Modern cryptography has got extremely complex and is a fundamental part of the internet. Whenever we go on a website we are using cryptography and whenever we send an email we are using cryptography. The technology has been developed and has existed for some time but it took the genius of Satoshi Nakomoto to bring them together - just like a car bringing wheels and Carnot engines together.
Bitcoin was created by taking a number of advances from across the field of cryptography and computer science and combining them - proof of work and a a variety of other techniques.
One of the most important bits of Bitcoin comes from a part of cryptography to do with elliptic curves and digital signatures.
What is Elliptic Curve Cryptography?
How do digital signatures in Bitcoin work?
This is where you get your address from which comes from your public key which in turn comes from your private key. You can make a public key from a private key but you cant generate a private key from a public key. These are the secrets behind bitcoin that make it the cash part.
The inability to double spend comes from the blockchain and decentralised nodes verifying transactions and only allowing one transaction to be spent once.
And this is how you have money that exists on the internet and in the figments of our imaginations!
Digital money is always a cryptocurrency but bitcoin is a decentralised crypto currency. There will be other forms of digital money issued by corporations, games or nation states and these will most likely be centralised crypto currency - where the nation or company is verifying the transactions.
This is one of the problems with bitcoin in that it uses a proof of work amongst all its participants to confirm transactions and ledger history - this can be quite expensive and wasteful with energy... but there are solutions that come in the form of Proof of Stake.
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