Homework on Hash Functions - Questions

Blockchain and Bitcoin 101
#3094

  1. Hash functions are a security help to check if binary files have been manipulated as it is impossible to trace back to the original source.

  2. Bitcoin’s blockchain uses hash algorithm characteristics to run its consensus mechanism.

  3. Collision Attack on a cryptographic hash tries to find two inputs producing the same hash value, i.e. a hash collision.

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#3095

Homework on Hash Functions - Questions

1. Describe hash functions with your own words
A hash function is a one way function. This means that each unique input creates a unique output. If the slightest thing is changed in the input it will create a totally different 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 cryptocurrencies like bitcoin are used for security purposes and constitute the backbone of crypto security. A hash function turns a random input of data into a string of bytes with a fixed length and structure. The hash of a transaction makes it easy to identify transactions on the blockchain.

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).
Hash functions need to be collision resistant in order to protect the function. If a hash function is not collision resistant it is easy for an attacker to find multiple messages which produce the same hash.

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#3096
  1. a hash function encrypt an input and results in a unique output and by changing anything in the input results in a different output. SHA-256 is a novel hash function computed with 32-bit words. They use different shift amounts and additive constants. The SHA-2 family of algorithms are patented in US patent 6829355. The United States has released the patent under a royalty-free license. Currently, the best public attacks break preimage resistance for 52 out of 64 rounds of SHA-256. For a hash function for which L is the number of bits in the message digest, finding a message that corresponds to a given message digest can always be done using a brute force search in 2 L evaluations. This is called a preimage attack and may or may not be practical depending on L and the particular computing environment. The second criterion, finding two different messages that produce the same message digest, known as a collision, requires on average only 2 L /2 evaluations using a birthday attack. Constructing a password that works for a given account requires a preimage attack, as well as access to the hash of the original password (typically in the shadow file) which may or may not be trivial. Reversing password encryption (e.g., to obtain a password to try against a user’s account elsewhere) is not made possible by the attacks. (However, even a secure password hash cannot prevent brute-force attacks on weak passwords. More info here https://en.wikipedia.org/wiki/SHA-2
  2. Several cryptocurrencies like Bitcoin use SHA-256 for verifying transactions and calculating proof of work or proof of stake. The rise of ASIC SHA-2 accelerator chips has led to the use of scrypt-based proof-of-work schemes. The next step is using quantum computing.
  3. Some of the applications that use cryptographic hashes, such as password storage, are only minimally affected by a collision attack.
    In cryptography, a collision attack on a cryptographic hash tries to find two inputs producing the same hash value, i.e. a hash collision. This is in contrast to a preimage attack where a specific target hash value is specified.
    There are roughly two types of collision attacks:

Collision attack
Find two different messages m1 and m2 such that hash(m1) = hash(m2) .

More generally:

Chosen-prefix collision attack

Given two different prefixes p1 and p2 , find two appendages m1 and m2 such that hash(p1 ∥ m1) = hash(p2 ∥ m2) , where ∥ denotes the concatenation operation.

SHA-3 ( Secure Hash Algorithm 3 ) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. The National Institute of Standards and Technology ( NIST ) is a physical sciences laboratory and a non-regulatory agency of the United States Department of Commerce.
SHA-3 is a subset of the broader cryptographic primitive family Keccak designed by Guido Bertoni, Joan Daemen, Michaël Peeters, and Gilles Van Assche, building upon RadioGatún. Keccak is based on a novel approach called sponge construction. Sponge construction is based on a wide random function or random permutation, and allows inputting (“absorbing” in sponge terminology) any amount of data, and outputting (“squeezing”) any amount of data, while acting as a pseudorandom function with regard to all previous inputs. This leads to great flexibility.

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#3097
  1. a hash function is a mathematical way of encrypting an input. the diffence with a normal function is that the hashfunction makes an encryption so the input can not be know with the output.
  2. hashfunction are used to encrypt a transaction
  3. it means that 2 inputs can not generate the same hash and/or output
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#3098

There are no keys involved. Hash functions just gives you an unique (scrambled but deterministic) fingerprint of a fixed lenght wich is practically impossible to reverse calculate the input from the output (hash)

#3099

  1. A hash function is when a unique input gives a unique output, this can act as a digital finger print.

  2. Hash functions are used to validate new transactions to the ledger.

  3. Collision resistance is when it is hard to find two inputs that create the same output.

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#3101

Thnx for the note. Indeed I have mixed up SHA and RSA.

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#3102

  1. A hash function can compute an output in a fixed size from any given input. It is not possible to conclude the input data from only the output data which makes it a function that only goes in one direction.

  2. Hash functions in cryptocurrencies are used for different reasons. A private key in the bitcoin blockchain is hashed to get the public key and from the public key the address. Also blocks are mined using a hash function. Mining requires all of the data that the block contains to be hashed together with a variable nonce (number only used once). The block hash has to be under a certain threshold so that it is deemed valid by all the other nodes.

  3. Collision resistant in cryptography means that it must be very difficult to get the same output from different inputs.

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#3103

A hash function is a computation for an input that creates an output. It is not possible to determine the input based on the output, so the hash is a digital fingerprint of the input.

Hash functions are used to encrypt data. The output can be generated / tested by applying the hash to the same data, but any difference in the input will create a completely different output hash.

A function is collision resistant if it is difficult to have 2 different inputs create the same output.

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#3104

  1. Hash functions are a way of converting any information including binary information into a unique digital fingerprint using a one way equation for only ONE output.

  2. To verify every transaction using computing power.

  3. Collision resistant meaning that you will only get one out put for each and every input. This will make sure 2 items do not get the same hash…EVER.

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#3105

-Hash functions are the output of characters generated by using an algorithm from any kind of data in order to verify the data is correct and has not been tampered/corrupted. If any part of that data has changed it will completely change the output (hash function) to something entirely different in this case.
-BTC miners use hash functions with the nonce, in order to essentially win the lottery by guessing the hash of the nonce.
-Hash functions are collision resistant when it is difficult to find 2 inputs that hash to the same output. That Is 2 inputs a and b such that H(a)=H(b). resistant does not mean that no collision exists simple it is just hard to find.

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#3106

Hash functions are a series of logical operations performed on data either existing in binary form or converted to binary form that produce an output that is binary (but can be converted to hexadecimal). Each binary input produces a unique output. And for a given output, it is statistically impossible to revere calculate in order to determine what the original input was. This prevents a person trying to determine what the initial input values are from being able to determine them by examining the outputs.

Hash functions convert sets of binary data into a unique (one output per input). These input/output sets are combined into a “block” and then the block is appended with (number or hexadecimal, wasn’t sure) that when converted to binary begins with a prescribed number of zeroes.
This appendage is determined by repeated attempts - and once determined and if the calculation is the first among all competitors, the block is added to the block chain and linked to the next block by starting that next block with the appendage from the predecessor. This links the blocks together mathematically and entire process allows for recording transactions or other data forms in statistically “impossible” ways to reverse or corrupt and creates and objective permanent record that can later be used for further transactions. The process is objective, permanent and transparent. Its used with bitcoin to allow for permanent, immutable recording of transactions of bitcoin.

Collision resistance calculates the probability that two separate inputs will produce the same output when hashed by a hash function. If that probability is high, the hash function has weak collision resistance. If it is miniscule, then the collision resistance is strong.

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#3107
  1. Functions are a one way process, no output can be turned back into the inputs.
  2. Hash functions in cryptos are used to hide transaction data from prying eyes and also to prevent fraud/phony duplicates.
  3. Collision resistant means the chances of two inputs having a single output is highly unlikely.
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#3108

  1. Describe hash functions with your own words
    its a unique one way function, where you insert a unique input to get a unique out put. it cannot be reversed.

  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).
    the hash function that bitcoin uses is SHA256, which produces a unique hash for whatever information is inputted. using 16 to 64 bit I think?

  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
    two different hash functions inputs cannot give you the same output.

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#3109
  1. Each unique input has a unique output.
  2. Miners have to solve complex functions in order to complete a block, the input to these functions are the new transactions that haven’t been confirmed.
  3. To be collision resistant is for it to be hard to find two inputs that produce the same output.
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#3110

  1. Hash function uses SHA-256 which is a input to output security method that takes 0-9 & letters abcdef and scrambles to represent a set of variable (output)

  2. Hash functions are used to write new transactions in the blockchain via mining they are linear and build upon each other previous block and so forth

  3. Because then the input to output will be broken. It should never be allowed to go from output to input then data could be manipulated

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#3111
  1. A hash function is a function that can take an input of different forms and sizes and generate a unique output with a consistent length that cannot be reversed.
  2. Transactions are hashed with previous transactions so that a chain of unique and secure data gets created and used in the next transaction. A small change in any part of the chain would result in a completely different hash.
  3. A hash function needs to be collision-resistant means that there cannot be two different inputs that generate the same output.
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#3112

Its 256 bit :slight_smile:

#3113

  1. A hash function produces a unique output for each unique input. It cannot be reversed: you cannot compute the input for a given output.

  2. Hashing is used to secure the transactions in a block chain. Each time a new transaction occurs, a hash is computed over the previous hash and the new transaction. This makes it impossible to change the history of such a chain of transactions.

  3. It should not be possible (or highly unlikely) that two different inputs create the same output.

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#3114

Hash functions can be considered a fingerprint for a value represented digitally. Hash functions take a digital sequence and apply a function in a way that creates another sequence of numbers (usually base 16).

Hash functions are used in bitcoin in the process of proof of work. Bitcoin uses a particular hash function that is applied to a random number created by a bitcoin miner. The resultant hash must be under a preestablished number in order for that miner to be awarded the bitcoin that is given to the miner that validates a block of transactions.

Collision resistant hash functions are ones that are very unlikely to produce the same output for two or more given inputs.

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