. It’s used as part of the mining process, where miners have to solve a hashing problem. Combining all the inputs and getting an output that meets certain requirements.

  3. That it is hard to find two inputs that have the same hash output.

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#3976
  1. Hash functions provide a unique fixed length encrypted output for a unique data input of letters :abcd: and numbers :1234: .
  2. A hash function is using an algorithm and is essential to the BTC blockchain to be decentralized and therefore secure. Hashing gives more secure and adjustable method of retrieving data and checking the data-integrity in the network while transact to finally confirm :white_check_mark: the transaction in the blockchain or to reject :no_entry: the passage in the transaction of cryptocurrencies.
  3. One property of Hash functions is useless :put_litter_in_its_place: when two or more inputs map the same output and the collision is easy to be found. Therefore, hash functions need to be collision :free: / resistant where only one input obtains a unique output.
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#3977
  1. Basically a hash function cannot be reversed.
  2. It is used to generate verifiably “random” numbers which is then used to write new transactions into the blockchain through the mining process.
  3. You cannot have two ways to get to the same output.
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#3978
  1. A mathematical process that takes a string of letters and/or numbers and return another string of letters and/or numbers of a fixed length.
  2. Hash functions are used to write new transactions into the blockchain.
  3. Hash functions should provide an unique output for each different input.
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