The Two Most Interesting And Useful Academic Things I Have Learnt in my Academic Career: DL and ECC

The Two Most Interesting And Useful Academic Things I Have Learnt in my Academic Career: DL and ECC

We are all motivated and interested in lots of different things — and that’s a very good thing. It would be a boring world if everyone did the same thing. Often, too, it is so easy for a research to chase after the “new shiny thing”, and end up never really developing deep knowlege in anything — a jack of all trades, and a master of none.

Unlike many job roles, I do two main things: I teach and I research. An easy trap for an academic to fall into is that their teaching does not overlap with their research. This means that everything you learn from your research does not quite feed into your teaching, and vice-versa. For me, everything I learn in my research area helps me to become a better teacher. Every probing question I receive from our students helps me to answer in a different way, and to make sure that I completely understand the topic, too.

To specialise in an area which is highly relevant is a good thing — I think — and allows you to continually advance your knowledge. The key focus is then to make your topic accessible to those new to the area — and not to take the knowledge gained for granted.

And, so, this weekend, I laid out the key knowledge in the two areas that I find most interesting, and that has built a whole new world of privacy and trust: discrete logarithms (DL) and elliptic curve cryptography (ECC). I didn’t use a fancy PowerPoint slide deck or recorded a headshot of me talking — it was just a bit of A2 paper and some Sharpies.

So, first up, is the area that got me into cybersecurity, and which fixed the security of the Internet: Discrete Logarithms. When I first saw the magic of the Diffie-Hellman method and how powerful it was, I instantly wanted to learn more. And, so, discrete logs build new key exchange methods, along with competing with RSA for digital signing (DSA) and encryption (ElGamal). While RSA has taken over the encryption part, and elliptic curves took over in digital signing (ECDSA) and key exchange (ECDH), they are still often used in research papers to define formal proofs.

So, here are discrete logarithms:

But, the star for me is Elliptic Curve Cryptography (ECC). It was co-invented by Neal Koblitz and Victor Miller and scaled the discrete log method (g^x) into a multiplicative space (x.G). The DH (Diffie-Hellman) key exchange method became ECDH and DSA (Digital Signature Algorithm) became ECDSA, and with a tweak, we can also encrypt with ECIES. As with discrete logs, their mathematical beauty and simplicity can be countered by their sheer strength against attacks. So, here’s my favouriate topic:

And, so, will my learning end? No! Discrete logs, RSA and ECC will all be cracked by quantum computers, and (possibly) replaced by lattice methods … so there’s a whole new world of learning out there.

For you? Find the area that you want to learn, and dive in. Forget all the superficial learning, and learn something properly. Feed your brain!