feat: Baseline FHE primitives (LWE, rLWE)

[0xJepsen]

We should prepare for an FHE boom and get some base FHE primitives down.

I watched this lecture a while back and thought it was pretty good.

LWE

[mrdaybird]

I was thinking of implementing this paper (https://eprint.iacr.org/2013/340.pdf). This scheme is conceptually simple to understand. I think it will be a good starting point.

[Autoparallel]

@mrdaybird I'd be happy to work with you on these too!

[mrdaybird]

@Autoparallel Awesome! Let's have a chat about it over the weekend.

[Autoparallel]

Sure thing! Feel free to ping me wherever you want. @Autoparallel on Telegram

[Autoparallel]

This resource seems pretty decent for LWE: https://65610.csail.mit.edu/2024/lec/l07-pke.pdf

[Autoparallel]

@mrdaybird I started on this a bit: #177

Want to join me?

[mrdaybird]

@Autoparallel missed your messages, apparently all my github message got moved to spam 😕

Want to join me?

Definitely, what would you like me to do?

This resource seems pretty decent for LWE: https://65610.csail.mit.edu/2024/lec/l07-pke.pdf

I will go through this resource in the meanwhile.

[mrdaybird]

Moving from a single bit to small messages would be interesting.
Also, it will be very interesting to think about how we will move from LWE encryption to a homomorphic encryption(maybe fully) scheme.

I will look into the latter.

[Autoparallel]

Yeah, I think the PR needs to change to allow encrypting larger payloads. I can look into this too.