 Our next speaker is Cecilia Boschini. She's a third year PhD student at the University of Lugano. And she is also from our Zurich labs. She has a passion for math and a knack for making super complicated topics easy to understand, such as lattice cryptography. So please welcome to the stage Cecilia. MUSIC Explain post-quantum cryptography based on lattices in five to seven minutes. I can do this. So let's start from a very unpopular opinion. To me, mathematics is fun. In elementary school, I was eager to do my math homework because it did not require boring learning by heart. I just had to understand the principles and I could answer any question. Oh, my math teacher created all sorts of fun problems for us to solve. I especially loved the adventures of this old troublesome lady in a motorized wheelchair called Missy Shaky Hands. Her adventures span from losing her groceries during a speed race on a wheelchair to running after the cat who ate one third of her cookies. And the only way to help Missy Shaky Hands out of troubles was to use my calculus abilities. So growing up, I figured that, well, while not all math teachers are fun, math is. So after five years of classical studies in high school, I decided it was time to have some real fun. And I started the Beachalows degree in math. So in math, once you learn the fundamentals, you can build all sorts of numerical spaces like polynomial rings. And the only limit is your imagination and the rules of logics. But what is most surprising is that all these spaces, as far from reality as they look, have the most unexpected applications in real life. Take number theory. Number theory studies the integer numbers like prime numbers and the properties. And this is exactly the kind of math that makes you wonder, how am I ever gonna use this? Well, with number theory, we can guarantee the security of all today's communications. I mean, how cool is that? Great, sounds awesome, you would say, but yeah, how does it actually work? So to understand it, let's take a step back and talk about cryptography. Simply put, cryptography is the science or somebody could even say the art of designing protocols to protect your data. When you send and receive data in a secure way over the internet, you're using what are called cryptographic schemes. For example, when you have to send your credit card number to buy an item from an online store, your card information is encrypted before sending it so that no one could read it and go on a shopping spree. And that's nice, right? Now, in the olden days, to securely encrypt a message, people would divide some very complex-looking algorithm and de-secure for the very good reason that, well, it looks very complicated. Now, luckily today we use a more scientific approach to guarantee the security of a crypto system like logging into your online banking account. We construct a mathematical security proof that is a convincing logical argument that says breaking the scheme and recovering your sensitive data is equivalent to solve some really, really difficult math problem. So as long as this problem is hard, the crypto system is secure and your data is safe. So how safe exactly? Well, the security of the systems that we use today is based on problems that would take ages to solve, even for someone that has access to the most powerful computer existing today. So from a theoretical point of view, I would say it's really safe. But now, what if someone could use a quantum computer? Well, I have good news and bad news, so let's start from the bad news. The problems on which the security of current cryptography is based are solvable with a quantum computer, but don't panic, there are many good news. In fact, to break these protocols, we would need a quantum computer with like thousands of qubits, and it took years for quantum computers to go from having one qubit to 50. Moreover, to make our data quantum secure again, it is enough to substitute the vulnerable problems with problems that are hard to solve for a quantum computer and obtaining what we call post-quantum cryptography. And that's easy, right? Now, we only need some quantum resistant mathematical problems, and we're done. So security is a very fast cops and robbers game. In the next five years, hackers will get smarter, and so will we. Hence, we need problems that can somehow grow with us, adapting to our future security needs while standing the test of time. And that's why we need lattices. So let me explain what a lattice is. No worries, I'll try to be simple. So you can imagine a two-dimensional lattice as a grid of points. Once you have this grid, a lattice problem requires you to find the points in the grid that is the closest to a fixed central point in the space called the origin. Now, in two dimensions, this is easy to solve. As you can just draw the grid of points and immediately see which one is the closest to the origin. But what about lattices in a larger number of dimensions, let's say a hundred? In this case, even visualizing a lattice is impossible. Moreover, there is no evidence that quantum computers could analyze as lattices better than today's fastest machine. And that is why we want to do post-quantum cryptography on those lattices. Now, we already have the quantum resistant versions of the basic protocols that our current internet infrastructure will need to be secure. And they're basically as efficient as the present ones. In fact, there is an ongoing process to standardize quantum resistant basic protocols by the national institutes of standards and technologies. What we and IBM are doing is getting ourselves and our partners ready for a full upgrade of the security infrastructures, creating more advanced protocols that are as secure and as invisible to the users as the present ones, keeping in mind the security of all kinds of users from the experts to all messy shaky hands. Thank you.