Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#1527

  1. Describe hash functions with your own words
    A hash function works by giving a string of data a unique fingerprint that can only give an output from a input but never the opposite while also very little chance of the same finger print twice.

  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).
    n 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. ā€¦ Itā€™s the need for this large amount of processing power that means new bitcoins get mined over a long period of time, not all at once.

  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 resistant basically means that its extreamly hard to have two inputs that have the same output.

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#1528
  1. The general principle of a hash function is to produce an output string of the specific length using an input of any length. In going so, any output must be certain in that it should produce consistent results if the same input value is used again. Other characteristics include pre-image resistance making it infeasible to determine the input value if the relevant output is known, and collision resistance which deals with the issues of security and any potential for breaking the code. Any algorithm also needs to be quick and sensitive to any, including the very minimal, changes, to the input.
  2. A blockchain is a linked list which has a number of blocks linked by hash pointers. A hash pointer is a variable containing an address and hashing data of the previous block. Each block also has a time stamp, merkle root and an arbitrary number called ā€˜nonceā€™. Any hash pointer is a variable, so the hash of the whole sequence of the blocks will change dramatically if there are even minimal changes to any of the blocks, meaning the system will reject any unauthorised entries being made to a copy of the distributed ledger.
  3. Collision resistance enhances the security of a hash function. The idea is that it should be infeasible to produce two identical hashes for different inputs, and so if it ever happens it is safe to assume that those two inputs were actually identical. In the context of bitcoin, if a collision occurs naturally, then the relevant block may not form part of the ledger, becoming an ā€˜orphanā€™ block. In practice it means nothing except for the fact that its creator does not get the remuneration that he would have been getting if the block was accepted to the ledger. Generally, a security breach may arise if it becomes too easy to artificially create the hash of a certain value as it may be used for breaking the code of the system.
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#1529

  1. It is a cryptographic deterministic function that takes an input and produces the same output for the exact same data that was used as input, it is fixed in size meaning that no matter the size of the input, the output of such hash function will be the same size always. It can be used as a digital fingerprint that is unique to a set of inputs.

  2. Hash functions are used to verify the integrity of blocks, in bitcoin, the pointer to last block is a cryptographic hash of the concatenation of some data from the previous block such as timestamp, nonce and so forth, this mechanism ensures that blocks have not been tampered with thus making it impossible to modify past data, this is what makes bitcoin immutable.

  3. Means that two inputs canā€™t have the same output

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#1530
  1. Hash function is a function which converts an input a value if any length) to an output (a value in a particular format an a fixed length).
  2. Hash function is used to write new transactions.
  3. Collision resistance means that it is unlikely (but not impossible) for two different inputs to result in the same hashes.
#1531

  1. A hash function is like a digital fingerprint. The input, no matter the length or form is generating an output of fixed length. Every input has its own output, different of all the others, exactly like the fingerprints in humans.

  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. It means that if we have two different inputs then is infeasible for their hashes to be equal.

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#1532

An even more significant use case is to cryptographically link the blocks in a chain :slight_smile:

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#1533

A hash function is the result of a unique input giving a unique output in which only the input can be given but not vice versa. A hash function is repeatable.

Hash functions are used in cryptocurrencies through linked list using hashed pointers. In bitcoin a Nonce is used to help randomize the hash in the headers.

When we say that hash functions need to be collision resistant, we mean unique. Unique in the sense that they are able to output such a unique hash that any brute-force attack or hash generated is not easily replicated or identified.

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#1534
  1. Describe hash functions with your own words

A hash function is a one way function to generate a unique output (fingerprint) with a fixed length.
Even the smallest change of the input generates a totally different output

  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).

In order for the bundled block to be added to the block chain, miners must find a hash that meets the difficulty. Each block contains a block header with the number of the block, the hash of the previous block, and a ā€œnonceā€ that contains a timestamp.

  1. 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).

It is practically impossible to find two different inputs that generate the same output

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#1535
  1. There are different hash functions such as SHA256 which is used for Bitcoin. A hash function is a function with two unique characteristics. First is that each input produces a unique output. Second is that it is not possible to find the input with a given output. The output always has a fixed length.
  2. In Bitcoin hash functions are used to write new transactions into the blockchain. In Bitcoin mining the for the functions are all the most recent, not confirmed transactions. (Additional inputs are timestamps and reference to the previous block). There are different rules which define if a new block is valid, such as the new hash must start with 18 zeros. The input must be changed as long until all rules are completed.
  3. That means it is hard to find two inputs with the same output.
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#1536
  1. hash functions are complex mathematical functions which take a string of data and convert it into a smaller, more compact version, sort of like a summary, abstract, tl;dr or a fingerprint if you want. the product is a hash string of finite length which is the same every time the original data string is pushed through the hash algorithm. if a miniscule change is made to the original data, the hashed value will change drastically.
  2. they are used for securing all incoming, outgoing data, used for signing transactions, verifying blocks on the bitcoin blockchain, etc. such algorithms prevent unwanted tampering with the data of currently mined blocks, previous blocks regardless of placement on the chain (a change in block ie 200 would have impact on all blocks after 200 as the hash value of the previous block is always included in the hash value of the next oneā€¦)
  3. it is hard to get 2 different inputs that would produce the same hash result value. if collision resistance is low, that would mean there are many ways to get the same results (for instance if the hash value consisted only of a string of length 2, with only numbers from 0-9). this kind of ā€˜securityā€™ hash can easily be tampered with. if collision resistance is high, it means that it would be highly unlikely to get the same result from 2 different input chains.
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#1537
  • Describe hash functions with your own words

Hash functions return a specific / unique output for each unique input, but are not reversible. Like this, it is possible to verify that a result (hash) y must be derived from input x, but input x cannot be calculated from the result y.

  • 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 to link one block (list of transactions) to the other in a unique way. The when verifying block n, the hash of block n-1 + current transaction list + nonce will be hashed to link to serve as input for block n+1.

  • 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).

This means that for each specific input the hash function has to return a unique output (fingerprint) of the input data. For two different input values, the hash function must never return the same result.

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#1538
  1. How are hash functions used in cryptocurrencies like bitcoin?

Hash functions are used to generate unique outputs using the transaction data as inputs. Bitcoin uses SHA-256, a 64 character string output hash is generated. The new hash becomes a reference for the next transaction data block.

  1. Describe a hash function in your own words.

A hash is a one way function that has several uses in blockchain and decentralized systems. All digital media, documents, ectara have strings of binary digits, ones and zeros. A hash function has this digital information and runs an algorithm to produce a fixed length and digital output known as a hash. The hash is normally smaller than the original input. Every time the digital information is put through the hash function, it produces the same hash, If any information is changed in the digital input, the hash is changed.

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

If a hash function is not collision-resistant, than an adversary can break the function with little effort.

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#1539

Hash functions are ways to encrypt data in a unique way. Sort of like creating a fingerprint of the input data. There is, however, no way to trace the input data knowing the output.

Hash functions are used in crypto currencies to record huge amounts of transactions into hash. That way, it is easier to remember just the particular hash instead of those transactions.

Hash functions need to be collision resistant, means that it needs to be almost impossible to find two different inputs which could produce the same hash.

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#1540

The purpose of hashing functions, like all cryptographic functions, is to securely transfer data from one person to another in a way that, if a third party acquires the data, it is useless and uninterpretable. Hashing functions are capable of taking an input of any sizeā€“for the word ā€œhelloā€ to a 100-page documentā€“and creating a fixed output of the same length.
In Bitcoin, hash functions like SHA-256, are used to secure transactions on the blockchain.

Simply put, a hash functionā€™s collision resistance is the extremely low probability of two inputs, say H(A) and H(B), producing the same output. Each hash is said to have ā€œits own fingerprint.ā€

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#1541

Describe hash functions with your own words

A hash function allows one input to correspond with one unique output, and it is infeasible to back track the input by using that output.

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).

To write new transactions onto the blockchain through the mining process.

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).

This means it is infeasible to hash two inputs into one same output.

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#1542

  1. Describe hash functions with your own words
    Each unique input always gives the same unique output. The output is always of a fixed length. It is a one way function - input will give the output, but the output will never give the input.

  2. How are hash functions used in cryptocurrencies like bitcoin?
    They create unique private and public keys and by converting large amounts of transaction data into easy to store encrypted hashes in the ledger.

  3. What does it mean when we say that hash functions need to be collision resistant?
    Collision resistant means two different inputs should not give the same output hash.

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#1543
  1. Describe hash functions with your own words

I would describe a hash function as a secure representation of a string of characters demonstrated as a unique fingerprint in the form of a hexadecimal output or QR code. The security is the key characteristic of the hash due to the fact the original input cannot be determined by using the hashed output.

  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).

The Bitcoin blockchain by design, produces a new block on average every 10 mins depending on the difficulty adjustment. As the current block is solved by the miners via POW and a new block begins, a unique fingerprint via a hash function is used and linked to the new block providing authenticity to the new block. Should any of the parameters change or an attempt to corrupt or any data, you would change the previous hash input and cause a chain reaction going against network consensus thereby invalidating your corrupt block, which would be rejected by the authentic Bitcoin network.

  1. 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 was present in the article attached to prior homework and was explained very well via the ā€œBirthday Paradoxā€. This basically explained that at ramdom anyone would have a 365 to 1 chance of having the same birthday as yourself however, as a few more people enter the classroom the statistical probability drops dramatically to a 1 in 182 chance or (H)(a) = (H)(b) therefore halving the probability of two different inputs providing the same hashed output. This is possible In SHA-256 but is extremely un-lightly due to the number of possibilities this protocol provides.

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#1544

  1. Hash function process an input into a SHA256 for the case of bitcoin, the hash function output cannot be traced back to the input, this is the all point of the hash function.

  2. Hash function are used by miners to create and validate new blocks.

3.collision resistance is the fact of getting the 1 output for two different input. in the case of bitcoin, you want to avoid collision

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#1545

thank you for the correction

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#1546

A unique output for each input. Directional. Hash functions verify a data set has not been changed or as verification that blocks have been mined. Hashing is collision resistant in that the probability of two inputs yielding the same output is unlikely.

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