Yes! When a user signs up on Authereum, a new contract-based account is deployed. Each account contract requires keys to manage it, so when you signed up a new key pair was also generated on your browser client-side. This key is encrypted with a password derived key (PBKDF2). Keys are stored in browser local storage and the encrypted keystore is stored on Authereum so that you can login in different devices.
A more detailed explanation can be read in the Authereum Key Architecture Explained article.