Cardano uses a new proof-of-stake algorithm called Ouroboros, which determines how individual nodes reach consensus on the network. The protocol was designed by a team led by OHK Chief Scientist Professor Aggelos Kiayias.
Ouroboros is the first proof of equity agreement that has been mathematically proven to have provable security, and is the first to pass peer review. It is the first proof to pass the peer review. This was when the leading encryption conference Crypto 2017 occurring.
Interactivity
The way Cardano plans to perform interactive operations is to implement side chains.
Sidechain as a concept has existed in the crypto circle for quite some time. The idea is simple; you have a parallel chain that runs with the main chain. The side chain will be connected to the main chain through a two-way hook.
Cardano will support the side chain based on Kiayias, Miller and Zindros (KMZ) research, involving "non-interactive proof of work."
According to Hoskinson, the concept of sidechain comes from two things:
Get a compressed version of the blockchain.
Create interoperability between chains.