Multi-party computation is a well known set of cryptographic solutions that enable to process secret data owned by several persons. It is the fastest provably secure technique for this purpose. By comparison with concurrent techniques, it is fast enough to train a model (unlike homomorphic encryption) and consists in direct interaction between data holders, without any trusted third party (unlike trusted enclaves). It has the additional feature that data owners keep the collective ownership of the model and of its usage (unlike homomorphic encryption, where any person holding the key can go away with the model)

Differential privacy is a set of techniques that enable to hide the individual data sources that contributed to train a model. For instance, any person in possession of a model describing customers will be unable to tell whether or not a specific customer was in the database that contributed to train it. It is the indispensable privacy enforcing gadget of secure computations.

When it comes to proving ownership of a secret model of or some secret data, you do not want to disclose it. Likewise, you may need to prove your friends that you provide properly formed data into their model, without showing the raw data. Finally you may want to prove to your friends that you did correct computations on their secret data, without exposing your secret computation recipe in detail. Zero knowledge proofs are a cryptographic technique that solves all these issues: it is the ultimate trust enforcer of secure computation