The ML example blog provides is amusing. It tends to make some people think that neural network can somehow "see" the patterns in encrypted data. Plain wrong.

The ML example blog provides is amusing. It tends to make some people think that neural network can somehow "see" the patterns in encrypted data. Plain wrong. What happens in reality is this: the neural network is encrypted and can only work on encrypted data producing only the encrypted results. The data can only be decrypted by the data owner who would not share his private key with anybody. That's it. In this way, the whole algorithm works in a so called encrypted domain. When used in this role, homomorphic encryption (HE) engine resembles a custom CPU. That CPU is not Turing-complete because it lacks conditional branching, but it is almost there providing two basic operations: addition and multiplication. This is enough for a lot of tasks. Does a CPU know a type of data or something special about them? Not at all. It executes primitive instructions of a program, one by one producing the output result from a set of inputs. The program P that HE "CPU" executes can be any program suitable for the given instruction set. Not only ML. It can be any other program! That's why homomorphic encryption is a very important technique in the area of cryptographic obfuscation. It allows to hide the data processed by a program P. And if that program P is a virtual machine (sometimes called Universal Circuit or UC) by itself, it would allow to hide the code as well, reaching the state of indistinguishability obfuscation. There are some practical problems along the way, but we are moving there. Yep, that sounds like magic, but it's based on a pure "boring" math with a few bright ideas here and there. What was thought as an impossible feat in the past, gradually becomes a reality. Isn't that the reason why Nobel is a no go for mathematicians? Otherwise, they would get plenty of Nobels (almost all of them, for sure).