Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#2191

  1. A hash function condenses a numeric value into a fixed size.

  2. Bitcoin uses the SHA-256 hash algorithm. Bitcoin uses the hash function to relay the transactions, pending transactions, time stamp, and block reference.

  3. Hash functions need to be collision resistant because it makes them more secure to non brute-force attacks. The more inputs that hash to the same output are prone to collision and are easier to reverse engineer.

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#2192

  1. Hash functions generate a string of data where a unique input produces a unique output containing alpha-numeric characters.

  2. Hash functions are used for Bitcoin in hashing algorithm which write new transactions into blockchain with the mining process.

  3. The hash functions canā€™t hash out two different inputs to the same output.

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#2193
  1. Hash functions gives each input its own unique identity
    2 . The transactions is placed into input that runs through the bitcoin algorithm that gives it its own identity
  2. Because every input has its own unique identity makes it almost impossible for two inputs to match with the same hash
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#2194
  1. Hash functions take information and creates a digital signature which can not be manipulated.
  2. Hash functions are used in the blockchain by miners to verify transactions to find the next block to mine.
  3. Collision resistant means itā€™s not mathematically impossible but implausible to get the same output from a different input.
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#2195

Hash functions are complex mathematical functions that convert a text string into a unique coded output that can not be reverse read. An entire manuscript could be hashed and will always give the same output as long as not a single thing is changed, letter, number, space etc.

blockchain hashes uses one-way hash functions like SHA-256 which are very difficult to break. This helps maintain the security of the chain. All sizes of input produce a 64 digit output that can not be reverse engineered back to the original statement.

Collision resistant means that each hash input creates a unique hash output and that it is extremely extremely unlikely that you will ever encounter the same hash output for different hash inputs.

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#2196
  1. A hash function is a function such that you can go from input to output, but not from output to input (one way function).
  2. Hash functions are used in mining.
  3. Itā€™s hard to find two inputs that produce the same output.
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#2197
  1. Describe hash functions with your own words

Hash function is basically a function that takes an input string of any length and produces a unique output of fixed length.

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

Hash functions are used in cryptocurrencies to secure the system, so that input transaction is hashed into a string of fixed length, thus creating an fast & efficient way of handling input data.

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

It means that there should be no same hashes for two different inputs.

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#2198

  1. Hash functions are calculations which convert a string of text to a hexidecimal representation of that text.

  2. Hash functions are used to confirm the underlying data is accurate, and also to show proof of work.

  3. There must be almost no chance of two different hashes matching the same input.

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#2199

1.a hash function is a one way function to get an output from an input without being able to get an input from the output
2Bitcoin is simply a digital ledger of hashes that utilizes proof of work combined with SHA-256 to obtain mathematical traceability and unbreakability.
3 hash funtions need to be difficult enough in order for two or more nodes not to get the same answer

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#2200
  1. Describe hash functions with your own words
    -A hash function creates a unique output for every unique input. The same input always results in the same hash function output (hash functions are deterministic). With a hash function (that works as intended) you can go from input to output but not from output to input. That is, there is no way to determine the input of the hash function given the output. A small change in the input to the hash function causes a large change to the output.
  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).
    -In bitcoin, each block is assigned a unique hash code based on both the previous block and the current block. That is, the two blocks are concatenated and then the hash function is executed. This creates a link between the current block and the previous block (thus the designation ā€œchainā€). There is no way for anyone to try to alter history on the blockchain because the hash has already been fixed. An attempt to alter history would be rejected by the network because it would result in a hash that is different than the existing hash on the blockchain. Each block is therefore permanently tied to all previous blocks.
  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).
    -Collision resistance means that it is hard to find two inputs that result in the same output.
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#2201
  • Describe hash functions with your own words
    A hash function takes any input and transforms it in 256bits in Blockchain case. It is not deterministic from the ouput 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). In Bitcoin, the miner compute the hash with a random word(nonce) concatenate with the information until the hash string is the requiered length of zero.
  • 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).
    The collision is the statistical possibility two different informations result in the same hash string after the function. So the reader is unable to know which information he is supposed to get from the hash string
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#2202

  1. A has function takes an input of data and produces an ouput from that data that is completely unique compared to any other input you enter no matter how small the change to the origional input.

  2. Within Bitcoin, Hash functions are used to hash the data within a given block, this data is combined with a random nonce and that string is then hashed once again to produce an output - that output is compared to the bitcoin difficulty target: if the output is below the target, the block is added to the blockchain - if not, the nonce is changed and the new string is hashed again in an attempt to solve the problem of finding a hash output that is bellow the difficulty target of the bitcoin network.

  3. Collision resistant means that no two data inputs should give the same output once hashed.

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#2203

Hash functions take an input and produce a unique output. Each new input in the function will have its own corresponding, unique output.

Each block on the chain has a partial known input and a hash target. Miners compute the rest of the input to match the hash target and are rewarded with bitcoin.

Since a hash function has a finite amount of outputs to turn infinite amounts of data into hashes, some of the output hashes can be identical. The harder it is to have two unique inputs become the same hashes the more secure the algorithm.

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#2204
  1. input string of data of any length and produces a unique output by converting it into 256 bits
  2. Bitcoin uses SHA265 to produce a unique output for every unique input and is a one-way function
  3. 2 different inputs should not receive the same output
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#2205

1: A hash function is a mathematical process that takes input data of any size, performs an operation on it, and returns output data of a fixed size.

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: 1. Collision resistant means that it is highly unlikely to get the same output from two diffrent inputs.

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#2206

  1. Describe hash functions with your own words
    An algorithm that always generates the same fixed number string of characters associated with that specific input. The function is oneway, meaning input > output, but never output > input.

  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 of a block is embedded into the next block to secure the sequence of blocks. If any content in a confirmed block, the hash value will change, therefore flag tampering has occurred.

  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).
    A hash collision is when two input values producing the exact same output hash value.

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#2207

This is the property of a hash function (or any mathematical function for that matter) that the input will always return the same output no matter on what part of the world, computer, programing language is used.
Collision resistance is the probability for a hash function to return the same output from two different inputs :slight_smile:

#2208

Correct, but can you give a practical example how is this used in Bitcoin? :slight_smile:

#2209

  1. the hash function is an input that is broken down into a special language.

  2. the hash function works by taking your signature from your private key, decodes it, and sends it to the other recipientā€™s public key.

  3. That means that it is very difficult to have same same array of digits twice.

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#2210

  1. Describe hash functions with your own words
    It is a mathematical function which when applied to an input produces a unique output in a fixed length string of characters. For Bitcoin this is SHA-256 which provides a 256 character hexadecimal string as the output.

  2. How are hash functions used in cryptocurrencies like bitcoin?
    The hashed outputs are building blocks for the blockchain and connect back to the preceding block and so on until the first Genisis Block.

  3. What does it mean when we say that hash functions need to be collision resistant?
    This is where a pair of inputs give the same output. Collision resistant means that this is very unlikely - but it can occur.

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