I never understood how monero and zcash work and I don't know if they work that way, I highly doubt it.
Monero combines multiple
pearls of cryptography, i.e. zero knowledge proofs and blind signatures to achieve the privacy preserving properties it has.
There are a few easier to understand articles on how monero works on the internet.
You don't need to doubt anything, it is mathematically proven.
The new coin will be like bitcoin. People will provide their addresses to get paid. Miners will mine for the coinbase. What is the difference with bitcoin? Blockchain.
Blockchain right now is a bunch of files anyone can read. A public ledger that is readable to anyone.
Addresses do not exist on a technical level in bitcoin.
And the blockchain is what makes it final and tamper-proof.
How are you going to solve this if not with a tamper-proof form of storage (e.g. blockchain) ?
I propose a new way of cash that would make transactions invisible.
The sender, instead of sending the structure of a bitcoin transaction to all the nodes can now send it encrypted with elliptic curve cryptography.
The receiver will provide the public key to the sender. The sender will encrypt it and then share it to nodes.
Encrypted for the recipient?
How will it be verified? Who sees the amount? Who checks whether the amount sent is indeed the amount received?
Who makes sure that i am not sending 1 coin to an address which receives 2? Where do the checks take place?
Now comes the hard part. How exactly can someone confirm that he has a coin? I'm not fully sure about this, but I think that by signing and verifying.
Signing and verifying? Like a chain of signatures?
You could define a "coin" as a chain of signatures (e.g. signed transactions), and then.. you would basically have bitcoin again.
I'm stuck at here thought. I'm not 100% sure that a coin like that could work.
It won't.
You can not create a trustless and decentralized system which is
fully private or anonymous without advanced cryptography.
That's what zero knowledge proofs, blind signatures, etc.. are for.
You can not take the concept of bitcoin, change a few things without having any idea on how this can work (i.e. without having an idea on how "coins" and transactions are defined, verified, etc..) and expect to have a private/anonymous coin.
No offense here, but if you don't fully(!) understand how monero works, you'll never be able to create a concept for an anonymous coin.