Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#421
  1. A hash function takes any string of data and converts it into a hex number.
  2. In Bitcoin the Hash function hashes the previous transaction data with the current transaction data
  3. It means that there is no two inputs that result in the same output.
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#422

  1. A hashfunction takes an input and makes an output of a fixed length. The output is an unique digital fingerprint of the input.

  2. It is used to create the public key from the private key, the digital signature, to hash the block.

  3. A hash function is collision resistant if it is extremely hard to find two inputs that hash to the same output.

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#423
  1. Each unique input of any length gives us unique output of fixed lenth.
  2. Hash functions are used in mining Bitcoin
  3. It is hard to find 2 inputs that would produce the same output.
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#424

  1. A hash function receives a unique input and generates a unique output (fingerprint). It is important to note that one cannot obtain the input from the output.

  2. Hash functions are used in Bitcoin to validate blocks in the blockchain. If one block were to be tampered with, it would produce a completely different hash and be easily recognizable by the network.

  3. A collision in this context is the instance of two inputs generating the same output. No hash function is collision free, but finding a collision usually takes a long time.

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#425

  1. Hash functions are one-way functions that are deterministic, collision resistant, sensitive, quick, and puzzle-friendly. They are essentially impossilbe to reverse, and they allow for data integrity checks.

  2. They are used to perform data integrity checks on blocks of transactions. They also aid in the immutability of the blockchain.

  3. Different values should not have the same output (e.g., if H(A) = H(B) ==> A = B)

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#426

  1. a oneway computation of inputs that generates a unique digital fingerprint.

  2. A private keys corresponding public key is hashed several times over using a mixture of SHA-256 and RIMEMD-160 and BASE58CHECK encoding to generate a bitcoin address or wallet.

  3. Collision resistant means use of a hashing function needs to be extremely unlikely that any 2 users generating random addresses - generate the same address. More unlikely than continued non-existence of life on this planet.

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#427
  1. Has functions are algorithms that convert an input into a deterministic output.
  2. Bitcoin uses the SHA-256 algorithm to ensure the cryptocurrency transaction is valid and one-way.
  3. Collision resistant means that two unique hash functions cannot result in the same output.
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#428

  1. Each unique input provides an unique output. You can only go from input to output, not vice versa ( output to input )

  2. Hash functions provide data integrity checks. SHA256 is secure. Transactions are taken as input and run through a hashing algorithm which provides an output of a fixed length.

  3. Collision resistance is a property of cryptographic hash functions: a hash function H 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 = H, and a ≠ b. Every hash function with more inputs than outputs will necessarily have collisions.

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#429
  1. A one-way function that produces a unique fingerprint for every input.
  2. The bitcoin miners hash the transactions and nonce until they get the desired result.
  3. It means that two inputs shouldn’t have the same output.
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#430
  1. Describe hash functions with your own words.

Hash functions are mathematical values using text as a function. It helps with security in the transmission of information to a recipient. A mathematical formula created the hash function and is complex enough that it can’t be manipulated.

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

Hashing algorithms are used to mask a transaction. Inputs of any length are converted into outputs of a fixed length. These inputs and outputs are used as private keys, passwords, addresses.

  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).

Collision Resistance means that the hash input and output should not match or should not be equal. In the unlikely case they do match, they are considered equal, and this is why we use the word resistance instead of proof. It is most likely that two different hash inputs will not collide (having the same output), but the infinitesimally minute chance that this does occur is a possibly.

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#431
  1. A hash function is the process of inputting a data set and outputting a value that’s used as a kind of thumbprint/index of the input given.
  2. Hash functions are used in cryptocurrency as a way of validating/building on past transactions/blocks. These form the links in the blocks that are mined, hence “Block-chain”
  3. When we say hash functions need to be collision resistant we mean that we need it to be difficult for 2 inputs to output the same value.
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#432

  1. A hash function is a mathematical algorithm where each input creates an output.

  2. With Bitcoin a transaction is taken as input and runs through a (secured hashing algorithm) (EG) SHA-256 which gives an output of a fixed length.

  3. Cryptographic hash functions are designed to be collision resistant as it is very difficult to find two inputs that hash to the same output.

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#433
  1. hash function describes a function where from an input data one receives a unique output data or
    fingerprint.
  2. hash functions in cryptocurrencies are used in the mining process by miners to add strings to the
    public ledger and earn bitcoin.
  3. collision resistance means that there should be no different input data that produces the exact
    same output hash. However it is possible but very unlikely.
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#434
  1. Each unique input will always produce the same unique output. It is oneway function - you always go from input to output, but so far, you can’t go from output to input. (Unless you use MD5, and that is why MD5 is not being used anymore).
  2. By linking the blocks through hashes. By using the consensus mechanism.
  3. To be provided that two different inputs don’t have the same output.
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#435
  1. The hash function has unique fixed-sized output for every input. The direction they work is only input=>output, never the other way around.
  2. They are used 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. To be collision resistant means two different inputs not computing the same uotput.
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#436

Hash is a private combination of letters and binary to keep each individual function separate and identifiable

Hash can provide each transaction whether its assets, personal, currency or any application its own specific set code that can be traced back only to the person who holds that specific code

The collision-resistant means that even if there are 2 inputs to one output but it is much harder to find two of the same inputs and if there is then there are other protocols to ensure that the input is the right one

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#437

Describe hash functions with your own word

  1. A hash function is simply taking a string of data and converting them into an encrypted output.

How are hash functions used in cryptocurrencies like bitcoin?

  1. They are used for every transaction to chain the blocks together.

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

  1. If a hash function is not collision-resistant (there is no such thing as collision-free in [hash] functions because their output has a fixed length) then an adversary can break the function with little effort.
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#438

1 The hash function creates a unique row of letters and numbers. Input output. Same input - same output. The way back output to input do not work!

2 Output unique hashes for mining, transactions, provenance, consesus, etc

3 That the same output come together. Like the “Birthday effect”. Meeting a human with the same birthdate in a room of maybe 50 people.

#439
  1. The process in which data is converted into a string of text using SHA256 (Bitcoin)
  2. The miners are attempting to guess the random sequence of characters in order to produce the next block and obtain the mining reward
  3. Collision resistance meaning that it is very statistically improbable to guess the input of data from reading the output hash function
#440

  • Describe hash functions with your own words
    A Hash Function can be described as a function that takes any unique information and gives it a unique cryptographic finger print.

  • 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).
    A Hash function is used in Bitcoin by taking a data structure, finding the binary equivalent, sending that equivalent through the SHA256 function and expressing it in a Base 16 number. These hash functions are very important as every block is hashed, all transaction data on the block is hashed and the Nonce, which helps to verify if a block can be made is also hashed.

  • 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).
    All hash functions should be collision resistant, however it is currently infeasible to make any hash function 100% collision resistant. Eventually, because there is a limited amount of digits to use, a resulting output will have to ‘collide’ with a prior output that has the same digital result.

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