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I want to create a website where my users can register and login but not using any kind of database. I want to use public/private key. Let's take https://www.myetherwallet.com/. It says that It doesn't store keys for me. so where are they? when I want to login on that website and type private key, how does it make me login at all?
Main question is: How do I do the same principle by using php and website that myetherwallet.com has right now?
Neither MyEtherWallet or MyCrypto store your wallets, anywhere. You own your wallets. Every time you access your wallet via either services, it's being done locally, in your browser. You can even access your wallets offline, without having a connection to the internet!
Your private key, keystore file or hardware wallet derive your public key, which derives your address. MyEtherWallet or MyCrypto never touch your funds, the logic for accessing your wallet is all in the local interface. The only time either services come into play is when you want to retrieve the balance of the account, or send a signed (locally signed!) transaction. Both of these actions can be done without using MyEtherWallet or MyCrypto, by e.g. running your own node or using Etherscan.
Aloha : )
I am not entirely sure for php, but I did the same scenario in Node.js:
You should download web3 library ( https://www.npmjs.com/package/web3 ) [take a look]. When you successfully import it, you could start experimenting, and my warm recommendation is to start from and rely on documentation! :)
https://web3js.readthedocs.io/en/1.0/web3-eth-accounts.html#create
When you create the keys, they'll be returned to you ( in a form of callback ), so afterwards you should decide what to do with them.
Answer to your main question is - It's impossible without some kind of 'database' ( even if it is just a file on hard drive or something ), because you need to verify that given private key exists in order to let user in.
Last piece of recommendation: When you realize that it is impossible to go by w/o some kind of database, at least think of security concerns.
I hope I helped, at least a bit.
All the best! :)
I would answer you in a comment, but it's to long ( sorry in advance ).
Well, they communicate all the time with Ethereum node ( you could do the same via aforementioned 'web3' library. Firstly they create wallet for you ( they call ethereum node via web3, and wait for response ), after that they return private key and UCT file to you. Afterwards, if you decide to 'login' to their website, they just send information you provided to them to communicate with ethereum node, and get information about your account, that are afterwards presented to you ( it's excatly the same as you've logged in/authenticated, except they don't save that info into their database, just communicating with node back and forth)
In the case of Etheruem Wallet, the private key is encrypted with a passphrase and stored locally in an extensionless keystore file (JSON format, but no extension) with some additional data.
The public key is generated from the private key, and then encrypted into a json (keystore) file with your passphrase and something called salt, which is a randomly generated value.
The public key can be derived from the private key but the reverse is not possible. One can not derive the private key from the public key. The passphrase is used to encrypt the private key. So with the help of the passphrase, one can derive private key and with the help of private key one can derive public key. Passphrase -> Private Key ->Public Key
This is an inherent feature of the asymmetric cryptographic algorithm.
According to an accepted answer of this question, ethereum uses Elliptic Curve Digital Signature Algorithm to generate the key pair. You will have to implement the same in PHP.
