Introduction

For those that haven’t read my About page, my name is Ciaran Gallagher and I’m a 4^th year BSc(Hons) Ethical Hacking and Countermeasures student at the University of Abertay Dundee.

This blog is all about my honours project, and if you haven’t guessed it yet, it’s about Homomorphic Encryption. Homomorphic encryption, in a nutshell, is computer magic. It is an encryption method that allows the data to be manipulated by another program whilst still encrypted and then return the output, still encrypted. To anyone that knows anything about encryption, this is pretty magical. To those that don’t know anything about encryption, try this link. For a more detailed explanation, read on.

Now, I know I said I’d give a more detailed explanation, but I’m not. Not in this post anyway. If I was able to explain it in just one blog post then it wouldn’t be a very good research topic for an honours project. It’s going to take several posts, and even then you’ll probably need to re-read them a couple of times to fully understand it. Oh, and be prepared for a lot of maths. Firstly, though, you need to understand the limitations of Homomorphic Encryption, because there are a lot:

1. It is not efficient at all.
2. Only simple functions can be carried out (add, subtract, multiply).
3. The more complex the functions, and more output values, the computational time grows exponentially (don’t quote me, don’t know if it’s actually exponential, but it’s a lot).
4. There are more efficient cryptosystems, but these are only partially homomorphic and can lose some security.
5. It is an incomplete research topic.

I cannot stress the final point enough; homomorphic encryption is a very new topic and one that still has a long way to go (hence why I’ve chosen it). As it stands, fully homomorphic encryption is not meant to be very practical, but there is a lot of room for improvement.

So finally, why would I choose a topic that is complex, incomplete and has so many limitations? Well, that’s exactly the reason. An honours project should be challenging and I believe (given the research I have already undertaken) that this should make for a very challenging research area. The end aim of the project (from discussions with the dissertation supervisor) will hopefully be a working demonstration of a homomorphic encryption technique. Whether or not this will be a demonstration of a fully homomorphic system is currently unknown, but follow the blog and see.

It should be an interesting few months, so watch this space as I go deeper into the rabbit hole of homomorphic encryption.

- Ciaran

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