Hey, this is Brett and this 2020 GMC Sierra 2500 Crew Cab Short Box 84 is stock number 13394Z. I am here at Summit Automotive in Fond du Lac, Wisconsin, near New and used heavy-duty truck headquarters. This 2020 GMC Sierra 2500 has the 6.6-liter Duramax diesel engine. It's the L5P engine, which puts out 445 horsepower. It's paired up with the Allison 10-speed automatic transmission. This truck has been fully-safetyed and inspected by our service shop, has a fresh oil and filter change. All the fluids have been checked and topped off, and this truck is 100% ready to go. I'm going to go all the way around in this video inside, underneath, start it up, take a look under the hood, and give you the most accurate representation of the vehicle that I can. In this video, Summit White is the color, and I shoot all my videos in 4K, so if you have HD capabilities, I recommend turning them on right now because it is your best way to check out the quality, condition options, and of course, cleanliness of the vehicle before seeing it in person.  I didn't see any major dents or dings on there. Looks really good. Front fender is in excellent shape as well. What's cool about these is these light up when the lights are on, and we'll actually turn all the lights on here in a little bit. If you like the video, you can subscribe to my YouTube channel, which is youtube.com slash Summit Auto. Click the bell notification so you get updates on the videos I do each and every day. Here at Summit Auto Mode, this one comes with the 20-inch painted and polished aluminum rims. Really good looking rims on this truck, and it comes with these really good looking BF Goodrich All-Terrain TA tires. These are LT29565R20s, and I would say they have probably about 70% of the tread left on them. It does come with the Rancho shocks, part of the AT4 off-road suspension, still a Z71, technically. LED headlamps, LED running lights. We'll turn all those on as well as the LED fog lamps. Front bumper is in pretty nice shape. I didn't see any major dents or dings on there. It does have the red tow hooks. Get kind of this silver finish grille trim on there. True cobble induction hood. I'll show you how that works as well at the end of the video. We're not too far away. A couple of minutes. Didn't see any dents or dings on that hood, and this passenger side front fender is in fantastic condition as well. No major scuffs or scrapes on the passenger side front rim. As you go down this side of this 2020 GMC Sierra 2500, take note of how clean the body is, how reflective and mirror-like that paint is. I take these HD videos, so if you are far away or even if you're close by and you just cannot make the trip down, but you're still interested in purchasing the vehicle, you can see the truck, hear the truck, and of confidence in the vehicle that you're looking at before you even get here. So when you do get here, there's absolutely no surprises, and you can make a smart and informed buying decision from wherever you're at. If this video helps you make that buying decision, let your salesman know that you saw the video that it was helpful and that Brett sent you. Back rim is in excellent shape as well, and the back tires have just as much tread as the front tires, maybe even a little bit more. These look like probably 80 to 90% of the tread on those tires. You do get the felt wheel well liner, which keeps your frame and underbody looking good as all the remaining factory exhaust, so it hasn't been altered in any way. The lower rockers and cab corners all look really good on this truck. Comes with some nice painted step bars. You get the side box steps. These light up too when all the lights are on. That rear cap is in fantastic condition. Didn't see any chips or anything on that. Looks really good. Coming around to the back, the rear bumper is in great condition. It does have the rear bumper steps, the full towing package, which includes a receiver hitch, seven pin wiring, and then it has two hookups for cameras that would go on your trailer. LED tail lamps, you get the multi-pro tailgate. I'll show you how that works. First way is just the... This comes down like so. What you can do is you can stack wood in here and kind of gives you a longer bed, if you will. Then this also turns into a stack. So if we press the other one, if you press the whole tailgate, that goes down like so. And then that goes down. And then it's a step assist. So that's pretty sweet. You do get the spray-in bed liner. This one has LED bed lighting back here. The fifth wheel and gooseneck prep package. You get a 120 volt, 400 watt plug-in back here. And you also get four pin and seven pin wiring right there. This is your handle for the step assist. The only thing I'm not crazy about is this is kind of tricky when it's down. But it's not too bad. Anyways, tailgate's in really nice shape. That works nicely. And the cap shuts nice and solidly. Coming around to the driver's side once again for full disclosure, this back room is in fantastic condition. And down the rest of the side looks very clean. This one has the telescopic tow mirrors, LED side lights. These mirrors are heated, built-in directional signals. They power telescope out. They power fold in. I'll show you how that works. Inside, the AT4 comes with a really good-looking interior. It's like the black and brown leather interior. You get the brown stitching. Almost kind of a copper stitching, not quite. Anyways, love the seats in here. You get the AT4 stitched into the headrest. And it also comes with special AT4 all-weather floor mats right here. So those are pretty good-looking. Auto headlamps, cargo lamps, fog lights, push-button four-wheel drive, tilt, telescopic steering wheel, power windows, power locks, power mirrors, memory driver seat, Bose sound. And like I said, these mirrors do power scope out. I was showing both sides. So you know that both sides are working properly. And then they do power fold in, like so. We'll take a quick look at the back seats. Back seats are just as clean as front seats. These seats are heated on the outboard side as well.  You get storage behind the backrest on the driver and passenger side. You also get a little bit of storage underneath here. This one does have a winter front all-weather floor mat back here. There are your heated seat buttons. You get a USB, USB and a 12-volt power point right there. Child safety locks on the back doors and the bottoms of the doors all look fantastic on this truck. I'll hop inside so we can check out the miles, the radio, and everything that this truck has to offer on the interior. See that this one has 31,367 miles. You get the instrument cluster there is very nice and clean. All your information systems outside temp or compass display. And once we started up, I can show you all the features on there. Heated leather wrap steering wheel, cruise controls on the left. Steering wheel is an excellent shape. Bluetooth and information center controls on the right. Note that you do get that orange stitching or brown stitching on the steering wheel as well. Comes with the Allison 10-speed automatic transmission with the optional tap shift. And then it does have the Chevy infotainment, I'm sorry, the GMC infotainment system. Has the factory navigation system on there. Does have highway 41, so you know that is working properly. And you get AM, FM, and SiriusXM radio capabilities. And you have your home screen on here. You have Apple CarPlay, Android Auto, where you can project your cell phone to the screen. So that's pretty cool. And then you can check out the backup camera. This one has the 360 camera, I believe. You can also zoom in on your receiver hitch. That was the front camera. And you can, that's the cargo cam. So if you didn't have a cap on there, you can see what's going on in the bed. And I thought this one had a 360 cam, maybe not. We'll start it up in just a second here and check all those out.  That's for the plug-in that's in the bed of the truck. You can turn that on, downhill sys control, factory brake controller, another USB-C, USB, and 12 volt power point. And then this is a 110 volt, 120 volt, I'm sorry, 120 volt, 150 watt plug-in. Has the wireless cell phone charge pad, keyless entry with remote start on there, and drop down tailgate. Passenger side format and seat are in fantastic condition as well. Headliner is in nice shape and it does have the power sunroof. Up here you get home link buttons for your garage door security systems and lane systems and on-star capabilities up there as well. We'll start it up and then take a look under the hood. Starts right up, no check engine lights or anything like that. Has a full tank of fuel as well. And yeah, you can see the backup camera is working nicely. We'll take a look under the hood, also turn on all those lights so you can see how bright they are. I also wanted to show you the tire and loading information sticker, as well as the trailering information sticker. It's nice that GM puts that on there for you. And we'll take a look under the hood. I would personally like to thank you for checking out the video today and hopefully from this HD video, you've been able to verify the quality condition options and cleanliness of this truck all the way around. Those lights are super bright, look really good. All the cab lights are working as well. Under the hood, we have the 6.6 liter Duramax diesel engine. Engine bay is very clean, runs very smooth. This is the L5P engine, which puts out 445 horsepower. Once again, this truck has been fully safety and inspected by our service shop. Has a fresh oil and filter change. All the fluids have been checked and topped off and this truck is 100% ready to go. So that co-induction hood, air comes in there, comes down to there, right into the air cleaner.  And I would highly recommend this truck from a quality and condition standpoint and to see more pictures of this truck or one of our other 550 new and used cars, trucks, SCVs, minivans, Wranglers, halftones, three quarter tons, one tons. You name it, we gotta go to that website right there at summitauto.com. Full pictures and descriptions of every single vehicle from two locations all at summitauto.com. And if you'd like to check out more HD videos, you can go to youtube.com slash summitauto. Remember to like, subscribe and share on this video and all the videos that you see there. Click the bell notifications and you'll get updates in the videos I do each and every day here at Summit Automotive. In fact, in a second you'll see a link to subscribe to my YouTube channel in the upper left. The link to more GMC Sierra 2500 truck videos like this one in the upper right. Link to this vehicle on our website in the lower left in any link to one of our latest YouTube videos in the lower right. Click those, check us out and we're super excited to help you with this Ultra Clean 2020 GMC Sierra 2500 Crew Cab Short Box AT4 in Summit White Clear Coat. Thanks again for checking out the video and remember to like, subscribe and share on the YouTube channel. I really appreciate it. Thanks again.


Sizzigie, do you mean the font on my slide? Yeah, I'm not sure I can really fix that. The font is small. I'm mostly focusing on the pictures anyway. Yeah, you have to zoom on it. A lot of the slides were really made for my website. This is the website in case anybody wants to go on it. So, this is the website where I have just basically my own hobby website where I have basically these slides in a website version. So, what I guess I'll do is just kind of walk through some of the images in my, basically on my website and talk about each topic and I'm happy to go slow or take any questions in local. I don't think you guys can talk voice but you can post your questions in local chat and I'm happy to reply. I can't really see IMs because it's too much check IM so please use local. So, just as background, let's see. Yeah, right. I'll try to focus on the pictures. I mean it is too hard really to get into the detail in this kind of thing. So, basically my interest in particular in astrobiology, which is generally the search for life beyond Earth, my interest especially is in the search for microbial life. So, like bacteria, that kind of thing. On beyond Earth, especially if it's life that's cellularly very different and separately evolved from life on Earth, that would be fascinating. So, that's sort of my interest. I think the huge development, sort of the gorilla in the middle of the room recent years in terms of the search for microbial life beyond Earth is that there appear to be large subsurface oceans on moons in the solar system, maybe even on Mars, but at least in moons, like moons of Jupiter and Saturn. So, if those, it's pretty clear that those subsurface oceans actually exist underneath generally a large amount of ice. Have liquid water and where there's large amounts of liquid water, there may very well be life, at least that's what the thought is. Since life just basically loves or needs water, life as we know it anyway. So, I think that's just a fascinating thing. So, that's what got me interested in my graduate studies. I did research on extremophile bacteria. These are bacteria that live under really weird difficult conditions, like extreme salinity, extreme heat, etc. And that led me to get interested in the possibility that there could be differently evolved cellular life extremophiles, right? And exo-moons, sure. Syzygy, yeah. This is a fascinating thing. There's just a whole neighborhood of the sun 50-100 light years is filled with other star systems, planets, moons, that may be better candidates than moons in the solar system for harboring life. They may even have surface liquid water, which is generally not believed to exist right now in the solar system. The problem with exo-moons is that you're just really far away. You've got to go to a different star system. Whereas, of course, the planets and the moons revolving around the planets on Earth are very close, relatively speaking. Yeah, I don't know. I have some slides on exo-moons that I could take a look at. It seems like there's good evidence that there are, well, there are clearly exoplanets, right? And there seems to be some pretty good, although indirect, evidence of exo-moons. But there could even be life on exoplanets. It's just that it seems like it's very hard to get real detailed information about astronomical objects that are just that far away. Right? So that, I mean, I think it's intriguing. But as far as relatively near-term possibilities, search for life beyond Earth, it seems to me that it's in our neighborhood. It's in the solar system. There's huge lakes under the surface of ice on Europa, on Enceladus. You know, moons of planets in the solar system. And it seems to me there's a good chance of life in those bodies of water underneath the surface of these moons. So I should really probably start to go through some of these slides. So I'm actually looking at my website and kind of matching it up. So, but feel free, if anyone has thoughts in local chatter or wants me to focus on anything, I'm happy to do so. So I already talked about the general search for life on Earth. So let me see what would be the next slide to go to. So I don't know whether I should start kind of with the older stuff, but I guess I will. So there was something called the Uri Miller apparatus, where it was determined that you can find you can sort of create the conditions for early life. And what you get is chemicals that develop that suggest that life could have evolved from the conditions that were present on primitive Earth. I want to pull up that slide for a second. Let me just see here. No, that's not it. One, two. Sorry, just let me pull up the correct slide. It's a little hard to organize slides in second life. So let's see. Day, if I'm pronouncing it correctly, says that work was done at my alma mater University of Chicago. I didn't know that. Haven't the Uri Miller conditions been questioned? Sumo says, you know, I'm not sure. I mean, everything I've read it about it suggests that it may not prove everything, but it proves a lot. At least if you guys can see this slide with the colored rectangles, I think the basic theme of this seems to be continued to be valid or sort of confirmed. Start with water vapor, and you've just got simple gases, methane, ammonia, hydrogen, and you apply they in this experiment, applied repeated application of electrical sparks to basically to simulate primitive lightning, and what you get out of it is simple organic compounds, which include amino acids, which are the building blocks of life. Now it doesn't mean that you're going to get cells out of the deal. It doesn't prove that life could have evolved, but it suggests that complex amino acids, which are critical to life, could have happened through this natural, random process, and I think it at least points to the possibility of the evolution of life. Uri Miller is decades old.  Baragon, I don't know. That I don't know. I feel like it kind of was like proof of principle, that you can get complex life-important chemicals developing through random conditions similar to that that was present on Charlie. Let's see. To have such simple conditions for cycling pills for a short amount of time and have it produce organic chemicals is an impressive. Yeah, I mean, I find that at least it's suggestive that the possibility of evolution of complex life-important chemicals, if not cells, is possible. Alright, so let me move on. So in my area of interest, order is crucial. So as far as people know, order is fundamental to life. So that doesn't mean that there isn't life out there that doesn't depend on water, but life as we know it is completely dependent on water. You have to have water for all the chemical processes to exist for cells to exist, and so forth. So I'm going to put up a slide that I think is interesting. The water topic, although it may be a little complex. So hang on just one second while I pull up a slide that I'd like to show about water. Let me read. Let's see. I guess no subsequent demonstrations contradict the findings of the original experiment. Bargain, I think that's true. I mean, to be fair, I think later experiments suggested that just because you show that amino acids can develop from these primitive conditions doesn't really prove that life could have evolved. And I think that's correct, but I think it is suggestive. Let's see. And it says, right, haven't thoughts about what those conditions? That's another thing, Sumo. I remember reading that. That's an important point that the primeval conditions might have been much different than people thought. And so the conditions of the Urim-Miller apparatus might really not be relevant to the time period. However, I still think it proves the principle. I think if you change around the conditions you'd still probably find that the principle continues to be valid that you can get complex life-important molecules developing from relatively random conditions. Anyway, so in this slide so this is kind of a complex slide, but I don't know, it's kind of my pet topic. So I guess I'll focus on it for a minute. So basically, let's see, right, those agreed, those molecules can, yeah that's it. That's about it, Sumo. So anyway, so life on Earth requires water. And we've recently found scientists have recently found that there are these huge bodies of subsurface oceans on moons in the solar system. And it wasn't believed that that was the case previously. Why? Because to have liquid water, you need pressure and you need heat. If you don't have pressure, it all evaporates and you don't have liquid water. It's got to be sort of pressed down. And you also need heat to keep it warm or it's going to be ice. So how do you get that? There's a couple of ways that you can get it. Let me just read a tagline. Anything resembling life processes at the speed to which we're customer cars solve in media, it seems. Yeah, I think that's right. Something life like that lives with processes at very slow rates could be difficult to perceive. I'll look for it. Yeah, that's all, I think that's all true. So there's possibilities that life could exist separately from water as a solvent. Even potentially separate from liquids as solvents. But it would have to be radically different from life on Earth. So like the best guess is that if we're going to find life, even if it's pretty different from life on Earth, it's probably going to be found liquid water. Liquid water has a myriad of qualities which cause it to be amenable to the processes of life as we know it. So anyway, so in this slide, the basic gist here is you've got a couple of ways that, a couple of ways that you can get liquid water. And one is on Earth, how do you have liquid water?  And you've also got heat from the sun. And that pressure, plus the heat from the sun, can give you liquid water. So it turns out that you can get liquid water on moons in the solar system that don't really have enough heat. So you would think you would just have ice. But on moons like Europa, it turns out that the varying distances of Europa from Jupiter cause like a pulling and a contracting and an expansion which creates friction which creates heat. So the pull, the tidal forces create heat and then those tidal forces, right. And the tidal forces from the pull of Jupiter and the back and forth create enough heat to create liquid water and that's what this is supposed to show. Now you still need pressure and on Europa you have that pressure from, it could be several miles worth, of solid ice. But you could then have liquid water underneath that ice. And although there are other conditions necessary for life, if you've got a subsurface ocean of liquid water, I think that's a convincing start that you might have life. So these are some of the fundamental things that got me interested in this whole topic is that there's oceans of liquid water underneath the surface of moons right in the solar system that may very well have life. Or at least I think that may have life because liquid water and life just seem to go hand in hand. So there's a lot of other aspects to my presentation Let's see what should I talk about next though. I want to talk about something something interesting visually maybe biochemistry. So I'll start with biochemistry. So let me see. I'm going to go to my slide on biochemistry one page seven. Hang on one second while I pull up this slide. So this is just basically a visual. So it turns out that life on Earth it's sort of interesting. Life on Earth uses glucose as pretty much the sole medium of energy exchange. Everything, all life on Earth pretty much depends on glucose in one way or another for energy. It's interesting to think that if we found life on other planets or moons, if it used anything else other than glucose for energy, that would be intriguing. It would be a whole different cellular metabolism. So this is something if we find life beyond Earth and it's different than life on Earth then we have a sense that how life can be different and where we can look to find different types of life, etc. So all life on Earth is pretty streamlined so if we find it beyond Earth and it's evolved separately and very different it would be just an intriguing and intriguing thing. Again if anybody has questions or wants me to focus on any particular topics just let me know otherwise I'm basically going to go through the half a dozen or so major topics on my website and just deal with questions from there and maybe talk about some current topics too. Possibility of liquid water surface of Mars. Alright so let's see what's next on my cellular metabolism is something I talk about my website but it's kind of detailed. I think let's go to Europa. So just give me one second while I pull up my slide for Europa. Okay so let's see let me read this as it goes along because of too much on it. Do you think Perseverance rover will find life in the Jezero crater on Mars in February. So day I don't know about that. I'm not familiar with the details there. I don't think there's life on Mars actually I doubt that there's even liquid water in or on Mars. I think it's dead but I could be wrong. There's recent evidence recent articles that suggest that there could be active magma inside of Mars that creates liquid subsurface lakes on Mars and if there's underground water then I would love to be wrong because then there could potentially I think be life and increases of life dramatically. But Mars just seems too cold for that and I'm not really buying the magma thing but I don't know maybe more research is to be done on it. Anyway so I'm kind of more excited about some place like Europa that's the subject of this slide. So if you look at this slide the basic thing is Perseverance rover is looking for fossil life. I mean I don't know if fossil life seems unlikely to me too. I think it's like if there was life on Mars it would have to be many millions of years ago and it's hard for me to believe that the fossils would even be findable. Doesn't magma imply plate tectonics Mars has no tectonics. Barragan I'm not sure but I but it does seem surprising to me that there would be active magma on Mars so I'm not so sure about that. But yeah I think it's underground water on Mars that's the thought. But again I'm not yet convinced on it. Anyway so Europa, what is Europa? Europa is a moon of Jupiter and it's a lot of people have heard of Europa for good reason. It's a moon in the solar system where people think scientists think that there could potentially be life. So if you look at this slide just basically, let me just read this though. Alarmons is the largest volcano solar system on Mars. Well that's the thing right I mean could there have been life on Mars 50 million years ago? I think yeah absolutely maybe now I doubt it. Anyway but Europa here's a different story. The yellow surface of Europa you can think of that as largely ice and then rocky ice and then that blue part though that's an enormous subsurface ocean underneath the surface ice on Europa. It's almost certain that unlike the Mars thing on Europa this subsurface ocean almost certainly exists. And there could be hydrothermal vents. These hydrothermal vents are very important because let's see. I think that hydrothermal vents are kind of like underwater volcanoes. What they do is they can stir up the water, they can mix minerals and other chemicals into the water and create the conditions that could possibly allow that mix for life in the liquid water. So and as I recall there's evidence that there could be hydrothermal vents in Europa that could combine with the subsurface oceans potentially present conditions that are similar to hydrothermal vents on Earth. And in hydrothermal vents on Earth that is these underwater volcanoes at the bottom of oceans there is life around them from the heat and the minerals and the flow that they create. You have large ecosystems of life around these hydrothermal vents on Earth. Could something like that be the case on Europa? I think absolutely it could be. So I think that's exciting. Playtech Connix on Mars has been debated blah blah blah. Yeah I don't know enough about Playtech Connix on Mars. It just seems like Mars might have had life but it was millions of years ago. Now I don't know. Then Getaka was what got me looking into the possible life on Europa. I don't know what Getaka is Violet. Hydrothermal vent life demonstrates that life doesn't need sunlight to ex-paragon. Yeah that's a key thing that I didn't mention. It used to be that people believed that you needed sun. Light for life. So that's a whole different thing and then you'd need surface water. But here you have life way under the ocean that is provided everything it needs not by the sun but by the heat and the minerals that come from the underwater volcanoes, the hydrothermal vents. And if there's life on Europa it's not going to be driven by sunlight. It's going to have to be driven by something like a hydrothermal vent. So that's a key point. There is life in the Earth hundreds of meters below. Roger and yeah I think that would be a hydrothermal vent thing. And that's what's so exciting about this. Once you know that there's subsurface oceans on moons in the solar system you combine that with the very real possibility of hydrothermal vents which are like underwater volcanoes just like Earth. Why wouldn't you have life on other planets? It almost seems like it would probably be the case. NASA is planning a submarine rover called Pryoba to look for life on the oceans. I didn't know that. I love it. Honestly I feel like the money should be spent on that kind of thing as opposed to landing on the moon again or landing on Mars based on what we know now. Looking for signs of life above or at Europa and Salatus moons in the solar system to me that's so much more bang for the buck. Anyway okay so I should probably go on. Maybe let's look at Titan. I think Titan is an exciting possibility for life beyond Earth. So image that I have isn't as exciting as the possibility for life but let me pull it up anyway. So this here is an image of the surface essentially of Titan. See but it's believed that it may have subsurface liquids even though it doesn't have much to look at on its surface. And there's even been evidence that it's got a thin atmosphere as I recall. And in its thin atmosphere there are chemicals that suggest the possibility of life metabolic processes happening. There's been speculation that there could be microbes. Also there's believed to be hydrocarbon surface lakes on Titan. So now we're not talking about subsurface but surface lakes of bodies of not water but bodies of liquid hydrocarbon liquids. And there's some evidence that there could be an exchange of gases with the thin atmosphere of Titan and hydrocarbon lakes that could suggest the presence of life. So Titan is also really interesting. Yeah and an atmosphere is an important thing because then you can have surface liquid and when you have surface liquid you can have a gas exchange with an atmosphere and that seems to increase the possibility. Alright so that's Titan which hasn't been focused on but I think it's important. Then another one is Enceladus this is another moon in the solar system that I think is a significant candidate for life. Again Enceladus has a subsurface liquid ocean a lot like I guess I won't go on about that because it's pretty similar to Europa. It's less exciting on its surface but it's got subsurface oceans and it could have volcanic activity so it could have life. So let me read what's going on. If anybody has trouble hearing me please let me know but I guess you'd let me know. Alright let's see what else Titan used to be. Let me read this actually. Titan used to be the darling for ET. If you know Baragon I didn't know that. I thought I discovered Titan. Evidently I'm late to the party but maybe it's a good candidate. Alright so moving on so there are these moons in the solar system with subsurface oceans of liquid water that could harbor life but there's other possibilities for life that seems speculative but it's not. I don't think that hard to believe that there could be non-water solvents for life. So Ammonia is one possible solvent for life and Titan would be a candidate for that. So let me pull up my slide on that real quick. So this is sorry for the slight delay. Let me pull up this slide. Second for me. Here it is I think. Tyrants of Titan is my favorite Vonnegut. Yeah you know I never read Tyrants of Titan. It sounds fun. So this is kind of a complex slide again a public slide that I lifted but Ammonia is a non-liquid possible solvent for life other than water. And Ammonia water mixtures that may exist on Titan or in Titan on subsurface and so it's possible that life can exist in these hydrocarbons but it would have to be much different than life on Earth but these hydrocarbons are liquids at extremely low temperatures which means that there could be life in or on moons or bodies where temperatures are extremely low where water couldn't exist or probably doesn't exist in liquid form but hydrocarbons could. So that's something else that makes the idea of hydrocarbons as a solvent for life really interesting. Anyway so let's see another possibility for a hydrocarbon solvent for life is methane and I'm not a chemist but Titan also is believed to have surface lakes of hydrocarbons including methane and Sane and it has an atmosphere so yeah I mean I guess that's why Titan has been sort of a darling. So here's an interesting photo. This is an image of Titan showing light reflecting off its liquid seas. I mean it's pretty cool you're actually going to be looking at sun reflecting off the surface of liquid lakes on Titan. So I'm going to pull that slide up from my inventory just to give you a quick look. I think this is it. No that's not it. Hang on well I just pulled this slide up. Sorry this is taking a minute I'm not finding this. Sorry one second one a second right so this is it so that took a while sorry about that but if you can see this image that the bright spots here are is believed to be light sunlight literally bouncing off liquid hydrocarbon oceans on Titan. Let's see would ammonia with a high PHD be good for life? Yes would have to construct methane based life inside out chemically speaking with roof right yeah I agree based on ammonia as a solvent would be really different from life on Earth so it's pretty speculative but it's possible and you get liquid hydrocarbon lakes on Titan so that that also increases the probability for life when you have the gas exchange with the atmosphere. So that's another interesting possibility. Let's see so moving on in my presentation or on my what let's see high pressure and temperature chemistry is different yeah so you guys know more about the chemistry I think than I do my general sense of it is that life based on anything or using anything other than water as a solvent would have to be pretty radically different than life on Earth right but it's possible and it's interesting I mean I still think you know the low hanging fruit are the subsurface liquid water oceans of moons in the solar system and maybe Mars maybe I'll come back to Mars but it's also interesting to look at some sort of speculative possibilities and that's one of them. Now speaking of speculative possibilities yeah another so the home run of astrobiology is radio setting so the search for extraterrestrial intelligence using radio transmissions so it turns out that radio transmissions can go hundreds potentially of light years massively distant and not degrade or in some cases not be blocked so it's possible that radio transmissions could come from civilization sending them from many light years away from a planet in a different star system and what would take a long time it could reach Earth and we could find it I mean of course that's been the subject of some movies so maybe I'll start with one of my favorite slides just give me one second I haven't figured out a way to organize my SL inventory efficiently yet maybe someday I will just hang on for me so one of my favorite actresses Jody Foster this is a shot from the movie the 1997 movie contact where she yeah that's right where she finds listens and detects a signal seems to be repeating regular signal that could suggest intelligent life sent it my friend worked on the movie oh that's interesting so I'd like to know more about that anyway so I think this is just intriguing this seems like really sci-fi stuff I don't think it's that radical my personal view is that it seems likely that intelligent life does exist throughout the galaxy it's probably just really spread out and because it's really spread out not just in space but in time you have to have a real confluence of events to find it I don't know that much about the radio telescope work but it seems like man it's a big spectrum it's very hard to survey it all in detail they're working on it even now with the SETI projects but it's everything I can determine seems like it is entirely possible that there could be life it could be 50 100 200 light years away sending radio transmissions they get to the Earth that we find and although it'll be very old it could literally be listening in on the messages from extraterrestrial life so I just think it's cool I think it's still possible too it seems like it I wish I knew more about the radio telescope part but it seems like it really hasn't been done yet the whole spectrum hasn't been fully checked out let's see indeed very big but usually searches are a scissor I'd love to talk to you about this sometime but usually searches are around the H 21 centimeter line or the OH 21 centimeter line yeah you know more about this than me I wasn't I mean if I can't find it from Google or Wiki it's hard for me you know I can't be I don't I don't have that much depth in it however um that sounds interesting so I want to pull up another slide this is called the cosmic water hole so let's see let's see if it's trying to find a slide that's a little bit visually the slide maybe isn't too visual but it's interesting in concept so let me just pull it up and I'll talk about it so this isn't going to look like much but I'll bet some of you perhaps uh perhaps scissor G or others might understand this better than I do let me see if organic intelligence is leapfrog by computer intelligence the H and O lines may not be the right place to look I don't know I mean so my my limited research suggests that there are these places in the spectrum so we're talking now what are we talking about radio transmission so there's got to be life out there with radio transmission capability sending out radio signals then maybe we find these signals and we sense a pattern a repeating pattern and then we can check into it further and maybe find patterns under that pattern and basically decode messages it's not a simple process but it's conceivable so how would that happen you would have to have radio transmissions that get to you without noise you have to be able to clearly see them so this this slide kind of demonstrates that it's believed that there are places in the spectrum which I think scissor G was probably referring to a moment ago where you could send messages that would be unlikely to be interfered with by natural sources so you could send them over light years and it could be received and if another intelligent life form gets them they could find the patterns and get the messages that's the idea I do think it's possible it seems to me that it's possible based on everything that I've so that's sort of they call that the cosmic water hole in the sense that it could be a place of quiet where we might be able to search and find radio transmissions from from intelligent extraterrestrial life alright so so let's see so now I mean expanding it even further in terms of where would you look for life in solar systems beyond our own maybe I'll pull up this slide see you pull up one of my later slides see hold on one second for me please that's not the one I want it's just taking a little while for these slides to res now so this is one that I wanted so this is a star map so in the neighborhood of the sun I forget the scale on this so you can see at the bottom the scale is like five light years so it's pretty distant but in the neighborhood of the sun as you get a few light years out so this is the distance where it takes light a few years to get to you so it's pretty far but there's only this it's maybe hard to see but there's one star I think it's called Proxima close to the sun but then as you go out 15 20 40 50 light years out this is by geometric proportions the amount of star systems and potential planets exoplanets moons and therefore places that could potentially harbor life and maybe even intelligent life that could be sending you radio signals so it gets interesting when you get out you know I don't know 25 50 light years or more there's just a lot there's a lot of star systems let's see just reading here depends on the strength of the transmitter the radio environment this is another thing where you knew what you knew what you know about this really like I don't know all those details it's hard to find out but it seems like it's possible so that'd be something that'd be something to talk about sometime anyway so um let's see just for giggles this is Proxima Centauri this is the sun's nearest stellar neighbor just for the heck of it I think I spelled it wrong I should fix that so let's see what else should I so um well I have some slides on like um habitable zones but I'm not sure it's worth showing so there's some speculation that there's this habitable zone of a certain distance from every star where it's kind of not too hot not too cold they could sometimes call it the Goldilocks zone planets moons in that range you could have liquid water you could have life I don't know I'm not sure about that anyway so uh maybe I'll go to my last slide or what should I go to now actually this is a cool slide that I want to show just because it's attractive um actually it might take me too long to find that so I guess I'll stop at that um give me one second I want to find an article so um that's pretty much the the long and the short of my presentation um in terms of the I'm just gonna throw a slide up here um this is Enceladus so it's about 40 minutes into the presentation and I don't know that's sort of just a highlight of these of these things that I've been looking into so let me read some chat um see it depends on the telescope and atmospheric scene and their angular separation yeah when they arrive they will request take me to Ledcephalin isn't B Rocky so I'm not sure where um where to go from here I guess I don't know I kind of would like to talk about Mars so I'm gonna go back to my Mars slide because it's in the news right now so I think it's kind of it's just relevant generally um so hang on a minute while I do that um I had that up earlier actually liquid water phase physics and this is 1a3a hang on one second for me please I hate the inventory in second life so so this I might have showed it I think I showed this slide earlier so I don't want to harp on it too much but if there is liquid water on Mars or in Mars then it's an intriguing possibility to find life so this slide shows that the bottom slide it's kind of complicated but the bottom line here is that the range of conditions on Mars where it says range on Mars that circle that allows for liquid water to exist is really really narrow so unless there's some weird stuff going on in Mars like magma creating heat then there's gonna be no significant amount of stable liquid water on Mars but if that turns out not to be the case then it gets interesting when we send radio signal out to the universe it would not be encrypted is that right how do we send the signal out on some kind of broad range signal checking on Google their angular separation yeah that gets beyond my knowledge the details of it get a little beyond my knowledge hey babe could you not be too noisy I'm kind of good on theme thanks um let's see is there any particular topic that anyone especially wants to hear about like I have a lot of details on a lot of different topics from organic chemistry to cellular metabolism Venus you know I don't have too much on Venus wasn't there something in the news on Venus because I don't remember Venus coming up on my astrobiology radar um let's see or chloride salts in the Martian soil can allow yeah so this idea that salts in the Martian soil can allow water to remain liquid down very low is interesting but it still doesn't seem I got the sense that it still wasn't possible to have liquid water on Mars um unless there's some sort of source of heat within Mars what's wrong yeah I don't know enough about Venus either it seems it seems unlikely uh so the idea isn't that there'd be liquid water on or in Venus is it that doesn't seem possible but maybe I'm missing something anyway I should maybe stick to what I know here so let me see well maybe I'll back up um maybe talk about liquid water or organic chemistry maybe liquid water is the interesting thing um I'm gonna pull up my liquid water slide one a three please so well this is a let's see uh Venus could have acetylphilic thermophilic extremophiles in its clouds well right but if it had if it had extremophile microbes in its clouds they would have to be gas based not not liquid solvent based I think um so that that would be fascinating but pretty radical um yeah I mean it does it does seem like Mars is pretty dead um drops of what yeah drops I mean from what I hear drops of water what I read even drops of water probably wouldn't be enough for life as we know what you'd need bodies stable significant bodies of water um so droplets uh 50 miles upward is one atmosphere of pressure maybe yeah I mean droplets of water are interesting but I can't see it being enough for life to evolve um and yeah you do have to have energy source um that's another issue but I mean just how it would exist without without water as solvent I don't know you know the the transfer of molecules in and out of the cellular membranes and everything it really requires a significant body of liquid water um anyway so this slide I have up is really attractive looking but it talks about all the different reasons why liquid water seems to be critical for life um it's liquid phase under a big range of conditions um and life it needs liquid generally life as we know it needs liquid for the reactions and the movement of the molecules um and also um uh water has this polar configuration which turns out to dissolve many substances and that makes it much easier for chemistry of life to happen that's why people think liquid water is is probably probably necessary for life anyway let me go to a more interesting looking sign um let me see here I'm just trying to find out a figure out a good slide to show so another thing is what would be the chemical sort of backbone on life everybody life on earth has as it's sort of chemical backbone carbon here's a slide on that one eight four so these are the different structures that carbon carbon is basically a molecule that can take all sorts of forms and that gives a great versatility for forming the sort of chemical backbone of life but let me read this here um Venus has been the weight is for 700 million years life could have gotten started in the first two million years when the sun was there yeah that sounds possible to me not now but then this is on the inner edge of the Goldilocks zone that's interesting it's atmospheres like hell yeah and then Venus and then as Venus became less hospitable its life metafoled a habitable zone I mean that part who knows um life in it in a in a non liquid ocean or lake it's have to be I think radically different life as we know it but it's but it's conceivable um let's see so there's 15 minutes left and I'm just trying to think of what anybody what might be interested in is there any particular topic that people find the most interesting a particular planet or a topic in this area there is let me know otherwise I'll just find something um let me see what might be interesting some of this stuff gets kind of detailed so I just want to show stuff that is more visible so I'm going to look for a slide biochemistry maybe no I talked about that gana chemistry if your gana chemistry is kind of an interesting topic um so let's see one a six let me pull up another slide one a six it's not too interesting so this is more of a let me read this now um see this stuff is just too much text so I've got to find let me find a slide that's not all text this is kind of an interesting one I'll go with that so this is one a eight I'm just pulling up a slide give me a second yeah so a lot of my slides are just kind of a lot of text I found this an interesting slide so in the search for microbes beyond earth how are you going to find them without actually being there well it turns out that the chemical action of microscopic microbes bacteria and other microbes can create macroscopic observable characteristics that can even be observed through um telescope work so and and other ways so this this shot is the atmosphere of earth and um the the atmosphere of earth is blue is visible in this blue area so what's interesting is that about what is it 19% or 21% I forget the exact number but about a fifth of the entire earth earth's atmosphere is elemental oxygen O2 which is the main source the main source of that has been photosynthesis by cellular life so 21% so 21% thanks to the G of the entire earth's atmosphere is elemental oxygen that was produced by microscopic microbes um performing photosynthesis um so I see it varies so you can potentially find chemical signatures in atmospheres that you can make guesses like if someone were to observe that the atmosphere of earth was so much oxygen they might guess where to come from it might have come from photosynthetic life and that guess would be right um and people have been looking at the atmospheres of moons in the solar system for those kinds of signatures um those kinds of uh build up of chemicals that suggest life algae farts yeah um let's see there's about 10 minutes left I'm not really sure I don't hear a lot of chat about any particular topic um so I'll look for another pretty picture let's see talked about Europa um I'm just looking for another slide that might be an interesting visual image carbon different elements of life a lot of this just gets into uh details that I don't think would be too exciting to show let me look at some of my articles this might take a minute so bear with me if you don't mind I'll look for some article slides that have interesting easy to see images let's throw them up one at a time and see what happens it's just taking a little while for these to res it seems maybe because of the traffic so this is just an interesting uh speculative image so this is an artist tradition um alright an envisioned habitable moon this would be the view from a hypothetical moon so the large surface that you're looking at in this image would be the view that you might see from around the moon with an atmosphere and liquid surface water um and it's inspired by an exoplanet um so you would see the host planet and other moons and it could be that there are moons like this in star systems with life let's see what I got here uh five quintillion tons of atmosphere yeah I'm going to throw some other article images up just because some of the images are interesting this is another artist rendition hopefully this shows pretty quickly do you guys see the uh yellowish planet with the blueish moon in front of it at this point can you tell me okay good at least these slides are coming up quickly even if I'm not finding them that quickly so this is an interesting slide um another artist rendition you can have a habitable moon that's kind of earth like orbiting a planet um and this would be the view from around the moon um which would be interesting like a scum covering in circus yeah alright um yeah it's interesting how life is on this this thin relatively thin surface of earth and anywhere probably let me throw another image some of these articles have interesting images so a little picture show at the end um another uh hypothetical exoplanet so if these planets exist and have water they might look kind of earth like and something like this I'm just going to move on and go through some slide some picture slides oh this is one of my favorite I'd say this is probably my favorite artist rendition image um I don't know why but um it just seems very uh science fiction to me so imagine that you were on um the surface of another planet this is so it would have a very different sky very different geology but you can see it could have liquid surface water and in the sky there's um two suns so this is just an artist rendition of something very exotic and different from earth ugly bags of mostly water sumo I don't remember that uh I don't remember that saying from star check ugly bags of mostly water um I what I like to imagine is when when life presumably came out of the oceans you know the primordial oceans it sort of took the water with it uh and thus bags bags of mostly water I mean we can't live without water so when life came on to land the cells had to keep the water and the organisms had to keep the water within it so that the chemical exchanges could happen and life uh could exist you just have to have water unless there's life that's radically different than life on earth I think liquid based life based on a liquid other than just water is possible maybe a mixture of hydrocarbons in water the chemistry gets complicated um I I I find that life life that's not based on carbon maybe silicon and life that's not uh liquid based is hard to envision it would have to be radically different than life on earth from everything that I know but that still leaves a lot of room and there's a lot of turns out there's a lot of liquid water apparently even in the solar system much less the galaxy so I'm going to put another image up it's a lot easier than finding articles so so this is back to Titan my favorite um my favorite candidate for uh life beyond earth um we have methane polar clouds uh in essentially the atmosphere of Titan um compared with polar clouds on earth interestingly similar you wonder if there might be other similarities all right um and of course Titan has liquid lakes yeah I don't know yeah Titan to me seems seems a bit the idea of liquid hydrocarbon lakes is intriguing to me and there was an article written a long time ago by an astrophysicist I think Chris McKay is his name that it gets detailed but there's up observations of the surface of Titan suggest and I think this is a slide that actually talks about in fact anyway um there have been telescope observations of the surface of Titan that suggest that there are hydrocarbon sort of emissions in the atmosphere of Titan that could have been created by I think methanogenic life uh metabolizing Sumo says yes so maybe it oh no this was the silicon based life yeah silicon based life is another possibility although it seems speculative anyway so on Titan uh there there's chemical signatures of molecules in the atmosphere and I forget the details but they suggest that they could have been metabolized by I think methanogenic bacteria that could live in the hydrocarbon lakes methane related or with methane lakes on literally on Titan so uh that's pretty interesting I think um and then you know you get into carbon so there's water so life needs liquid uh probably and maybe it needs water but it seems to also need carbon because all the the chemical structures of life are sort of built around carbon but it's possible that another chemically barring like or element like silicon could be the basis although it seems it would just have to be completely radically different than life on Earth just like in Star Trek um we're almost done now so I'll go through a little bit more but if anybody has any other questions I'm happy to stay on or whatever I'll just go through a couple more slides Daisy my favorite plot line in Star Trek is the idea that Voyager was captured by a planet with machine life who discovered Veager's mission and reprogrammed it to fill the mission gather all the knowledge and return the knowledge to its creator this is maybe not too exciting but archaea are the early form of microbe present on early and they still exist today and I think they exist around hydrothermal vents which are interesting because you get sort of none life that lives under under the sea not with energy not provided by the sun so this is at least a pretty picture speaking of archaea um I don't even I might be pronouncing but archaea are a type of microorganism this ancient form of life and they can exist they exist still on Earth and they show that life can endure all sorts of extremes which makes life beyond Earth more possible these archaea live around these um big hydrothermal vents um with great extremes of temperature and salt and whatnot now until the last minute here so this is just the Mars rover on the surface of Mars pretty cool probably not life I don't think but pretty cool hopefully these are resin quick enough but it seems like they are what is this I don't know yet I have to let it res I think this is just really cool this is a really high I don't know how clear it is to you guys but this is a high res image of the surface of Mars it's just striking to me how similar the geologies of surfaces of other planets are to Earth I bet it seems to me it's probably like that in many light years away there's so many similarities you have to think that maybe life is something that is similar to you know so it could exist elsewhere let me see maybe one or two more slides arid desolate yeah that's Mars but it's possible existed before we missed it life on Mars early in Mars' history seems entirely possible oh this one I showed already so it's after two o'clock so uh maybe I should stop how about one more slide I'll see what this one is it's taking me a little while for it to res oh more Titan and we had enough Titan Titan Titan Titan I'm just throwing up maybe one more slide this is kind of an interesting one this is an array of telescopes that maybe one day will help us find radio signals from extraterrestrial life I've only got a few more slides so maybe I'll look at one or two more I'm just waiting for this one to res yeah so back to contact which I just loved especially the start to the movie was just so exciting this would be the greatest thing to find and decode radio transmissions from extraterrestrial life so it's after two o'clock so I guess I'll stop with the presentation as such yeah it looks completely realistic to me we radio astronomers are always outside next to antennas sysigie have you actually done radio astronomy that's fascinating thank you very much Shiloh that's really interesting you're welcome Brioni thank you all for checking it out I appreciate it thanks day thanks Mike thanks tagline I appreciate it thanks Baragon thank you sysigie thanks for the applause Baragon I appreciate everybody coming if anybody wants to talk about anything please feel free to please feel free to IM me or friend me or whatever and I'll talk a little bit but the presentation is basically over so feel free to listen how did you go from microbiology to research a lot Dave thanks for asking let me think now so I did my microbiology research in graduate school when I was studying environmental science but then after I graduated there wasn't a lot of good work unless I wanted to go for a Ph.D like a little much an environmental in environmental science I took us a course in environmental law and then I found out about patent law which seemed like a nice way to combine my science background language interest in language I like language in English and that's kind of how I gravitated to patent law in retrospect I kind of wish I stayed in microbiology it would have been cool to research microbiology um patent attorney have to have science yeah that's right patent attorneys have to have a science degree in order to in order to become a patent attorney tagline yeah I did go to law school about a thousand years ago yet to be a patent attorney you have to have a long background you have to have a law degree and you have to pass a bar exam for at least one state and you have to pass the patent agent or patent bar exam which in order to take that exam you have to have a science degree basically it's kind of complicated but it makes for a good area because not too many people can do it so I'm going to stick around but I'm not necessarily going to keep constantly talking but if anybody wants to chat me or talk um I'll be around for a bit thanks again thanks a lot sumo daisy did I ever work for setting no um I didn't I would love to I would rather work for a NASA or a city or something intriguing but no


Welcome back to the School of Canada standing here in Mark's Gym, Marbella! So we kicked things off at Mark's Gym the weekend workshop in Marbella, not with crazy handstands and muscle ups and human flags, we've got to prepare the guys for the sessions that we're going to do, so that means some movement preparation work, Owen is taking the guys through some full body movements now and they're having a great time doing it but it's a nice, fun and enjoyable way to start to learn how to control and coordinate our bodies and start to move better whilst preparing for what we're going to do for the rest of the weekend. Check it out! You can never go too tight to a shot. You don't want anything snagging on the obstacle course, keep it nice and tight. And learn it! Mike, I'm coming for you. Where is he? Let's go have some fun! Aaron is killing it. Alright, we're flagging that Aaron towards the end. This one, long as we're burning. Good Holly, check out Holly! Second. This is madness. This is mad. Now I've got to put on a bag. Run through to catch his castle. And make my way back up here. There ain't nothing like it. And some of these guys, you can go. Jenny, redefining her own possible mentally and physically on some of the technical stuff is unbelievable. I am also scared of heights and some of this stuff challenges me. And it's just flipping awesome to see everyone is buzzing. She's buzzing, Mike is buzzing. It is going down in Montreal, Montpellier. There's only one exercise on this course which I always feel a little bit sketchy again. And this is it. Mike, what's this one called? Ninja Wars. Ninja Wars. It's a technique, but I feel like I might have to go first. And everyone is watching. So not only is it a little bit sketchy, I've also got a handle on the pressure. I'm on the edge of glory, mate. Edge of glory. Let's go!  It's all strategic. Strategic. Am I impossible? The hand of the weak and the redefining are impossible. It's crazy. Chest and shoulders. Shoulders and chest. With a touch of lats. What an epic weekend workshop with the School of Calisthenics at Mike's Gym in Marbella. And what better way to celebrate redefining your impossible than with a couple of sangrias here at the beach.


OK, so welcome to the second session on zero knowledge. First paper is entitled on the size of pairing based non-interactive arguments by Jens Gold from UCL. Unsurprisingly, the talk is given by Jens Gold. So I'm going to talk about non-interactive zero knowledge proofs. So the idea is that we have a common reference string. The prover makes some statement that x belongs to a particular language. The prover holds a witness that x really is in this relation that defines the NP language. The prover then creates a proof, sends it to the verifier, and the verifier checks it and says, OK, so OK. And completeness says that if the prover really has a witness and the statement really does belong to the language, it should be possible to convince an honest verifier. Now we want two security properties from this non-interactive zero knowledge argument. First is soundness, that if the verifier accepts the statement, it's because the statement really is true, x really does belong to the language. And the second one is zero knowledge, that the proof does not reveal anything, but that the statement really belongs to the language. And we typically define that through having a simulator that could simulate proofs. And there are lots of applications of non-interactive zero knowledge arguments ranging from digital signatures and encryption to various forms of eCache, eVoting, internet voting, multipartic computation, verifiable cloud computing. So I'm going to talk today about very efficient non-interactive zero knowledge arguments. So they have to be very small size. They have to be very efficient to verify. One typical example mentioned this context is verifiable computation. So you imagine you have a weak client, outsources a computation to the cloud, gets a result back, and would like to get a proof that the result is correct. But here we want the proof to be compact, we want the verification to be very efficient, because we don't want the client to do the entire computation itself to verify that it's correct. There are also various suggestions for using these kind of very efficient non-interactive arguments of knowledge in connection with the eCache system, zero coin and Pinocchio coin, for instance. OK, so there are two contributions. The first one is a construction of a non-interactive zero knowledge argument. It has perfect completeness. So if the statement is true, the prover can convince and will always convince the verifier. It has perfect zero knowledge. So it does not leak any information whatsoever, except that the statement is true. And then we'll prove computational soundness. And there we'll be using very strong assumption. We'll essentially use the generic group model in a binomial group. So it's sort of very aggressive choice of parameters to get optimal efficiency. So we're going to work with type three pairings, asymmetric pairings, because those are the most efficient pairings. And the proof size will be three group elements. And we will also have fairly low computation for the prover and the verifier. So the very small size, I have to have the argument, makes this what is called a snark, a succinct, non-interactive argument of knowledge. The second contribution is sort of looking at, from the other side, and saying, how low can we go? What is the best possible efficiency? And we'll prove that you cannot have a one group element proof. So we'll look at pairing-based, non-interactive, zero-knowledge arguments. We don't care whether there's zero-knowledge or not, it holds regardless. So as long as you have an argument that's complete and sound, there's low bound holds. There'll be a few restrictions on the type of argument because we wanted to capture the essence of a pairing-based argument. And we'll prove then an asymmetric pairing setting that you cannot have one group element proof. It's an open question, so there's a gap here, right? I have a three group element construction. I have a one group element impossibility result. I don't know whether you can do it with two group elements or not enough. I've been trying to think about it. I really have no intuition one way or the other. So that's a nice open problem. So I'm going to work in a pairing-based setting. So I'll assume we have a bilinear group of prime order p. So we'll have three cyclic groups, g1, g2 are the source groups, and gt is the target group. And I'll have a pairing that maps pairs of elements from the first and the second source group into the target group. And I'll assume here that the generic group operation, so deciding group membership, doing multiplications of group elements, computing the pairing result efficiently doable. So the two types of groups, the symmetric groups, where g1 and g2, the two source groups, are identical. An asymmetric setting, where they're not identical, where there's actually no efficiently computable isomorphism in either direction between the source groups. And for efficiency reasons, to get optimal efficiency, I'll be working mostly in the type 3 setting with asymmetric pairings. And that's where the lower bounds will hold. But the construction can also be instantiated with symmetric bilinear groups with almost no change. So first, I'll change notation a little because I want to use additive notation for these groups because that's much more efficient, easier to do. So I'll use this notation where I put an element in the brackets. 1 as meaning this a is the discrete logarithm of the element in source group 1. And b in brackets with a subscript 2 means that b is the discrete logarithm of the element in source group 2 and so forth. So in particular, here we'll have the generators now can be written as 1s in brackets. The neutral elements will be 0s in brackets. And the advantage of this notation is that now we can sort of use standard linear algebra notation. So I can define a dot product. So if I take a vector of group elements and take the inner product with a vector of scalar errors, then I'll efficiently compute the resulting group element. I can take vectors of group elements in first source group and in second source group. And I can take this dot product. And what I'm really doing is I'm taking the first group element in the first vector and the first group element in the second vector and pairing them together. And then I'm doing the same thing with the second group elements in each vector. And then I'm multiplying all those pairings. And that allows me to compute this inner product in the target group. And now you can also do things like taking a vector of group elements and multiplying a matrix on that. And you'll get another vector of group elements. So that's nice. Now we'll be doing a lot of linear algebra. So let me define what I mean by a pairing-based snark. So the way these constructions typically work is that we have some NP relation R. It has some statements. It has some witnesses. And the common reference string, what the setup does, it generates vectors, sigma 1 and sigma 2. And then it bets that in group elements in the first source group and in group elements in the second source group. And that will be your common reference string. The proof typically also works in two steps. So typically what the prover does, it gets the statement of the witness and it computes a couple of matrices. And then the way it computes the proof is it takes the first matrix and multiplies it with all the group elements in the common reference string from the first source group and computes a bunch of group elements in the first source group, which is first half of the proof. And then it does the same thing in the second source group. So if you look at sort of all the snarks that have appeared in literature, they all follow this structure here. The essence is that you can compute the proofs with linear operations on the group elements in the common reference string. Okay. And finally verification always works something like this. So we have the verifier. Okay, it takes us input the statement and it produces a bunch of matrices. Okay. And then it uses those matrices, essentially these are pairing product equations. It takes elements from the common reference string, takes elements from the proofs and it computes some sort of pairing product equations of all these elements. And you can write it in this nice matrix form. Okay, so this is the structure of all the snarks that, pairing based snarks that have appeared in the literature. Okay, and the nice thing is of course that everything here can be done just with generic group operations. Okay, so I'll start with the lower bound, okay? So I'll consider a language that has a hard decisional problem. So the two sampling algorithms, yes and no. And the yes algorithm samples statements that are in the language. No algorithms say sample statements that are not in the language. And I'll assume that it's hard to distinguish whether it's been sampled as a yes or a no instance. Okay, and I'll prove this theory that if you have a pairing based snark in the asymmetric setting, then, and you want to look at a language which has these hard decisional problems, then you need at least two group elements in the proof. So the intuition here is that if you just have a single element in the proof, then it has to be either an element in source group one or it has to be an element in source group two, right? And if you remember the kind of the test the verifier does, it does pairings of elements in source group one with elements in source group one, in source group two, right? But if the proof is only one of them, essentially what you get is a linear equation in the verification, okay? And we can in generalize this theorem here to rule out any linear decision procedure for the verifier. So essentially, linear complexity and verification is not sufficient for languages with hard to decide relations, okay?  I'll look at a very simple example. So I'll say, let's say I have the case where we have a proof that's just one group element, source group two, that's of course without loss of generality. And I'll also, for simplicity, say that we have just one verification equation. It's not too hard to generalize too many verification equations, okay? So if you have just one verification equation, it can be written as sort of a matrix A that does things with just elements in the common reference strings and then a vector B that does something with a proof. So I'll just, assuming that we have this type of verification equation, I'll construct a decision algorithm that decides whether a statement is in the language or not in the language. And the structure is less, there are sort of two phases. So in the first phase, what we do is we sample a lot of yes instances, okay? And then the algorithm constructs the corresponding matrices. In this case, it's just a vector because it's just one group element proof. It constructs the test matrices that the verify would use. And then we define a vector space that kind of takes all these good yes samples that would satisfy the verification equation, okay? So we'll generate a vector space, okay? And the idea is that if you sample enough, then we get sort of all possible solutions that you could think of in this vector space here, okay? Because, well, these matrices, they have polynomial dimensions. So eventually, if you keep sampling, you'll get more and more generators. At some point, they will start becoming linearly dependent and you've sampled all the solutions you could have in this space. Then in the second phase, the algorithm now looks at the statement that it wants to decide whether it's in language or not, right? And it simply samples this test equation and then it tries to solve whether it can find a solution in this vector space, okay? Is there some proof matrix or proof vector that will allow it to have something in the space? And if the answer is yes, it does find a solution. This is just a system of linear equations. So that's easy to solve, right? Then it will say yes. This is a statement in language. And if it cannot find a solution, it will say no, this is not in the language. So let's think about it. What if it's a yes sample? Well, there exists some witness. Prover doesn't know the witness, but by the existence of the witness, we could have constructed some proof vector. So there must be a solution, right? And the algorithm will find a solution. So it'll say yes. With high probability, it will be in the vector space and it will say yes. What if we are not in the language if Phi is not in the language? Well, by the completeness of the snark, then all these solutions that it samples will be correct. So anything it can find in the vector space corresponds to a solution to the verification equation, right? But by the soundness of the snark, if we have a statement none of the language should not be possible to find a solution, okay? And therefore, whatever it comes up with, any Pi vector it could think of, it must not lead to a solution, something that's in the vector space, and it should say no. So that gives us the lower bound that you cannot have one group element. You must have at least two group elements. Actually, you must have group elements both in source group one and in source group two because you cannot have a linear decision procedure, okay? Then I'll turn to the construction, okay? So I'll look at arithmetic circuit satisfiability. So I want to prove that I have some inputs and outputs to a circuit such that they respect all the multiplication and addition gates in the circuit, okay? And it will have perfect completeness that if the prover has a witness and it knows everything going on in the circuit, it's possible to convince the verifier. It'll have perfect zero knowledge that it does not leak any information about the witness that the prover has. And for soundness, I'll prove soundness in the generic group model. So I'll assume that we have an adversary that only uses generic group operation and show that such an adversary cannot break the scheme, okay? Again, for efficiency, I'm working in the asymmetric type three pairing setting and we'll get very low computation. We'll get very small proofs with just three group elements, okay? So let's look at an arithmetic circuit. So here's an example, right?  And you could think of maybe A1 is the statement, A2 is an output that's also part of the statement. What is the prover's witness? Well, that's A3 and A4, okay? Okay, so we can write this as a quadratic equation, okay? So this circuit is satisfied by all these A values if this equation here holds, okay? And notice here that it's very nice. We sort of get the addition gates for free. Actually, you just get one equation for every multiplication gate that you have. And generalize this a little, okay? So in general, we'll be looking at these sort of equations, quadratic equations that takes sums of the wire values with some weights, Ui, right? And then multiplies that to a sum of wire values with some weights, Vi, and hopes that the output is some sum of wire values with weights, Wi, okay? So in the equation before, the weights would be on the left-hand side, the Ui weights would be one for A1 and for A3 and zero for the other two, right? On the right-hand side, A3 would have weight, so V3 would be one, that's the weight of A3, right? And the other ones would be zero. And on the very right-hand side, we would have A2 has weight one and the other ones have zero. So that would give us this quadratic equation, okay? I'll use the convention that A0 is always one and that's to handle constants in these equations, okay? And an arithmetic circuit in this way defines an NP language that has statements A1 through AL and the rest of the wire values are witness values, okay? So I'll consider an equation then of this form here, okay?  If we just look at one equation to start with, okay? I'll define these polynomials, so I'll pick some R, I'll define polynomials such that these polynomials evaluate in R actually give us exactly these values here, okay? And then you can see that this equation is actually satisfied if these polynomial equation holds modulo x minus R, R. Why is that? Well, because if you plug R into these polynomials here, you get exactly those weights that we want for this equation, right? So R is a root in this equation here, okay? Now we pick such R's for every single equation that we have in this arithmetic circuit, okay? And we get that this way all the equations hold if this thing here is zero module that the product of all these roots here, okay? So what this is is actually a quadratic arithmetic program, right? So this is sort of a standard transformation from arithmetic circuits to quadratic arithmetic programs. And general quadratic arithmetic program is defined as a bunch of polynomials with some statements, some witnesses that correspond to these A values, okay? And they have to satisfy this polynomial equation. So that's an NP complete language and now we have a very efficient transformation from arithmetic circuits to quadratic arithmetic programs. Okay, so now I'll give the construction. I don't know a better way to present it than just give you all the gory details here and excuse myself with that. At least this is much more efficient and easy to understand than all the other constructions in the literature. Okay, so the idea is that you'll have common reference strings containing a bunch of different group elements and coding these polynomials in random alpha, beta, gamma, delta and X chosen by the setup algorithm. The prover will then create three values, A, B and C and encode these as group elements. And it turns out that it can do this just with linear group operations on the elements in the common reference string provided that it knows the witness. And then the verifier is going to accept this if this last equation here holds. Okay, so the verify pairs together A and B. It has alpha and beta in the common reference string pairs those together. This equation here can be seen as sort of loading the statement. So it takes the statement values which everybody can compute. Okay, and then we have something here in the very end, the C value to balance out everything. Okay, and completeness. Well, you look at the proof, plug it into the verification equation and you check very carefully that everything works out. Okay, for zero knowledge, that's actually pretty easy to see. What the simulator does, it picks A at random, it picks B at random. And that's just like it would be in a real proof because we have the R, delta and S, delta here that makes these completely random group elements. Okay, and then it computes the C that matches the verification equation and solves the verification equation. And that's a good simulation. And then for soundness, I'm not going to talk much about that. The model is that we have a generic group adversary and by very careful analysis of all these details here, you see that it is actually sound against a generic group adversary. Efficiency is pretty good, right? Because the proof is just three group elements, two elements in source group one and one element in source group two. Okay, so what we get here, so here I have a comparison with prior work and we can see that we have a smaller proof size and we also have more efficient computation for the prover and the verifier and we have less verification equations than previous works. Okay, now it's interesting to think about what is it that gives us this efficiency and that's sort of two sources, okay? First of all, one reason is that we're just using a more aggressive compilation technique than prior works, right? We're just proving soundness in a generic group model whereas prior works relied on various knowledge of exponent assumptions. And this is something you could apply to the other schemes and you would also reduce the complexity of these schemes. Okay, the second source and this is sort of the contribution, the interesting part is that we actually have a carefully crafted verification equation that does sort of carefully map out things into the two source groups and splits them apart and gives us just one verification equation instead of having many verification equations and that's sort of where there's also a saving coming from. And Alessandro and Madras are very nice to implement this in Lipsnark and report about factor four to five saving compared to prior work on the provers time in computing this and of course smaller size and so forth. And with that, I'll conclude with a summary, right? So we have a lower bond now that a pairing based snark has to have at least two group elements and then a construction that gives us a three group element snark and unfortunately there's still this open question, can we do two group elements and I just don't know. Okay, thank you. Thank you, we are a bit late so we don't have time for questions actually. We're gonna have to continue with the next talk immediately. So we have to take questions offline by the end. One next speaker is setting up, I can tell you that the next talk is entitled, Efficient Serial Knowledge Arguments for Arithmetic Circuits in a Discrete Lock Setting. This is by Jonathan Buulu, Andrea Tiroli, Pyrrhus Scheiders, Jens Groth and Christoph Petit. And it looks like Pyrrhus is going to give the talk once he's set up.


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