As far as I understand, RSA keys are usually generated based on a (strong) random generator.
Instead, I want to create them based on a password.
Or rather on its hash, for example sha512(sha512(password+salt)+password+pepper)
(Actually, I'm mentioning RSA but any secure asymmetrical encryption would suffice, I just need public-private encryption)
Addition: I need this because I'm building some secure communication solution, that doesn't need to rely on the connection or even the server to be secure.
I'm encrypting all content with AES using random keys, and the keys are RSA-encrypted. The idea is Alice can RSA-encrypt her content (or actually, the AES-key for her content) with Bob's public key (therefore Bob's public key must be stored online).
Later, when Bob enters his password again, his browser can deterministically calculate his RSA private & public key on the spot, download the content from Alice, and decrypt it locally using his private key.
Looks like Cryptico can help you, when you feed your password as a seed for RNG.