Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#5442
  1. A hash function is a computation that generates a hash from a given input.
  2. Hash functions are used to generate the public keys derived from private keys. They are also used by miners to make calculations that require high computation in order to mine blocks.
  3. Hash functions need to be collision resistant so that two different inputs do not hash to the same output.
#5443

Hash functions change input data into 256 bit data (in case of SHA 256) output of always the same lenght, which is completely unique and cannot be reversed. It changes data into binary data and any single changed bit in the input will produce completely different hashed value (output)

In BTC hash functions are used to proof that previous blocks are valid, because every block contains hashed header of the previous block and so proving itā€™s authenticity.

ā€˜Collision resistantā€™ means that no 2 input hashes provide the same output hash.

#5444

  1. Hash functions are algorithms that take an input of any size and produce an output of a fixed size. They are used to create unique identifiers for data and to verify the integrity of data.

  2. Hash functions are used in cryptocurrencies like bitcoin to create a unique identifier for each transaction. This identifier is used to verify the integrity of the transaction and to prevent double spending.

  3. Collision resistance means that it is difficult to find two different inputs that produce the same output. This is important for hash functions because it ensures that the output is unique and can be used to verify the integrity of the data.

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#5445

  1. Describe hash functions with your own words
    Each unique input (Change comma in a text) gives a unique output.
    Itā€™s like a fingerprint output that only matches with the input.
    You can go from input to output but never revert it.
    A Hash Function is a one-way function.

  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).
    A block is added to the blockchain. This block contains all 2000 transactions, a header with the previous hash, the merkle root and a nounce (Difficulty). This complete block runs as input through the hash functions until the correct output is given. This is done by adding a number to the block and try and change that number until you receive the target hash. For example 30 zeros in the beginning.

  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).
    An input will always output a specific hash. As soon as you change any detail of the input, the output will be different. There are no 2 different inputs that produce the same output.

#5446

  1. Hash function are one-way cryptographic function that takes almost any kind of input (strings, numbers, even some larger files) and convert to a fixed-length sized alphanumeric output. Itā€™s supposed to be impossible that you may use the output to recover the input and itā€™s almost impossible that two different outputs produce the same input.

  2. Hash functions are used in cryptocurrencies such bitcoin in the process called ā€˜miningā€™. The following happens: The input for the hash function are the hash of the previous block, data related to the time and the unconfirmed transactions which are there to be inserted at the next block. In order to ā€œsolveā€ the block, miners have to get all this information with some data of their own (called nonce) and achieve a result, which is a specified hash that is exactly the solution (starts with ā€˜0xā€™ and has a lot of zeroes ahead of it).

  3. It means that itā€™s almost impossible that two different inputs would generate the same output.

#5447

  1. Describe hash functions with your own words ā†’ hash functions are particular functions that given an input give a unique output, that can be seen as a fingerprint for the original data. An important characteristic is that with these functions you can go from input to output but you canā€™t go back from output to input.

  2. How are hash functions used in cryptocurrencies like bitcoin? ā†’ hash functions are used for mining, to create digital signatures, to generate a unique address for each user, to create the public key of wallets. Most importantly, hash functions are used to check the integrity of the chain, if something is changed it becomes immediately known!

  3. What does it mean when we say that hash functions need to be collision resistant? ā†’ it means that it has to be impossible to find two different inputs that produce the same output. This is called a hash collision.

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#5448
  1. Hash functions are mathematical algorithms that take an input (or ā€œmessageā€) and return a fixed-size string of bytes, which is typically a ā€œdigestā€ that is unique to the unique values of the input. The output, or hash, is usually a one-way function, meaning that it is computationally infeasible to determine the original input value from the output hash. This makes hash functions ideal for verifying the integrity of data, as any change to the input will result in a different hash output.
  2. Hash functions are used in cryptocurrencies like Bitcoin to secure transactions and to maintain the integrity of the blockchain, which is a public ledger of all confirmed transactions. When a transaction is made, the details of the transaction are hashed and the hash is then added to the blockchain. The hash functions used in Bitcoin are called SHA-256 and are designed to be both fast and secure. They help ensure that the transaction information cannot be tampered with, as any attempt to alter the transaction details will result in a different hash value and will be easily detected.
  3. Collision resistance means that it is difficult to find two different inputs that produce the same hash output, or a ā€œcollisionā€. In other words, a collision-resistant hash function makes it infeasible for an attacker to create two different messages that produce the same hash. This is important in cryptography, as collisions can be used to subvert the integrity of data, for example by creating a fake message that has the same hash as a legitimate message, thereby making it appear to be authentic. Collision resistance is a desirable property for hash functions used in secure applications, such as digital signatures, as it helps prevent tampering or forgery of data.
#5449
  1. Describe hash functions with your own words

Each unique input will give unique output. Hash encrypts demand needed to secure the information of the blockchain. Receive any form and size of data including digits, letters or ledger media files. Standard 64-128-256 bits. If you feed bitcoin hash exactly that same data, it will produce same hash.

  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 higher the hash rate, more computing power like mining to solve algorithms problems on the blockchain to rewarded with bitcoin. Blocks are added following successful verification of the hash. Hash is the backbone to the blockchain network and keep it secure and controlled.

  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 needs to be certain length between zero and maximum 256 digit value

#5450
  1. Hash functions are algorithms that can take any size of data and return a fixed-size output. Theyā€™re used for data validation, authentication, encryption, and indexing.
  2. Bitcoin uses the SHA-256 hash function to create a digital signature for each transaction and secure the blockchain network.
  3. Collision-resistant hash functions make it difficult to find two different inputs that have the same hash value, which is important for the security of cryptographic systems. If hash functions are not collision-resistant, it becomes easier to carry out attacks
#5451
  1. Describe hash functions with your own words
    you cant go output to input and its work not the same like basic functions ist when you type something you get code with 16 leters and numbers toghether
  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).
    Cryptographic hash functions are widely used in cryptocurrencies to pass transaction information anonymously
  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).
    In cryptography, 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
#5452
  1. A hash function is method by which to securely send data and having digital proof that it did not change in transit.
  2. Bitcoin uses the SHA256 cryptographic hash function in its algorithm to ensure the integrity of each transaction on the bitcoin network. Hashing is a key component of block creation.
  3. Hash functions need to be collision resistant so that no two input will ever compute the same ouput.
#5453

  1. Describe hash functions with your own words
    Hash functions are one way functions where an output is generated from an input, but the input cannot be derived from 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).
    Hash functions in cryptocurrency are used to in mining to record transactions into a block, to create parameters for adding a new block, to receive a reward for doing so, and to provide security to the network.

  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).
    What we mean by collision resistance is that each input will produce the same unique output every time it is hashed with the same algorithm, and that the slightest alteration in input results in a different, unique output. In other words, there are no two inputs that result in the same output.

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#5454

Asymmetric hashing and encryption are two different types of cryptographic security that are used for sending messages and data. They both work with two distinct keys. The difference is in how the key is used to encrypt and decrypt data. Asymmetric hashing uses a public key to encrypt the data, and then a private key is used to decrypt the message. Both encryption methods have their own advantages and disadvantages. It is important to understand what each method does and how they are used. This will help you decide whether asymmetric hashing or encryption is right for your needs. You can check this blog for further differences Asymmetric Hashing Vs Encryption

#5455

Hash functions are mathematical functions that take in any input data and produce a fixed-size output. The output generated by the hash function is often referred to as a hash, digest, or checksum. The hash is a unique representation of the original input data, and even small changes in the input data can lead to significant changes in the hash output. Therefore, hash functions are used to verify the integrity of data, detect data tampering, and ensure that the same input data always generates the same hash output.

In cryptocurrencies like Bitcoin, hash functions are used to create a digital signature of each transaction that occurs on the blockchain network. A hash function is applied to the transaction data, and the resulting hash is added to a block. The hash of the previous block is also included in the new block, creating a chain of blocks that are cryptographically linked together. This chain of blocks is referred to as the blockchain, and it serves as a public ledger of all Bitcoin transactions.

When we say that hash functions need to be collision-resistant, we mean that it should be computationally infeasible to find two inputs that produce the same hash output. In other words, if two different inputs generate the same hash output, it is called a hash collision. Hash collisions are a problem because they can potentially allow an attacker to modify data in such a way that it has the same hash output as the original data, thereby bypassing the hash functionā€™s integrity check. Therefore, to ensure the security of cryptographic systems that rely on hash functions, it is essential that hash functions are collision-resistant.

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#5456
  1. A hash function is a one-way conversion of data. Essentially, an input creates a defined output, creating a unique digital fingerprint. 2. Bitcoin uses hash functions in the process of mining blocks on the blockchain and verifying transactions.
  2. Hash functions being collision-free ensure that no two inputs will ever reach the same output.
#5457

  1. A hash function like SHA256 is a one way conversion of a string to a fixed length output.

  2. Hash functions play a critical role in the functioning of the Bitcoin network. They are used in several key areas, including:
    A) Mining: Bitcoin miners use hash functions to solve complex mathematical problems that validate transactions and add new blocks to the blockchain. The mining process involves finding a hash value that meets a specific target, which is difficult to achieve but easy to verify. The first miner to find the correct hash is rewarded with newly minted Bitcoins and transaction fees.
    B) Transaction Verification: Each transaction in the Bitcoin network is represented by a unique hash value. When a transaction is sent, it is broadcast to the network, and each node verifies the transaction by checking its hash value against the previous blockā€™s hash value. This ensures that the transaction is legitimate and hasnā€™t been tampered with.
    C) Address Generation: Bitcoin addresses are derived from public keys using a hash function. This provides a simple way to generate a unique address for each transaction, which helps maintain privacy and security.
    D) Proof of Work: Hash functions are used in the Bitcoin networkā€™s proof-of-work consensus algorithm, which is used to validate transactions and add new blocks to the blockchain. The algorithm requires miners to solve a complex math problem that involves finding a hash value that meets a specific target.

  3. When we say that hash functions need to be collision resistant, we mean that it should be computationally infeasible to find two different input messages that produce the same hash value. In other words, a collision occurs when two distinct messages generate the same hash output.

If a hash function is not collision resistant, an attacker could potentially modify one of the messages and replace it with another message that has the same hash value. This could allow the attacker to deceive the system, bypass security measures, and compromise data integrity.

In the context of cryptocurrencies such as Bitcoin, collision resistance is critical for maintaining the security and trustworthiness of the blockchain. If a collision attack were possible on the hash function used for the blockchain, it could enable attackers to create fraudulent transactions, double-spend coins, and potentially undermine the entire system.

Therefore, it is essential that hash functions used in important applications, such as cryptocurrencies, are designed and tested to be collision-resistant to ensure the integrity of the system.

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#5458

  1. Describe hash functions with your own words
    Hash functions go in one way direction , An input give you a unique 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).

Within the Bitcoin ecosystem the function of the hash is very important as long as it is efficient, and for this to be the case, the hash must be complex, thus offering a high degree of security, which implies that more time is required for its calculation and the process is more inefficient.

  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).
    Because It must be computationally difficult to find a pair
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#5459

  1. Describe hash functions with your own words. Hash functions convert any length of unique inputs into unique fixed-length outputs. These outputs cannot be used to identify the inputs that generated them.

  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 are used in mining and generating public keys.

  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). Any particular output can only be generated using the same input, different inputs will always generate different outputs.

#5460

  1. Describe hash functions with your own words
    An algorithm that takes an input of any length or size and converts it into a fixed output called a hash.

  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).
    Mining, Verifying transactions on the blockchain, Securing the blockchain, and Protecting privacy

  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).

ā€œit should be difficult to find two different inputs that hash to the same output valueā€ Chat GPT

#5461

Homework on Hash Functions - Questions

  1. Describe hash functions with your own words

Explaining that I must say, hush functions are transformation input to output, witch are coded information. There is many ways how you can do it and some are not secure (one can get input from output) and some are considered secure, where there is no way to reverce output to input in reallity witch we are liveing.

  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).

Answer is security and integrity most of all.

  • Hashes are crucial in Bitcoin for ensuring security and integrity.
  • Hashes serve as unique identifiers for blocks and transactions.
  • The proof-of-work mining process relies on hashes to find valid solutions.
  • Merkle trees use hashes to efficiently verify transactions within a block.
  • Hashing is involved in the generation of Bitcoin addresses.
  • Hashes play a vital role in securing the blockchain and establishing consensus.
  • They verify transactions, protect privacy, and enable efficient data organization.
  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).

Hash funcitions are just nummbers at the end of the day, but its extremly unlikely, that there will be two generated (290a96bb5f666c62d345001 like this for example) codes with no difference. So in real life its not gonna happen, so we call that COLLISION RESISTANT feature.

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