Equihash is used as a algorithm. This is a memory-oriented Proof-of-work. How much mining you can do is mostly determined by how much RAM you have, making it unlikely for everyone to build ASICs for mining in the foreseeable future.

Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARKs) is applied to make sure that all information (the sender, recipient, transaction volume) will be encrypted, making shielded transactions verified as valid under the network’s consensus rules.