 Next up is Gadik, he's going to do an impersonation of Ian talking about money. Alright, so I have no idea if I look like Ian Ray. Ian Ray, no Ian Jeffrey. Ian Jeffrey, yeah. Ian Jeffrey. Anyway, here in Montreal we are very pleased. There's a new accelerator program called Thunder Fuel. They gave a smallish amount of money to young startups, and I have no idea what they arranged, but I think it's around 20k to 60k. I thought it was like 10,000 initially and then 5,000. Not more than that, but that's all you need to start a web startup, because you know, you can run lean. And the very exciting thing about it is that it's just a cross street in Nutman House. They give you some room to run your startup, and it's time right now to apply because, you know when they're... I think it's even July 1st or August 1st. Yeah, you have no more than a few weeks to submit, to pitch an idea and to be approved, but it doesn't mean that you shouldn't stay all night to find out a great idea and to pitch to these guys to get your share of the big loot. Thank you, Eric. Okay, so next up is a proper flash presentation, and it's Sebastian and Franco. They're going to be talking about cryptography with save. I'll put the mic both of them. Stay very close. I have a bar. Can people hear me? Thank you for the invitation. So, Eric invited us to give a small demonstration on using Sage to explore cryptography. So, first I'll start off with a reminder of Sage. Some of you may have been here for our one hour presentation. Sage is a free open source, Python-based mathematics software system, and the goal is to support research and teaching in various areas of mathematics, one of them being cryptography. Both Sage's development model and the technology in Sage itself are distinguished by its openness and community cooperation and collaboration. And the idea is that we are building the car and not reinventing the wheel. So, instead of reinventing pieces of software, we're taking existing open source software systems out there and merging them together. And the overall goal of Sage is to create a free, viable open source alternative to maple, mathematical, magma, and MATLAB. The website for Sage is SageMath.org, and I'll mention quickly two killer features of the software. One is Scython, so here you should think Python to C compiler. So, it's a super set of the Python programming language which allows you to declare data types and to use C data types in your code, and it gets compiled to C. This makes things run off faster. The second is the Sage notebook, which is an interface to your software. You can run Python examples, include images, and so on. And it's great for doing presentations, as you can see here. Great. So, let's do the first example. So, it's an easy example of the first crypto system we learned as cool. So, take the alphabet from A to Z, and represent them with the integer... Oh, I'm speaking French. We understand the 0 to 25 entities to represent the entities. So, all I want to share here is that we can do this process by coding a message and then decoding it with Sage. So, of course, it's mostly for the beginning of the assignment here, so we don't have to decode messages here. So, if I do this example, I start by transforming the Python-Montréal string into a string on the alphabet of 26 letters in a single line. So, I'm going to use the Shift-1 simply to make it easy to verify that it's not wrong. But I can use another value here. So, the people who write the message in the alphabet, the P is transformed into Q, so that's good. So, the rest should be okay. And then, to decode the message, you have to connect the key. So, the key is the Shift. So, the person who receives the message can decode this message in this way and then get it back and go back. So, it should be able to illustrate this crypto-card system. It's pretty simple. So, the second example I'm going to illustrate here is the Diffie-Hellman Key Exchange. So, here, what we want is the key, the number 1. It was the same key that was used to decode the message. So, when we want the two people to share this key, we're using a non-secure file. So, there's a way to make sure that we can establish this key without the other people searching it. So, this is the system here that can be used to establish a key. So, here, I'm going to make an example. So, we don't have to consider the code. It allows us to display an Interact. It's very good. It allows us to illustrate the example. So, here, I can change the cursor, but I'm going to do it all at once. So, for example, let's say Bob agrees on two numbers, P and G, 109 and G equals 6. So, G is the base on which we're going to multiply. So, all that's chosen on their side is two explosions. So, for example, let's say we're going to choose the explosion, oh, it's 592. Bob is going to choose the explosion P equals 588. So, it's going to change the power of the base G with the explosion. And each of their sides can complete the power with their own explosion to obtain a key that's going to be common. So, in this case, it's 38. And then, they can start to exchange messages with these keys that they only know. And for more information... Oh, really? So, here, it's just to illustrate the Interact. So, I can choose... I can change the output here, which gives us the number of bits. So, here, we obtain a little more than 55 bits. Here, we obtain a key that's... A little more than half an hour. So, I finish by saying that there are two references here. So, these are people who have been using a lot of code in the sage, but who work in cryptography. So, the first one is Min, Val, Julienne. In addition, they made a thesis in education. So, the first example, they made a thesis. And the second one is more in research. So, he works on things that are more advanced. Thank you. Thank you.