Does Bitcoin encrypt transactions?

 *It is important to note that the core bitcoin network/ledger does not use any encryption. It is all hashing as explained here - https://www.narendranaidu.com/2022/05/ruminating-on-proof-of-work.html 

But each and every transaction is digitally signed by a user (or wallet). 

Hence a bitcoin network uses digital signatures and as we know a digital signature is nothing but an encrypted hash of the data. 

You can digitally sign any data in the following way (creating an encrypted hash of the data)

• Hash the data using SHA-256.
• Encrypt the generated hash using your private key. 
• Package this encrypted hash and your public key together. 

The public key is part of the digital signature, whereas the private key is securely stored in a digital wallet (never to be shared with anyone). 

In the bitcoin network, this digital signature is created using the Elliptic Curve Digital Signature Algorithm (ECDS). ECC encryption is not used! - Many folks get confused by this :)

Ruminating on Proof of Work

While I understood how bitcoin mining worked, there were still a few strings loose in my mind on why exactly was the 'Proof-of-Work' algorithm created that way? (i.e. finding a nonce that results in a hash lower than the target value)

The following video from Khan Academy gives an excellent understanding of PoW is very simple terms - https://www.khanacademy.org/economics-finance-domain/core-finance/money-and-banking/bitcoin/v/bitcoin-proof-of-work

Also the following snippets from Investopedia: https://www.investopedia.com/terms/n/nonce.asp would give a better idea on the challenge (finding the right nonce) that all bitcoin miners are trying to solve. 

"A nonce is an abbreviation for "number only used once," which, in the context of cryptocurrency mining, is a number added to a hashed—or encrypted—block in a blockchain that, when rehashed, meets the difficulty level restrictions. The nonce is the number that blockchain miners are solving for. When the solution is found, the blockchain miners are offered cryptocurrency in exchange.

A target hash is a numeric value that a hashed block header (which is used to identify individual blocks in a blockchain) must be less than or equal to in order for a new block to be awarded to a miner.

The Bitcoin network adjusts the difficulty of mining by raising or lowering the target hash in order to preserve an average 10-minute interval between new blocks.

The block header contains the block version number, a timestamp, the hash used in the previous block, the hash of the Merkle Root, the nonce, and the target hash. The block is generated by taking the hash of the block contents, adding a random string of numbers (the nonce), and hashing the block again.

Determining which string to use as the nonce requires a significant amount of trial-and-error, as it is a random string. A miner must guess a nonce, append it to the hash of the current header, rehash the value, and compare this to the target hash. If the resulting hash value meets the requirements (golden nonce), the miner has created a solution and is awarded the block.

It is highly unlikely that a miner will successfully guess the nonce on the first try, meaning that the miner may potentially test a large number of nonce options before getting it right. The greater the difficulty—a measure of how hard it is to create a hash that is less than the target—the longer it is likely to take to generate a solution."

Ultimately it is all about guessing a nonce and calculating the hash and comparing it. Hence the capacity of a bitcoin mining farm is calculated in terms of hash rate - i.e. number of hashes that can be computed per second. The term 'Bitcoin mining' is actually misleading as what the miners are actually doing is finding a hash that satisfies the challenge and this also validates the transactions in the block (and the block gets added to the chain). 

But as many miners jump on the bandwagon, there is lot of wastage of compute cycles and this is a controversial topic for many people.  

Numeric value of a hash

In the bitcoin network, miners have to compare the hash value during the 'Proof-of-Work' process.

The target hash value is stored in the header and is expressed as a 67-digit number. Miners must find a new hash of the transaction block  that is below the given target. 

To solve the hash puzzle, miners will try to calculate the hash of a block by adding a nonce to the block header repeatedly until the hash value yielded is less than the target.

But how is the value of the hash calculated? In the bitcoin network, the value of a hash is calculated as follows:

• Hashes are typically represented as a hexadecimal string. Convert the hexadecimal value to decimal value. 
• Get the base-2 log of the decimal value. 

This is the value that is compared against the target in the block header.