ZCash is a privacy driven cryptocurrency. It uses the Equihash as an algorithm, which is an asymmetric memory-hard Proof of Work algorithm based on the generalized birthday problem. It relies on high RAM requirements to bottleneck the generation of proofs and making ASIC development unfeasible.
ZCash uses zero-knowledge Succinct Non-interactive Arguments of Knowledge (zk-SNARKs) to ensure that all information (sender, receiver, amount) is encrypted, without the possibility of double-spending. The only information that is revealed regarding transactions is the time in which they take place.
ZEC Basic Information