[sota_pop]

Is this whole concept essentially a fundamental misunderstanding of the difference between "encryption" and "encoding"? I don't mean to be pedantic and don't want to make assumptions due to my respect for the source, but I don't understand how you can meaningfully manipulate the data that has been _actually_ encrypted? Doesn't the ability to accurately manipulate it imply that you have some understanding of its underlying meaning? The article is light on algorithmic details:

> "...a mathematical transformation, sort of like the Fourier transform. It encrypts data using a quantum-computer-proof algorithm..."

I am assuming there is some deep learning at play here i.e. it is manipulating the data within the latent space. If this is true, then would the embedding process really be considered "encryption"? You could argue it is security through obscurity (in the sense that the latent space basis is arbitrary/learned), but it feels like two different things to me.

[subset]

(Disclaimer: I am not a cryptographer and this is a heavily simplified explanation). Homomorphic encryption is built on the foundation of 'hard problems' (e.g. the Learning with Errors Problem) - loosely, computational problems that are thought to be impossible to reverse without being in the possession of a secret key.

The crux of HE is that it provides a _homomorphism_: you map from the space of plaintext to the space of cipher texts, but the mapping preserves arithmetic properties such as addition and multiplication. To be clear - this means that the server can add and multiply the cipher texts, but the plaintext result of that operation is still irreversible without the private key. To the server, it looks like random noise.

I don't think it's helpful to think about this as connected to deep learning or embedding spaces. An excellent resource I'd recommend is Jeremy Kun's guide: https://www.jeremykun.com/2024/05/04/fhe-overview/