Ouroboros

Ouroboros is a proof-of-stake and proof-of-security blockchain protocol developed by Aggelos Kiayias, Alexander Russel, Bernardo David, and Roman Oliynykov. The protocol begins in a "static stake" in which the leaders are assigned proportional blockchain slots based on their initial stake. once the initial stake of the leaders is set, each leader is assigned an effective stake which proportionally sets the protocols distribution during its execution.

The Ourobus blockchain protocol is proven to be secure against delayed adaptive corruptions. The protocol protects against delayed adaptive corruptions because block leaders are selected by weighting public keys and through using a sender anonymous broadcast channel provided by diffuse functionality that eliminates the delay between block user selections that are susceptible to delayed adaptive corruptions.

In March 2020 Cardano released published a research paper on their Ouroboros Hydra proof-of-stake (POS) algorithm. The Ouroborus Hydra algorithm can complete about 1000 transactions per second and each proof-of-stake pool hosts a head. The Cardano team made the following statement about the performance of Ouroborus Hydra:

If we have 1000 TPS and 1000 heads there could be a maximum theoretical performance rate of 1 million TPS. This would also allow fast finality like in traditional BFT protocols.