WEBVTT Kind: captions Language: en 00:00:01.160 --> 00:00:06.690 align:start position:0% [Music] 00:00:06.690 --> 00:00:06.700 align:start position:0% 00:00:06.700 --> 00:00:09.110 align:start position:0% [Music] 00:00:09.110 --> 00:00:09.120 align:start position:0% [Music] 00:00:09.120 --> 00:00:15.150 align:start position:0% [Music] PA 00:00:15.150 --> 00:00:15.160 align:start position:0% 00:00:15.160 --> 00:00:18.830 align:start position:0% please<00:00:16.160> um<00:00:16.680> uh<00:00:16.800> so<00:00:17.039> hello<00:00:17.560> everybody<00:00:18.560> uh<00:00:18.680> so 00:00:18.830 --> 00:00:18.840 align:start position:0% please um uh so hello everybody uh so 00:00:18.840 --> 00:00:21.670 align:start position:0% please um uh so hello everybody uh so today<00:00:19.080> I'm<00:00:19.199> going<00:00:19.400> to<00:00:19.680> present<00:00:20.039> to<00:00:20.359> you<00:00:21.359> uh<00:00:21.519> the 00:00:21.670 --> 00:00:21.680 align:start position:0% today I'm going to present to you uh the 00:00:21.680 --> 00:00:24.150 align:start position:0% today I'm going to present to you uh the tech<00:00:21.960> we<00:00:22.119> developed<00:00:22.720> to<00:00:23.160> uh<00:00:23.279> develop<00:00:23.760> the 00:00:24.150 --> 00:00:24.160 align:start position:0% tech we developed to uh develop the 00:00:24.160 --> 00:00:26.870 align:start position:0% tech we developed to uh develop the proof<00:00:24.480> system<00:00:25.000> of<00:00:25.199> linear<00:00:26.119> linear<00:00:26.519> actually 00:00:26.870 --> 00:00:26.880 align:start position:0% proof system of linear linear actually 00:00:26.880 --> 00:00:29.349 align:start position:0% proof system of linear linear actually use<00:00:27.640> many<00:00:28.000> many<00:00:28.359> different<00:00:28.679> proof<00:00:29.000> systems 00:00:29.349 --> 00:00:29.359 align:start position:0% use many many different proof systems 00:00:29.359 --> 00:00:31.390 align:start position:0% use many many different proof systems for<00:00:29.679> many<00:00:30.039> different<00:00:30.359> use<00:00:30.640> cases<00:00:30.920> it's<00:00:31.199> it<00:00:31.279> is 00:00:31.390 --> 00:00:31.400 align:start position:0% for many different use cases it's it is 00:00:31.400 --> 00:00:33.630 align:start position:0% for many different use cases it's it is a<00:00:31.599> complex<00:00:32.040> system<00:00:33.040> what<00:00:33.160> I'm<00:00:33.280> going<00:00:33.440> to 00:00:33.630 --> 00:00:33.640 align:start position:0% a complex system what I'm going to 00:00:33.640 --> 00:00:36.709 align:start position:0% a complex system what I'm going to present<00:00:33.920> to<00:00:34.079> you<00:00:34.719> is<00:00:35.360> uh<00:00:35.480> the<00:00:35.680> one<00:00:36.120> the<00:00:36.480> main 00:00:36.709 --> 00:00:36.719 align:start position:0% present to you is uh the one the main 00:00:36.719 --> 00:00:38.190 align:start position:0% present to you is uh the one the main one<00:00:36.960> that<00:00:37.120> we<00:00:37.239> use<00:00:37.480> for<00:00:37.680> proving<00:00:38.040> the 00:00:38.190 --> 00:00:38.200 align:start position:0% one that we use for proving the 00:00:38.200 --> 00:00:41.990 align:start position:0% one that we use for proving the execution<00:00:38.719> so<00:00:38.920> concretely<00:00:39.440> proving<00:00:40.200> evm 00:00:41.990 --> 00:00:42.000 align:start position:0% execution so concretely proving evm 00:00:42.000 --> 00:00:44.910 align:start position:0% execution so concretely proving evm execution<00:00:43.000> so<00:00:43.640> uh<00:00:43.800> I<00:00:43.879> should<00:00:44.280> present<00:00:44.600> myself 00:00:44.910 --> 00:00:44.920 align:start position:0% execution so uh I should present myself 00:00:44.920 --> 00:00:47.670 align:start position:0% execution so uh I should present myself I'm<00:00:45.199> alexand<00:00:46.199> uh<00:00:46.360> I've<00:00:46.640> been<00:00:46.960> working<00:00:47.320> in<00:00:47.480> this 00:00:47.670 --> 00:00:47.680 align:start position:0% I'm alexand uh I've been working in this 00:00:47.680 --> 00:00:50.830 align:start position:0% I'm alexand uh I've been working in this space<00:00:47.920> for<00:00:48.120> seven<00:00:48.440> years<00:00:48.800> now<00:00:49.800> uh<00:00:50.120> and<00:00:50.360> been 00:00:50.830 --> 00:00:50.840 align:start position:0% space for seven years now uh and been 00:00:50.840 --> 00:00:52.750 align:start position:0% space for seven years now uh and been focused<00:00:51.199> on<00:00:51.360> cryptography<00:00:51.960> for<00:00:52.160> five<00:00:52.399> years 00:00:52.750 --> 00:00:52.760 align:start position:0% focused on cryptography for five years 00:00:52.760 --> 00:00:56.549 align:start position:0% focused on cryptography for five years now<00:00:53.840> uh<00:00:54.840> I've<00:00:55.039> been<00:00:55.239> working<00:00:55.520> on<00:00:55.719> Linea<00:00:56.199> since 00:00:56.549 --> 00:00:56.559 align:start position:0% now uh I've been working on Linea since 00:00:56.559 --> 00:00:58.790 align:start position:0% now uh I've been working on Linea since the<00:00:56.760> beginning<00:00:57.239> even<00:00:58.079> and<00:00:58.239> doing<00:00:58.480> research 00:00:58.790 --> 00:00:58.800 align:start position:0% the beginning even and doing research 00:00:58.800 --> 00:01:01.150 align:start position:0% the beginning even and doing research and<00:00:58.960> roll<00:00:59.199> up<00:00:59.359> even<00:00:59.559> before<00:00:59.760> that 00:01:01.150 --> 00:01:01.160 align:start position:0% and roll up even before that 00:01:01.160 --> 00:01:03.670 align:start position:0% and roll up even before that uh<00:01:01.960> so<00:01:02.199> yeah<00:01:02.399> just<00:01:02.559> to<00:01:02.879> talk<00:01:03.160> a<00:01:03.280> little<00:01:03.480> bit 00:01:03.670 --> 00:01:03.680 align:start position:0% uh so yeah just to talk a little bit 00:01:03.680 --> 00:01:07.469 align:start position:0% uh so yeah just to talk a little bit about 00:01:07.469 --> 00:01:07.479 align:start position:0% 00:01:07.479 --> 00:01:11.590 align:start position:0% myself<00:01:08.479> okay<00:01:08.720> so<00:01:09.720> uh<00:01:10.680> uh<00:01:10.840> I'd<00:01:10.960> like<00:01:11.119> to<00:01:11.280> involve 00:01:11.590 --> 00:01:11.600 align:start position:0% myself okay so uh uh I'd like to involve 00:01:11.600 --> 00:01:14.070 align:start position:0% myself okay so uh uh I'd like to involve the<00:01:11.720> audience<00:01:12.040> a<00:01:12.159> little<00:01:12.400> bit<00:01:12.759> who<00:01:12.960> knows<00:01:13.840> uh 00:01:14.070 --> 00:01:14.080 align:start position:0% the audience a little bit who knows uh 00:01:14.080 --> 00:01:17.749 align:start position:0% the audience a little bit who knows uh What<00:01:14.560> uh<00:01:14.960> zvk<00:01:15.680> evm 00:01:17.749 --> 00:01:17.759 align:start position:0% What uh zvk evm 00:01:17.759 --> 00:01:20.630 align:start position:0% What uh zvk evm is<00:01:18.759> right<00:01:18.920> so<00:01:19.119> that's<00:01:19.640> a<00:01:19.799> good<00:01:20.000> half<00:01:20.320> a<00:01:20.439> good 00:01:20.630 --> 00:01:20.640 align:start position:0% is right so that's a good half a good 00:01:20.640 --> 00:01:25.109 align:start position:0% is right so that's a good half a good third<00:01:21.640> um<00:01:22.040> so<00:01:22.240> a<00:01:22.439> zvm<00:01:23.200> layer<00:01:23.680> is<00:01:24.280> uh<00:01:24.640> a<00:01:24.799> layer 00:01:25.109 --> 00:01:25.119 align:start position:0% third um so a zvm layer is uh a layer 00:01:25.119 --> 00:01:26.030 align:start position:0% third um so a zvm layer is uh a layer two 00:01:26.030 --> 00:01:26.040 align:start position:0% two 00:01:26.040 --> 00:01:30.149 align:start position:0% two solution<00:01:27.040> uh<00:01:27.360> which<00:01:27.799> is<00:01:28.360> whose<00:01:28.640> purpose<00:01:29.159> is<00:01:29.320> to 00:01:30.149 --> 00:01:30.159 align:start position:0% solution uh which is whose purpose is to 00:01:30.159 --> 00:01:33.389 align:start position:0% solution uh which is whose purpose is to help<00:01:30.560> ethereum<00:01:31.560> scalability<00:01:32.560> the<00:01:32.720> idea<00:01:33.119> is 00:01:33.389 --> 00:01:33.399 align:start position:0% help ethereum scalability the idea is 00:01:33.399 --> 00:01:35.469 align:start position:0% help ethereum scalability the idea is instead<00:01:33.720> of<00:01:33.840> sending<00:01:34.320> transactions<00:01:35.040> on<00:01:35.200> the 00:01:35.469 --> 00:01:35.479 align:start position:0% instead of sending transactions on the 00:01:35.479 --> 00:01:37.670 align:start position:0% instead of sending transactions on the ethereum<00:01:35.960> main<00:01:36.200> net<00:01:36.439> you<00:01:36.600> send<00:01:36.880> them<00:01:37.360> to<00:01:37.560> a 00:01:37.670 --> 00:01:37.680 align:start position:0% ethereum main net you send them to a 00:01:37.680 --> 00:01:41.950 align:start position:0% ethereum main net you send them to a certain<00:01:38.000> party<00:01:38.600> linear<00:01:39.520> linear<00:01:40.040> runs<00:01:40.920> uh<00:01:41.759> an 00:01:41.950 --> 00:01:41.960 align:start position:0% certain party linear linear runs uh an 00:01:41.960 --> 00:01:44.429 align:start position:0% certain party linear linear runs uh an ethereum<00:01:42.439> virtual<00:01:42.840> machine<00:01:43.840> will<00:01:44.079> process 00:01:44.429 --> 00:01:44.439 align:start position:0% ethereum virtual machine will process 00:01:44.439 --> 00:01:46.630 align:start position:0% ethereum virtual machine will process the<00:01:44.680> transaction<00:01:45.680> it<00:01:45.880> will<00:01:46.040> be<00:01:46.200> processed 00:01:46.630 --> 00:01:46.640 align:start position:0% the transaction it will be processed 00:01:46.640 --> 00:01:48.910 align:start position:0% the transaction it will be processed separately<00:01:47.200> from<00:01:47.360> the<00:01:47.479> main<00:01:47.719> net<00:01:47.960> so<00:01:48.560> the 00:01:48.910 --> 00:01:48.920 align:start position:0% separately from the main net so the 00:01:48.920 --> 00:01:50.469 align:start position:0% separately from the main net so the contracts<00:01:49.360> that<00:01:49.479> are<00:01:49.600> deployed<00:01:49.960> on<00:01:50.079> Main<00:01:50.280> net 00:01:50.469 --> 00:01:50.479 align:start position:0% contracts that are deployed on Main net 00:01:50.479 --> 00:01:52.830 align:start position:0% contracts that are deployed on Main net are<00:01:50.600> not<00:01:50.799> the<00:01:50.920> same<00:01:51.520> necessarily<00:01:52.200> the<00:01:52.320> same<00:01:52.719> as 00:01:52.830 --> 00:01:52.840 align:start position:0% are not the same necessarily the same as 00:01:52.840 --> 00:01:54.550 align:start position:0% are not the same necessarily the same as the<00:01:52.960> on<00:01:53.159> that<00:01:53.280> are<00:01:53.439> deployed<00:01:53.799> on<00:01:53.960> linear<00:01:54.399> the 00:01:54.550 --> 00:01:54.560 align:start position:0% the on that are deployed on linear the 00:01:54.560 --> 00:01:55.990 align:start position:0% the on that are deployed on linear the state<00:01:54.880> are 00:01:55.990 --> 00:01:56.000 align:start position:0% state are 00:01:56.000 --> 00:01:58.709 align:start position:0% state are separated<00:01:57.000> uh<00:01:57.640> but<00:01:57.799> we<00:01:57.920> can<00:01:58.079> bridge<00:01:58.439> between 00:01:58.709 --> 00:01:58.719 align:start position:0% separated uh but we can bridge between 00:01:58.719 --> 00:02:00.870 align:start position:0% separated uh but we can bridge between the<00:01:58.880> two<00:01:59.240> I'm<00:01:59.360> not<00:01:59.520> going<00:01:59.920> to<00:02:00.200> describe<00:02:00.719> much 00:02:00.870 --> 00:02:00.880 align:start position:0% the two I'm not going to describe much 00:02:00.880 --> 00:02:03.990 align:start position:0% the two I'm not going to describe much more<00:02:01.200> how<00:02:01.360> we<00:02:01.560> bridge<00:02:02.159> between<00:02:02.520> ethereum<00:02:03.360> and 00:02:03.990 --> 00:02:04.000 align:start position:0% more how we bridge between ethereum and 00:02:04.000 --> 00:02:07.550 align:start position:0% more how we bridge between ethereum and iner<00:02:05.000> uh<00:02:05.320> but<00:02:05.560> what<00:02:05.719> is<00:02:06.399> uh<00:02:06.560> important<00:02:07.079> to<00:02:07.439> uh 00:02:07.550 --> 00:02:07.560 align:start position:0% iner uh but what is uh important to uh 00:02:07.560 --> 00:02:09.550 align:start position:0% iner uh but what is uh important to uh remember<00:02:08.160> here<00:02:08.319> is<00:02:08.479> that<00:02:08.959> we<00:02:09.160> basically 00:02:09.550 --> 00:02:09.560 align:start position:0% remember here is that we basically 00:02:09.560 --> 00:02:12.030 align:start position:0% remember here is that we basically bundle<00:02:10.119> the<00:02:10.319> execution<00:02:10.879> of<00:02:11.039> many<00:02:11.360> transaction 00:02:12.030 --> 00:02:12.040 align:start position:0% bundle the execution of many transaction 00:02:12.040 --> 00:02:14.670 align:start position:0% bundle the execution of many transaction and<00:02:12.239> submit<00:02:12.879> one<00:02:13.120> proof<00:02:13.440> at<00:02:13.560> the<00:02:13.680> end<00:02:14.280> we<00:02:14.519> give 00:02:14.670 --> 00:02:14.680 align:start position:0% and submit one proof at the end we give 00:02:14.680 --> 00:02:17.710 align:start position:0% and submit one proof at the end we give you<00:02:14.920> one<00:02:15.160> number<00:02:16.120> uh<00:02:16.239> every<00:02:16.800> finalization 00:02:17.710 --> 00:02:17.720 align:start position:0% you one number uh every finalization 00:02:17.720 --> 00:02:20.710 align:start position:0% you one number uh every finalization finalizes<00:02:18.440> on<00:02:18.680> average<00:02:19.200> 65,000<00:02:20.200> transaction 00:02:20.710 --> 00:02:20.720 align:start position:0% finalizes on average 65,000 transaction 00:02:20.720 --> 00:02:24.390 align:start position:0% finalizes on average 65,000 transaction at<00:02:21.040> once<00:02:22.040> uh<00:02:22.360> and<00:02:23.040> since<00:02:23.720> uh<00:02:23.879> we<00:02:24.000> are<00:02:24.120> using 00:02:24.390 --> 00:02:24.400 align:start position:0% at once uh and since uh we are using 00:02:24.400 --> 00:02:27.030 align:start position:0% at once uh and since uh we are using snack<00:02:24.840> proof<00:02:25.120> systems<00:02:26.000> meaning<00:02:26.480> they<00:02:26.680> have<00:02:26.879> a 00:02:27.030 --> 00:02:27.040 align:start position:0% snack proof systems meaning they have a 00:02:27.040 --> 00:02:29.229 align:start position:0% snack proof systems meaning they have a very<00:02:27.200> short<00:02:27.519> very<00:02:28.120> time<00:02:28.560> which<00:02:28.680> is<00:02:28.879> mostly 00:02:29.229 --> 00:02:29.239 align:start position:0% very short very time which is mostly 00:02:29.239 --> 00:02:31.110 align:start position:0% very short very time which is mostly independent<00:02:30.080> from<00:02:30.280> how<00:02:30.400> many<00:02:30.640> transactions 00:02:31.110 --> 00:02:31.120 align:start position:0% independent from how many transactions 00:02:31.120 --> 00:02:34.309 align:start position:0% independent from how many transactions are<00:02:31.480> executed<00:02:32.480> that's<00:02:32.720> how<00:02:32.920> we<00:02:33.120> get 00:02:34.309 --> 00:02:34.319 align:start position:0% are executed that's how we get 00:02:34.319 --> 00:02:37.070 align:start position:0% are executed that's how we get scalability<00:02:35.319> verifying<00:02:36.319> the<00:02:36.440> final<00:02:36.800> proof 00:02:37.070 --> 00:02:37.080 align:start position:0% scalability verifying the final proof 00:02:37.080 --> 00:02:39.750 align:start position:0% scalability verifying the final proof which<00:02:37.200> is<00:02:37.319> a<00:02:37.480> PL<00:02:37.760> proof<00:02:38.080> TX<00:02:38.920> uh<00:02:39.040> a<00:02:39.159> few 00:02:39.750 --> 00:02:39.760 align:start position:0% which is a PL proof TX uh a few 00:02:39.760 --> 00:02:42.470 align:start position:0% which is a PL proof TX uh a few milliseconds<00:02:40.760> but<00:02:41.159> it's<00:02:41.360> for<00:02:41.599> 65,000 00:02:42.470 --> 00:02:42.480 align:start position:0% milliseconds but it's for 65,000 00:02:42.480 --> 00:02:44.070 align:start position:0% milliseconds but it's for 65,000 transaction<00:02:42.959> so<00:02:43.159> that's<00:02:43.400> why<00:02:43.680> it's<00:02:43.879> much 00:02:44.070 --> 00:02:44.080 align:start position:0% transaction so that's why it's much 00:02:44.080 --> 00:02:47.390 align:start position:0% transaction so that's why it's much cheaper<00:02:44.519> and<00:02:44.720> that's<00:02:45.239> how<00:02:45.800> uh<00:02:46.159> the<00:02:46.400> kvms<00:02:47.120> can 00:02:47.390 --> 00:02:47.400 align:start position:0% cheaper and that's how uh the kvms can 00:02:47.400 --> 00:02:51.869 align:start position:0% cheaper and that's how uh the kvms can achieve<00:02:48.040> a<00:02:48.319> much<00:02:48.519> lower<00:02:48.840> gas 00:02:51.869 --> 00:02:51.879 align:start position:0% 00:02:51.879 --> 00:02:56.110 align:start position:0% price<00:02:52.879> all<00:02:53.120> right<00:02:54.080> uh<00:02:54.440> so<00:02:54.720> maybe<00:02:54.959> a<00:02:55.080> few<00:02:55.280> word 00:02:56.110 --> 00:02:56.120 align:start position:0% price all right uh so maybe a few word 00:02:56.120 --> 00:03:02.070 align:start position:0% price all right uh so maybe a few word uh<00:02:56.800> on<00:02:57.440> um<00:02:57.800> on<00:02:57.959> zkp<00:02:58.400> and<00:02:58.840> snar<00:02:59.920> zkps<00:03:00.920> uh<00:03:01.200> I<00:03:01.280> mean 00:03:02.070 --> 00:03:02.080 align:start position:0% uh on um on zkp and snar zkps uh I mean 00:03:02.080 --> 00:03:04.869 align:start position:0% uh on um on zkp and snar zkps uh I mean usually<00:03:02.680> we<00:03:03.159> say<00:03:03.480> zkp<00:03:04.000> but<00:03:04.159> most<00:03:04.360> of<00:03:04.480> the<00:03:04.640> time 00:03:04.869 --> 00:03:04.879 align:start position:0% usually we say zkp but most of the time 00:03:04.879 --> 00:03:07.710 align:start position:0% usually we say zkp but most of the time what<00:03:05.000> we<00:03:05.159> use<00:03:05.400> in<00:03:05.560> production<00:03:06.120> are<00:03:06.840> ZK 00:03:07.710 --> 00:03:07.720 align:start position:0% what we use in production are ZK 00:03:07.720 --> 00:03:11.190 align:start position:0% what we use in production are ZK argument<00:03:08.200> of<00:03:08.640> knowledge<00:03:09.640> uh<00:03:10.040> and<00:03:10.519> in<00:03:10.640> order<00:03:11.000> to 00:03:11.190 --> 00:03:11.200 align:start position:0% argument of knowledge uh and in order to 00:03:11.200 --> 00:03:13.630 align:start position:0% argument of knowledge uh and in order to for<00:03:11.400> a<00:03:11.599> protocol<00:03:12.120> to<00:03:12.239> be<00:03:12.640> uh<00:03:12.840> Z<00:03:13.080> key<00:03:13.239> argument 00:03:13.630 --> 00:03:13.640 align:start position:0% for a protocol to be uh Z key argument 00:03:13.640 --> 00:03:16.149 align:start position:0% for a protocol to be uh Z key argument of<00:03:13.799> knowledge<00:03:14.440> it<00:03:14.599> needs<00:03:14.920> three<00:03:15.280> property<00:03:16.000> you 00:03:16.149 --> 00:03:16.159 align:start position:0% of knowledge it needs three property you 00:03:16.159 --> 00:03:18.750 align:start position:0% of knowledge it needs three property you need<00:03:17.000> zero<00:03:17.360> knowledge<00:03:17.959> zero<00:03:18.239> knowledge<00:03:18.560> means 00:03:18.750 --> 00:03:18.760 align:start position:0% need zero knowledge zero knowledge means 00:03:18.760 --> 00:03:21.070 align:start position:0% need zero knowledge zero knowledge means that<00:03:18.920> the<00:03:19.040> proof<00:03:19.280> does<00:03:19.480> not<00:03:19.840> reveal<00:03:20.239> more<00:03:20.840> than 00:03:21.070 --> 00:03:21.080 align:start position:0% that the proof does not reveal more than 00:03:21.080 --> 00:03:24.110 align:start position:0% that the proof does not reveal more than what<00:03:21.239> it<00:03:21.360> should<00:03:21.599> reveal<00:03:22.440> you<00:03:22.640> need<00:03:23.040> to<00:03:23.319> have 00:03:24.110 --> 00:03:24.120 align:start position:0% what it should reveal you need to have 00:03:24.120 --> 00:03:25.910 align:start position:0% what it should reveal you need to have completeness<00:03:24.879> meaning<00:03:25.239> that<00:03:25.400> if<00:03:25.519> you<00:03:25.599> want<00:03:25.760> to 00:03:25.910 --> 00:03:25.920 align:start position:0% completeness meaning that if you want to 00:03:25.920 --> 00:03:27.270 align:start position:0% completeness meaning that if you want to prove<00:03:26.200> something<00:03:26.560> that<00:03:26.680> is<00:03:26.799> true<00:03:27.000> you<00:03:27.080> should 00:03:27.270 --> 00:03:27.280 align:start position:0% prove something that is true you should 00:03:27.280 --> 00:03:31.190 align:start position:0% prove something that is true you should always<00:03:27.640> be<00:03:28.560> capable<00:03:29.040> of<00:03:29.200> generating<00:03:30.200> proof 00:03:31.190 --> 00:03:31.200 align:start position:0% always be capable of generating proof 00:03:31.200 --> 00:03:33.149 align:start position:0% always be capable of generating proof meaning<00:03:31.560> for<00:03:31.720> instance<00:03:32.040> if<00:03:32.159> you<00:03:32.319> want<00:03:32.480> to<00:03:32.879> know 00:03:33.149 --> 00:03:33.159 align:start position:0% meaning for instance if you want to know 00:03:33.159 --> 00:03:35.350 align:start position:0% meaning for instance if you want to know that<00:03:33.280> you<00:03:33.400> prove<00:03:33.640> the<00:03:33.799> square<00:03:34.040> root<00:03:34.319> of<00:03:35.159> some 00:03:35.350 --> 00:03:35.360 align:start position:0% that you prove the square root of some 00:03:35.360 --> 00:03:36.949 align:start position:0% that you prove the square root of some number<00:03:35.680> it<00:03:35.799> should<00:03:36.000> work<00:03:36.200> for<00:03:36.400> every<00:03:36.599> number 00:03:36.949 --> 00:03:36.959 align:start position:0% number it should work for every number 00:03:36.959 --> 00:03:40.949 align:start position:0% number it should work for every number and<00:03:37.120> not<00:03:37.360> just<00:03:37.840> your<00:03:38.040> favor<00:03:38.920> just<00:03:39.280> one<00:03:39.959> number 00:03:40.949 --> 00:03:40.959 align:start position:0% and not just your favor just one number 00:03:40.959 --> 00:03:43.789 align:start position:0% and not just your favor just one number and<00:03:41.439> the<00:03:41.640> most<00:03:41.879> important<00:03:42.360> one<00:03:42.840> is<00:03:43.480> uh 00:03:43.789 --> 00:03:43.799 align:start position:0% and the most important one is uh 00:03:43.799 --> 00:03:46.589 align:start position:0% and the most important one is uh argument<00:03:44.560> is<00:03:45.080> knowledge<00:03:45.480> sness<00:03:46.200> or 00:03:46.589 --> 00:03:46.599 align:start position:0% argument is knowledge sness or 00:03:46.599 --> 00:03:48.229 align:start position:0% argument is knowledge sness or essentially<00:03:47.200> computational<00:03:47.879> knowledge 00:03:48.229 --> 00:03:48.239 align:start position:0% essentially computational knowledge 00:03:48.239 --> 00:03:52.190 align:start position:0% essentially computational knowledge sness<00:03:49.000> it<00:03:49.159> is<00:03:49.640> how<00:03:49.840> you<00:03:50.000> say<00:03:50.360> that<00:03:51.000> you<00:03:51.200> know 00:03:52.190 --> 00:03:52.200 align:start position:0% sness it is how you say that you know 00:03:52.200 --> 00:03:55.270 align:start position:0% sness it is how you say that you know that<00:03:52.360> you<00:03:52.519> prove<00:03:52.799> that<00:03:52.959> you<00:03:53.120> know<00:03:54.120> uh<00:03:55.079> what 00:03:55.270 --> 00:03:55.280 align:start position:0% that you prove that you know uh what 00:03:55.280 --> 00:03:56.910 align:start position:0% that you prove that you know uh what you're<00:03:55.680> proving<00:03:56.079> you 00:03:56.910 --> 00:03:56.920 align:start position:0% you're proving you 00:03:56.920 --> 00:04:01.589 align:start position:0% you're proving you know<00:03:57.920> um<00:03:58.200> and<00:03:58.360> so<00:03:59.840> as<00:03:59.959> I<00:04:00.120> mentioned<00:04:00.519> earlier<00:04:01.360> uh 00:04:01.589 --> 00:04:01.599 align:start position:0% know um and so as I mentioned earlier uh 00:04:01.599 --> 00:04:04.750 align:start position:0% know um and so as I mentioned earlier uh we<00:04:01.920> are<00:04:02.640> building<00:04:02.959> a<00:04:03.159> ZK<00:04:03.480> VM<00:04:04.040> but<00:04:04.239> really<00:04:04.560> the 00:04:04.750 --> 00:04:04.760 align:start position:0% we are building a ZK VM but really the 00:04:04.760 --> 00:04:07.630 align:start position:0% we are building a ZK VM but really the ZK<00:04:05.360> is<00:04:05.640> not<00:04:06.480> it's<00:04:06.640> not<00:04:06.840> about<00:04:07.079> zero<00:04:07.360> knowledge 00:04:07.630 --> 00:04:07.640 align:start position:0% ZK is not it's not about zero knowledge 00:04:07.640 --> 00:04:09.670 align:start position:0% ZK is not it's not about zero knowledge or<00:04:07.799> hiding<00:04:08.120> things<00:04:08.400> it's<00:04:08.599> really<00:04:09.319> about 00:04:09.670 --> 00:04:09.680 align:start position:0% or hiding things it's really about 00:04:09.680 --> 00:04:12.229 align:start position:0% or hiding things it's really about proving<00:04:10.159> that<00:04:10.360> we<00:04:10.760> know<00:04:11.400> valid<00:04:11.799> execution 00:04:12.229 --> 00:04:12.239 align:start position:0% proving that we know valid execution 00:04:12.239 --> 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verification to be suent to be<00:04:19.880> small<00:04:20.759> and<00:04:20.959> we<00:04:21.199> want<00:04:22.199> uh<00:04:22.479> also<00:04:23.320> the 00:04:23.510 --> 00:04:23.520 align:start position:0% be small and we want uh also the 00:04:23.520 --> 00:04:25.310 align:start position:0% be small and we want uh also the verification<00:04:24.199> the<00:04:24.400> protocol<00:04:24.880> to<00:04:25.000> be<00:04:25.120> non 00:04:25.310 --> 00:04:25.320 align:start position:0% verification the protocol to be non 00:04:25.320 --> 00:04:27.110 align:start position:0% verification the protocol to be non interactive<00:04:25.840> it<00:04:25.919> should<00:04:26.080> be<00:04:26.360> a<00:04:26.479> single<00:04:26.840> proof 00:04:27.110 --> 00:04:27.120 align:start position:0% interactive it should be a single proof 00:04:27.120 --> 00:04:29.070 align:start position:0% interactive it should be a single proof a<00:04:27.240> single<00:04:27.600> message<00:04:28.000> and<00:04:28.400> from<00:04:28.639> that<00:04:28.800> we<00:04:28.880> should 00:04:29.070 --> 00:04:29.080 align:start position:0% a single message and from that we should 00:04:29.080 --> 00:04:33.110 align:start position:0% a single message and from that we should be<00:04:29.280> capable<00:04:29.800> of<00:04:30.360> verifying<00:04:31.360> uh 00:04:33.110 --> 00:04:33.120 align:start position:0% be capable of verifying uh 00:04:33.120 --> 00:04:36.469 align:start position:0% be capable of verifying uh approve<00:04:34.120> okay<00:04:34.280> so<00:04:34.520> let's<00:04:34.800> apply<00:04:35.199> all<00:04:35.440> that<00:04:35.639> to 00:04:36.469 --> 00:04:36.479 align:start position:0% approve okay so let's apply all that to 00:04:36.479 --> 00:04:39.110 align:start position:0% approve okay so let's apply all that to uh<00:04:36.680> the<00:04:36.919> evm<00:04:37.919> uh<00:04:38.039> the<00:04:38.240> etherum<00:04:38.759> virtual 00:04:39.110 --> 00:04:39.120 align:start position:0% uh the evm uh the etherum virtual 00:04:39.120 --> 00:04:41.629 align:start position:0% uh the evm uh the etherum virtual machine<00:04:39.759> is<00:04:40.120> a<00:04:40.639> state 00:04:41.629 --> 00:04:41.639 align:start position:0% machine is a state 00:04:41.639 --> 00:04:45.110 align:start position:0% machine is a state machine<00:04:42.639> uh<00:04:42.960> you<00:04:43.160> on<00:04:43.400> which<00:04:43.600> we<00:04:43.759> can<00:04:44.080> execute 00:04:45.110 --> 00:04:45.120 align:start position:0% machine uh you on which we can execute 00:04:45.120 --> 00:04:48.950 align:start position:0% machine uh you on which we can execute code<00:04:46.120> uh<00:04:46.440> and<00:04:46.720> a<00:04:46.960> transaction<00:04:47.479> in<00:04:47.680> zvm<00:04:48.199> is<00:04:48.440> like 00:04:48.950 --> 00:04:48.960 align:start position:0% code uh and a transaction in zvm is like 00:04:48.960 --> 00:04:52.189 align:start position:0% code uh and a transaction in zvm is like an<00:04:49.160> instruction<00:04:49.840> from<00:04:50.039> the<00:04:50.680> user<00:04:51.680> uh<00:04:51.840> of<00:04:52.039> that 00:04:52.189 --> 00:04:52.199 align:start position:0% an instruction from the user uh of that 00:04:52.199 --> 00:04:55.070 align:start position:0% an instruction from the user uh of that virtual<00:04:52.600> machine<00:04:53.560> uh<00:04:53.840> it<00:04:54.039> has<00:04:54.199> a<00:04:54.360> lot<00:04:54.680> it<00:04:54.800> is 00:04:55.070 --> 00:04:55.080 align:start position:0% virtual machine uh it has a lot it is 00:04:55.080 --> 00:04:57.510 align:start position:0% virtual machine uh it has a lot it is specialized<00:04:55.600> for<00:04:55.759> running<00:04:56.039> smart<00:04:56.520> contract 00:04:57.510 --> 00:04:57.520 align:start position:0% specialized for running smart contract 00:04:57.520 --> 00:05:00.430 align:start position:0% specialized for running smart contract it<00:04:57.840> has<00:04:58.199> a<00:04:58.360> lot<00:04:58.560> and<00:04:58.720> a<00:04:58.840> lot<00:04:59.039> of<00:04:59.199> features<00:04:59.840> and 00:05:00.430 --> 00:05:00.440 align:start position:0% it has a lot and a lot of features and 00:05:00.440 --> 00:05:02.950 align:start position:0% it has a lot and a lot of features and that<00:05:00.840> interact<00:05:01.680> in<00:05:01.800> a<00:05:02.000> complex<00:05:02.400> way<00:05:02.639> between 00:05:02.950 --> 00:05:02.960 align:start position:0% that interact in a complex way between 00:05:02.960 --> 00:05:07.110 align:start position:0% that interact in a complex way between each<00:05:03.240> other<00:05:04.240> and<00:05:04.960> uh<00:05:05.639> and<00:05:05.880> not<00:05:06.680> every 00:05:07.110 --> 00:05:07.120 align:start position:0% each other and uh and not every 00:05:07.120 --> 00:05:08.909 align:start position:0% each other and uh and not every computation<00:05:07.759> that<00:05:07.880> are<00:05:08.120> easy<00:05:08.360> to<00:05:08.520> do<00:05:08.680> on<00:05:08.800> the 00:05:08.909 --> 00:05:08.919 align:start position:0% computation that are easy to do on the 00:05:08.919 --> 00:05:11.350 align:start position:0% computation that are easy to do on the evm<00:05:09.320> are<00:05:09.560> necessarily<00:05:10.199> easy<00:05:10.440> to<00:05:10.639> prove<00:05:10.919> so<00:05:11.120> for 00:05:11.350 --> 00:05:11.360 align:start position:0% evm are necessarily easy to prove so for 00:05:11.360 --> 00:05:14.029 align:start position:0% evm are necessarily easy to prove so for instance<00:05:12.360> I'm<00:05:12.560> thinking<00:05:12.919> about<00:05:13.160> the<00:05:13.360> Kash 00:05:14.029 --> 00:05:14.039 align:start position:0% instance I'm thinking about the Kash 00:05:14.039 --> 00:05:16.469 align:start position:0% instance I'm thinking about the Kash function<00:05:14.440> that<00:05:14.680> very<00:05:14.880> smart<00:05:15.160> contract<00:05:15.840> uses 00:05:16.469 --> 00:05:16.479 align:start position:0% function that very smart contract uses 00:05:16.479 --> 00:05:19.390 align:start position:0% function that very smart contract uses all<00:05:16.680> the<00:05:16.919> time<00:05:17.759> like<00:05:17.919> it's<00:05:18.120> free<00:05:19.000> it's<00:05:19.160> really 00:05:19.390 --> 00:05:19.400 align:start position:0% all the time like it's free it's really 00:05:19.400 --> 00:05:21.189 align:start position:0% all the time like it's free it's really not<00:05:19.560> free<00:05:19.840> to 00:05:21.189 --> 00:05:21.199 align:start position:0% not free to 00:05:21.199 --> 00:05:24.550 align:start position:0% not free to prove<00:05:22.199> um<00:05:22.600> and<00:05:22.840> and<00:05:22.919> so<00:05:23.080> if<00:05:23.199> we<00:05:23.400> want<00:05:23.720> to<00:05:24.240> solve 00:05:24.550 --> 00:05:24.560 align:start position:0% prove um and and so if we want to solve 00:05:24.560 --> 00:05:26.870 align:start position:0% prove um and and so if we want to solve that<00:05:24.840> problem<00:05:25.840> uh<00:05:25.919> so<00:05:26.120> of<00:05:26.240> course<00:05:26.440> we<00:05:26.560> need<00:05:26.720> to 00:05:26.870 --> 00:05:26.880 align:start position:0% that problem uh so of course we need to 00:05:26.880 --> 00:05:28.870 align:start position:0% that problem uh so of course we need to deal<00:05:27.120> with<00:05:27.280> the<00:05:27.520> inent<00:05:28.080> complexity<00:05:28.600> of<00:05:28.759> the 00:05:28.870 --> 00:05:28.880 align:start position:0% deal with the inent complexity of the 00:05:28.880 --> 00:05:31.189 align:start position:0% deal with the inent complexity of the evm<00:05:29.240> but<00:05:29.360> we<00:05:29.759> so<00:05:30.080> need<00:05:30.280> a<00:05:30.440> proof<00:05:30.720> system<00:05:31.080> that 00:05:31.189 --> 00:05:31.199 align:start position:0% evm but we so need a proof system that 00:05:31.199 --> 00:05:33.629 align:start position:0% evm but we so need a proof system that is<00:05:31.360> flexible<00:05:31.919> enough<00:05:32.240> to<00:05:32.759> solve<00:05:33.199> all<00:05:33.400> the 00:05:33.629 --> 00:05:33.639 align:start position:0% is flexible enough to solve all the 00:05:33.639 --> 00:05:35.550 align:start position:0% is flexible enough to solve all the problem<00:05:34.080> that<00:05:34.240> we<00:05:34.360> need<00:05:34.479> to<00:05:34.639> solve<00:05:34.919> to<00:05:35.160> execute 00:05:35.550 --> 00:05:35.560 align:start position:0% problem that we need to solve to execute 00:05:35.560 --> 00:05:36.189 align:start position:0% problem that we need to solve to execute the 00:05:36.189 --> 00:05:36.199 align:start position:0% the 00:05:36.199 --> 00:05:37.830 align:start position:0% the evm 00:05:37.830 --> 00:05:37.840 align:start position:0% evm 00:05:37.840 --> 00:05:42.189 align:start position:0% evm concretely<00:05:38.840> um<00:05:39.560> in<00:05:39.680> order<00:05:40.000> to<00:05:40.520> prove<00:05:40.800> the<00:05:41.199> evm 00:05:42.189 --> 00:05:42.199 align:start position:0% concretely um in order to prove the evm 00:05:42.199 --> 00:05:44.749 align:start position:0% concretely um in order to prove the evm we<00:05:42.360> have<00:05:42.639> traces<00:05:43.639> of<00:05:43.840> execution<00:05:44.440> that<00:05:44.560> are 00:05:44.749 --> 00:05:44.759 align:start position:0% we have traces of execution that are 00:05:44.759 --> 00:05:47.070 align:start position:0% we have traces of execution that are instantiated<00:05:45.520> by<00:05:45.919> polinomial<00:05:46.520> we<00:05:46.680> call<00:05:46.880> them 00:05:47.070 --> 00:05:47.080 align:start position:0% instantiated by polinomial we call them 00:05:47.080 --> 00:05:48.309 align:start position:0% instantiated by polinomial we call them colon<00:05:47.479> in<00:05:47.600> our 00:05:48.309 --> 00:05:48.319 align:start position:0% colon in our 00:05:48.319 --> 00:05:52.390 align:start position:0% colon in our framework<00:05:49.319> uh<00:05:49.639> and<00:05:50.560> it<00:05:51.080> could<00:05:51.319> be<00:05:51.639> summed<00:05:52.039> up 00:05:52.390 --> 00:05:52.400 align:start position:0% framework uh and it could be summed up 00:05:52.400 --> 00:05:54.629 align:start position:0% framework uh and it could be summed up as<00:05:52.720> a<00:05:52.919> collection<00:05:53.360> of<00:05:53.520> airs<00:05:53.880> that<00:05:54.080> communicate 00:05:54.629 --> 00:05:54.639 align:start position:0% as a collection of airs that communicate 00:05:54.639 --> 00:05:57.150 align:start position:0% as a collection of airs that communicate with<00:05:54.840> each<00:05:55.000> other<00:05:55.360> by<00:05:55.520> sub<00:05:56.039> argument<00:05:57.039> and 00:05:57.150 --> 00:05:57.160 align:start position:0% with each other by sub argument and 00:05:57.160 --> 00:05:58.749 align:start position:0% with each other by sub argument and there<00:05:57.280> are<00:05:57.440> many<00:05:57.759> different<00:05:58.120> sub<00:05:58.360> argument 00:05:58.749 --> 00:05:58.759 align:start position:0% there are many different sub argument 00:05:58.759 --> 00:06:00.270 align:start position:0% there are many different sub argument that<00:05:58.880> are<00:05:59.120> possible<00:05:59.400> to<00:05:59.720> use<00:05:59.880> we<00:05:59.960> can<00:06:00.120> have 00:06:00.270 --> 00:06:00.280 align:start position:0% that are possible to use we can have 00:06:00.280 --> 00:06:03.189 align:start position:0% that are possible to use we can have lookups<00:06:01.080> we<00:06:01.199> can<00:06:01.360> have<00:06:01.560> projection<00:06:02.199> queries 00:06:03.189 --> 00:06:03.199 align:start position:0% lookups we can have projection queries 00:06:03.199 --> 00:06:05.430 align:start position:0% lookups we can have projection queries uh<00:06:03.360> we<00:06:03.520> also<00:06:03.800> support<00:06:04.440> variance<00:06:04.840> of<00:06:05.000> lookups 00:06:05.430 --> 00:06:05.440 align:start position:0% uh we also support variance of lookups 00:06:05.440 --> 00:06:07.070 align:start position:0% uh we also support variance of lookups that<00:06:05.560> we<00:06:05.680> call<00:06:06.120> conditional<00:06:06.479> lookup<00:06:06.919> or 00:06:07.070 --> 00:06:07.080 align:start position:0% that we call conditional lookup or 00:06:07.080 --> 00:06:08.589 align:start position:0% that we call conditional lookup or fractional 00:06:08.589 --> 00:06:08.599 align:start position:0% fractional 00:06:08.599 --> 00:06:12.189 align:start position:0% fractional lookups<00:06:09.599> um<00:06:10.199> and<00:06:10.639> so<00:06:10.840> in<00:06:10.960> order<00:06:11.240> to<00:06:11.680> make<00:06:11.919> this 00:06:12.189 --> 00:06:12.199 align:start position:0% lookups um and so in order to make this 00:06:12.199 --> 00:06:13.950 align:start position:0% lookups um and so in order to make this work<00:06:12.479> we<00:06:12.599> need<00:06:12.840> a<00:06:13.000> proof<00:06:13.280> system<00:06:13.639> that<00:06:13.759> is 00:06:13.950 --> 00:06:13.960 align:start position:0% work we need a proof system that is 00:06:13.960 --> 00:06:16.350 align:start position:0% work we need a proof system that is really<00:06:14.280> flexible<00:06:14.840> and<00:06:15.039> can<00:06:15.199> deal<00:06:15.440> with<00:06:16.160> all 00:06:16.350 --> 00:06:16.360 align:start position:0% really flexible and can deal with all 00:06:16.360 --> 00:06:18.670 align:start position:0% really flexible and can deal with all the<00:06:16.680> polymorphism<00:06:17.560> that<00:06:17.680> is<00:06:17.840> inherent<00:06:18.319> to 00:06:18.670 --> 00:06:18.680 align:start position:0% the polymorphism that is inherent to 00:06:18.680 --> 00:06:24.270 align:start position:0% the polymorphism that is inherent to proving<00:06:19.680> uh<00:06:19.919> linear<00:06:20.440> arithmetization 00:06:24.270 --> 00:06:24.280 align:start position:0% 00:06:24.280 --> 00:06:27.589 align:start position:0% okay<00:06:25.280> so<00:06:25.639> in<00:06:25.759> order<00:06:26.000> to<00:06:26.160> do<00:06:26.319> that<00:06:26.520> we<00:06:26.720> designed 00:06:27.589 --> 00:06:27.599 align:start position:0% okay so in order to do that we designed 00:06:27.599 --> 00:06:30.950 align:start position:0% okay so in order to do that we designed uh<00:06:27.960> the<00:06:28.160> with<00:06:28.599> framework<00:06:29.280> which<00:06:29.400> is<00:06:29.639> is<00:06:30.639> uh<00:06:30.800> the 00:06:30.950 --> 00:06:30.960 align:start position:0% uh the with framework which is is uh the 00:06:30.960 --> 00:06:34.510 align:start position:0% uh the with framework which is is uh the main<00:06:31.720> uh<00:06:32.199> um<00:06:32.680> the<00:06:32.840> main<00:06:33.120> gateway<00:06:33.599> between 00:06:34.510 --> 00:06:34.520 align:start position:0% main uh um the main gateway between 00:06:34.520 --> 00:06:36.230 align:start position:0% main uh um the main gateway between describing<00:06:35.080> the<00:06:35.240> constraints<00:06:35.680> to<00:06:35.840> represent 00:06:36.230 --> 00:06:36.240 align:start position:0% describing the constraints to represent 00:06:36.240 --> 00:06:38.469 align:start position:0% describing the constraints to represent evm<00:06:36.680> and<00:06:36.919> actually<00:06:37.280> proving 00:06:38.469 --> 00:06:38.479 align:start position:0% evm and actually proving 00:06:38.479 --> 00:06:40.950 align:start position:0% evm and actually proving things<00:06:39.479> uh<00:06:39.639> it<00:06:39.840> has<00:06:40.000> a<00:06:40.199> very<00:06:40.599> neat 00:06:40.950 --> 00:06:40.960 align:start position:0% things uh it has a very neat 00:06:40.960 --> 00:06:43.589 align:start position:0% things uh it has a very neat particularity<00:06:41.840> is<00:06:42.039> that<00:06:43.000> in<00:06:43.120> the<00:06:43.280> wiard 00:06:43.589 --> 00:06:43.599 align:start position:0% particularity is that in the wiard 00:06:43.599 --> 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commit<00:06:51.880> to<00:06:52.039> things<00:06:52.360> or<00:06:52.599> how<00:06:52.960> which 00:06:53.230 --> 00:06:53.240 align:start position:0% going to commit to things or how which 00:06:53.240 --> 00:06:55.150 align:start position:0% going to commit to things or how which argument<00:06:53.680> you're<00:06:53.880> going<00:06:54.039> to<00:06:54.360> you<00:06:54.479> just<00:06:54.680> say 00:06:55.150 --> 00:06:55.160 align:start position:0% argument you're going to you just say 00:06:55.160 --> 00:06:56.830 align:start position:0% argument you're going to you just say what<00:06:55.280> you<00:06:55.479> want<00:06:55.960> and<00:06:56.120> then<00:06:56.240> you<00:06:56.360> have<00:06:56.479> a<00:06:56.639> list 00:06:56.830 --> 00:06:56.840 align:start position:0% what you want and then you have a list 00:06:56.840 --> 00:06:59.589 align:start position:0% what you want and then you have a list of<00:06:57.039> technique<00:06:57.440> like<00:06:57.599> a<00:06:57.960> menu<00:06:58.960> uh<00:06:59.160> which<00:06:59.280> you 00:06:59.589 --> 00:06:59.599 align:start position:0% of technique like a menu uh which you 00:06:59.599 --> 00:07:02.869 align:start position:0% of technique like a menu uh which you apply<00:06:59.919> to<00:07:00.199> that<00:07:00.919> uh<00:07:01.400> protocol<00:07:01.919> statement<00:07:02.720> and 00:07:02.869 --> 00:07:02.879 align:start position:0% apply to that uh protocol statement and 00:07:02.879 --> 00:07:05.950 align:start position:0% apply to that uh protocol statement and it<00:07:03.000> will<00:07:03.479> create<00:07:03.800> for<00:07:04.000> you<00:07:04.440> uh<00:07:04.680> a<00:07:04.840> proof<00:07:05.160> system 00:07:05.950 --> 00:07:05.960 align:start position:0% it will create for you uh a proof system 00:07:05.960 --> 00:07:08.670 align:start position:0% it will create for you uh a proof system as<00:07:06.120> complicated<00:07:06.879> as<00:07:07.039> you<00:07:07.160> need<00:07:07.360> it<00:07:07.560> to<00:07:07.680> be<00:07:08.560> and 00:07:08.670 --> 00:07:08.680 align:start position:0% as complicated as you need it to be and 00:07:08.680 --> 00:07:11.189 align:start position:0% as complicated as you need it to be and so<00:07:08.840> that's<00:07:09.080> perfect<00:07:09.400> for<00:07:09.599> us<00:07:10.319> it<00:07:10.560> turns<00:07:10.879> out 00:07:11.189 --> 00:07:11.199 align:start position:0% so that's perfect for us it turns out 00:07:11.199 --> 00:07:14.230 align:start position:0% so that's perfect for us it turns out that<00:07:11.400> this<00:07:11.599> is<00:07:11.919> how<00:07:12.199> in<00:07:12.479> Academia<00:07:13.479> they 00:07:14.230 --> 00:07:14.240 align:start position:0% that this is how in Academia they 00:07:14.240 --> 00:07:17.469 align:start position:0% that this is how in Academia they describe<00:07:15.240> uh<00:07:16.039> complex<00:07:16.479> protocol<00:07:17.000> like<00:07:17.160> if<00:07:17.280> you 00:07:17.469 --> 00:07:17.479 align:start position:0% describe uh complex protocol like if you 00:07:17.479 --> 00:07:21.830 align:start position:0% describe uh complex protocol like if you take<00:07:17.720> for<00:07:18.759> example<00:07:19.759> uh<00:07:19.879> the<00:07:20.039> grow<00:07:20.400> 16<00:07:21.280> uh<00:07:21.400> proof 00:07:21.830 --> 00:07:21.840 align:start position:0% take for example uh the grow 16 uh proof 00:07:21.840 --> 00:07:24.749 align:start position:0% take for example uh the grow 16 uh proof system<00:07:22.840> uh<00:07:23.000> if<00:07:23.120> you<00:07:23.639> had<00:07:23.800> a<00:07:23.960> look<00:07:24.120> at<00:07:24.240> the<00:07:24.400> paper 00:07:24.749 --> 00:07:24.759 align:start position:0% system uh if you had a look at the paper 00:07:24.759 --> 00:07:26.990 align:start position:0% system uh if you had a look at the paper before<00:07:25.039> you<00:07:25.160> would<00:07:25.360> see<00:07:25.599> that<00:07:25.879> they<00:07:26.400> say<00:07:26.800> okay 00:07:26.990 --> 00:07:27.000 align:start position:0% before you would see that they say okay 00:07:27.000 --> 00:07:28.710 align:start position:0% before you would see that they say okay so<00:07:27.280> this<00:07:27.400> is<00:07:27.520> the<00:07:27.680> constraint<00:07:28.160> system<00:07:28.440> at<00:07:28.599> the 00:07:28.710 --> 00:07:28.720 align:start position:0% so this is the constraint system at the 00:07:28.720 --> 00:07:30.710 align:start position:0% so this is the constraint system at the beginning<00:07:29.120> then<00:07:29.319> we<00:07:29.800> do<00:07:30.039> something<00:07:30.440> that<00:07:30.599> is 00:07:30.710 --> 00:07:30.720 align:start position:0% beginning then we do something that is 00:07:30.720 --> 00:07:33.070 align:start position:0% beginning then we do something that is called<00:07:30.960> qap<00:07:31.919> and<00:07:32.039> then<00:07:32.199> we<00:07:32.360> do<00:07:32.520> something<00:07:32.919> that 00:07:33.070 --> 00:07:33.080 align:start position:0% called qap and then we do something that 00:07:33.080 --> 00:07:36.270 align:start position:0% called qap and then we do something that is<00:07:33.240> called<00:07:33.599> NP<00:07:34.599> and<00:07:34.800> then<00:07:35.360> uh<00:07:35.479> in<00:07:35.720> continuous 00:07:36.270 --> 00:07:36.280 align:start position:0% is called NP and then uh in continuous 00:07:36.280 --> 00:07:37.990 align:start position:0% is called NP and then uh in continuous and<00:07:36.520> at<00:07:36.639> the<00:07:36.759> end<00:07:36.919> you<00:07:37.039> have<00:07:37.199> a<00:07:37.400> conrete<00:07:37.759> proof 00:07:37.990 --> 00:07:38.000 align:start position:0% and at the end you have a conrete proof 00:07:38.000 --> 00:07:40.430 align:start position:0% and at the end you have a conrete proof system<00:07:38.319> which<00:07:38.440> is<00:07:38.520> a<00:07:38.639> gross<00:07:38.919> 16<00:07:39.280> proof<00:07:39.520> system 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implementation so what we do is that we actually<00:07:53.919> Implement<00:07:54.479> every<00:07:54.800> possible<00:07:55.199> step 00:07:56.189 --> 00:07:56.199 align:start position:0% actually Implement every possible step 00:07:56.199 --> 00:07:58.029 align:start position:0% actually Implement every possible step so<00:07:56.440> that<00:07:56.759> this<00:07:56.960> step<00:07:57.199> can<00:07:57.319> be<00:07:57.479> reused<00:07:57.879> for 00:07:58.029 --> 00:07:58.039 align:start position:0% so that this step can be reused for 00:07:58.039 --> 00:08:00.629 align:start position:0% so that this step can be reused for other<00:07:58.280> proof<00:07:58.599> systems<00:07:59.759> and<00:08:00.000> we<00:08:00.120> don't<00:08:00.319> have<00:08:00.479> to 00:08:00.629 --> 00:08:00.639 align:start position:0% other proof systems and we don't have to 00:08:00.639 --> 00:08:02.270 align:start position:0% other proof systems and we don't have to really<00:08:00.919> mentally<00:08:01.319> work<00:08:01.560> out<00:08:01.759> with<00:08:01.879> the<00:08:02.080> work 00:08:02.270 --> 00:08:02.280 align:start position:0% really mentally work out with the work 00:08:02.280 --> 00:08:03.230 align:start position:0% really mentally work out with the work the<00:08:02.400> whole 00:08:03.230 --> 00:08:03.240 align:start position:0% the whole 00:08:03.240 --> 00:08:05.629 align:start position:0% the whole protocol<00:08:04.240> in<00:08:04.400> the<00:08:04.680> case<00:08:04.840> of<00:08:05.000> Lina<00:08:05.400> it<00:08:05.479> would 00:08:05.629 --> 00:08:05.639 align:start position:0% protocol in the case of Lina it would 00:08:05.639 --> 00:08:07.430 align:start position:0% protocol in the case of Lina it would just<00:08:05.759> be 00:08:07.430 --> 00:08:07.440 align:start position:0% just be 00:08:07.440 --> 00:08:09.909 align:start position:0% just be impossible<00:08:08.440> and<00:08:08.639> on<00:08:08.840> top<00:08:09.000> of<00:08:09.159> that<00:08:09.360> we<00:08:09.479> made<00:08:09.720> it 00:08:09.909 --> 00:08:09.919 align:start position:0% impossible and on top of that we made it 00:08:09.919 --> 00:08:12.270 align:start position:0% impossible and on top of that we made it in<00:08:10.080> such<00:08:10.280> a<00:08:10.440> way<00:08:10.720> that<00:08:11.039> if<00:08:11.240> anybody<00:08:11.639> wants<00:08:11.919> to 00:08:12.270 --> 00:08:12.280 align:start position:0% in such a way that if anybody wants to 00:08:12.280 --> 00:08:14.790 align:start position:0% in such a way that if anybody wants to add<00:08:12.960> their<00:08:13.120> own<00:08:13.400> compilers<00:08:14.039> or<00:08:14.240> do<00:08:14.440> their<00:08:14.599> own 00:08:14.790 --> 00:08:14.800 align:start position:0% add their own compilers or do their own 00:08:14.800 --> 00:08:17.430 align:start position:0% add their own compilers or do their own tweak<00:08:15.639> or<00:08:15.919> are<00:08:16.159> their<00:08:16.360> own<00:08:16.680> type<00:08:16.879> of 00:08:17.430 --> 00:08:17.440 align:start position:0% tweak or are their own type of 00:08:17.440 --> 00:08:20.350 align:start position:0% tweak or are their own type of constraints<00:08:18.440> uh<00:08:19.240> the<00:08:19.400> framework<00:08:19.879> will<00:08:20.039> allow 00:08:20.350 --> 00:08:20.360 align:start position:0% constraints uh the framework will allow 00:08:20.360 --> 00:08:23.629 align:start position:0% constraints uh the framework will allow that<00:08:20.639> without<00:08:20.919> changing<00:08:21.319> the<00:08:21.479> core<00:08:21.720> of 00:08:23.629 --> 00:08:23.639 align:start position:0% that without changing the core of 00:08:23.639 --> 00:08:27.149 align:start position:0% that without changing the core of it<00:08:24.639> all<00:08:24.800> right<00:08:24.960> so<00:08:25.280> as<00:08:25.400> I<00:08:25.520> mentioned<00:08:26.159> earlier 00:08:27.149 --> 00:08:27.159 align:start position:0% it all right so as I mentioned earlier 00:08:27.159 --> 00:08:29.790 align:start position:0% it all right so as I mentioned earlier the<00:08:27.319> proof<00:08:27.680> system<00:08:28.520> uh<00:08:28.680> the<00:08:28.879> protocol<00:08:29.639> that 00:08:29.790 --> 00:08:29.800 align:start position:0% the proof system uh the protocol that 00:08:29.800 --> 00:08:32.469 align:start position:0% the proof system uh the protocol that you<00:08:30.520> are<00:08:30.800> going<00:08:31.000> to<00:08:31.199> construct<00:08:32.039> you<00:08:32.159> have<00:08:32.279> to 00:08:32.469 --> 00:08:32.479 align:start position:0% you are going to construct you have to 00:08:32.479 --> 00:08:35.350 align:start position:0% you are going to construct you have to describe<00:08:32.880> it<00:08:33.080> in<00:08:33.200> an<00:08:33.399> ideal<00:08:33.800> model<00:08:34.800> and<00:08:35.080> this 00:08:35.350 --> 00:08:35.360 align:start position:0% describe it in an ideal model and this 00:08:35.360 --> 00:08:37.829 align:start position:0% describe it in an ideal model and this ideal<00:08:35.760> model<00:08:36.599> involves<00:08:37.120> what<00:08:37.279> we<00:08:37.479> call<00:08:37.719> the 00:08:37.829 --> 00:08:37.839 align:start position:0% ideal model involves what we call the 00:08:37.839 --> 00:08:41.909 align:start position:0% ideal model involves what we call the wizard<00:08:38.279> Oracle<00:08:39.279> the<00:08:39.440> wizard<00:08:39.800> Oracle<00:08:40.519> is<00:08:41.399> from 00:08:41.909 --> 00:08:41.919 align:start position:0% wizard Oracle the wizard Oracle is from 00:08:41.919 --> 00:08:43.350 align:start position:0% wizard Oracle the wizard Oracle is from the<00:08:42.080> point<00:08:42.279> of<00:08:42.440> view<00:08:42.640> of<00:08:42.719> the<00:08:42.880> protocol 00:08:43.350 --> 00:08:43.360 align:start position:0% the point of view of the protocol 00:08:43.360 --> 00:08:46.750 align:start position:0% the point of view of the protocol designer<00:08:43.919> a<00:08:44.200> trusted<00:08:44.640> third<00:08:45.000> party<00:08:45.959> it<00:08:46.160> knows 00:08:46.750 --> 00:08:46.760 align:start position:0% designer a trusted third party it knows 00:08:46.760 --> 00:08:48.670 align:start position:0% designer a trusted third party it knows everything<00:08:47.240> it<00:08:47.399> remembers<00:08:47.959> everything<00:08:48.519> it 00:08:48.670 --> 00:08:48.680 align:start position:0% everything it remembers everything it 00:08:48.680 --> 00:08:51.150 align:start position:0% everything it remembers everything it does<00:08:49.000> computation<00:08:49.560> for<00:08:49.800> free<00:08:50.399> it<00:08:50.519> is<00:08:50.720> always 00:08:51.150 --> 00:08:51.160 align:start position:0% does computation for free it is always 00:08:51.160 --> 00:08:55.350 align:start position:0% does computation for free it is always honest<00:08:52.160> it's<00:08:52.560> like<00:08:53.480> something<00:08:53.760> you<00:08:53.959> really<00:08:54.920> uh 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future<00:09:10.279> as<00:09:10.399> we<00:09:10.600> compile<00:09:10.959> the<00:09:11.079> protocol<00:09:11.839> so<00:09:12.040> the 00:09:12.190 --> 00:09:12.200 align:start position:0% future as we compile the protocol so the 00:09:12.200 --> 00:09:14.670 align:start position:0% future as we compile the protocol so the protocol<00:09:12.680> can<00:09:12.880> also<00:09:13.120> be<00:09:13.360> described<00:09:13.800> in<00:09:14.000> a 00:09:14.670 --> 00:09:14.680 align:start position:0% protocol can also be described in a 00:09:14.680 --> 00:09:16.910 align:start position:0% protocol can also be described in a multiun<00:09:15.399> fashion<00:09:16.000> I<00:09:16.120> mentioned<00:09:16.640> at<00:09:16.760> the 00:09:16.910 --> 00:09:16.920 align:start position:0% multiun fashion I mentioned at the 00:09:16.920 --> 00:09:19.190 align:start position:0% multiun fashion I mentioned at the beginning<00:09:17.279> that<00:09:17.399> we<00:09:17.519> need<00:09:17.720> non<00:09:18.200> interactivity 00:09:19.190 --> 00:09:19.200 align:start position:0% beginning that we need non interactivity 00:09:19.200 --> 00:09:21.470 align:start position:0% beginning that we need non interactivity but<00:09:19.360> the<00:09:19.560> protocols<00:09:20.040> s<00:09:20.320> this<00:09:20.480> out<00:09:20.760> using<00:09:21.320> the 00:09:21.470 --> 00:09:21.480 align:start position:0% but the protocols s this out using the 00:09:21.480 --> 00:09:24.910 align:start position:0% but the protocols s this out using the fat<00:09:21.880> Shamir<00:09:22.880> uh<00:09:23.399> the<00:09:23.560> fet<00:09:23.800> Shamir 00:09:24.910 --> 00:09:24.920 align:start position:0% fat Shamir uh the fet Shamir 00:09:24.920 --> 00:09:27.630 align:start position:0% fat Shamir uh the fet Shamir trick<00:09:25.920> uh<00:09:26.160> it<00:09:26.320> put<00:09:26.560> some<00:09:26.760> limitation<00:09:27.279> it<00:09:27.399> means 00:09:27.630 --> 00:09:27.640 align:start position:0% trick uh it put some limitation it means 00:09:27.640 --> 00:09:29.750 align:start position:0% trick uh it put some limitation it means that<00:09:27.760> the<00:09:27.880> verifier<00:09:28.360> can<00:09:28.480> only<00:09:28.720> send<00:09:29.399> random 00:09:29.750 --> 00:09:29.760 align:start position:0% that the verifier can only send random 00:09:29.760 --> 00:09:31.910 align:start position:0% that the verifier can only send random challenges<00:09:30.240> to<00:09:30.399> the<00:09:30.560> prover<00:09:31.360> but<00:09:31.560> that's<00:09:31.720> a 00:09:31.910 --> 00:09:31.920 align:start position:0% challenges to the prover but that's a 00:09:31.920 --> 00:09:33.870 align:start position:0% challenges to the prover but that's a common<00:09:32.200> limitation<00:09:32.760> that<00:09:32.959> every<00:09:33.360> protocol 00:09:33.870 --> 00:09:33.880 align:start position:0% common limitation that every protocol 00:09:33.880 --> 00:09:36.630 align:start position:0% common limitation that every protocol have<00:09:34.120> nowaday<00:09:34.600> it's<00:09:34.800> very<00:09:35.279> uncommon<00:09:35.839> to<00:09:36.399> be<00:09:36.560> in 00:09:36.630 --> 00:09:36.640 align:start position:0% have nowaday it's very uncommon to be in 00:09:36.640 --> 00:09:40.310 align:start position:0% have nowaday it's very uncommon to be in a<00:09:36.839> contrary<00:09:37.959> situation<00:09:38.959> and<00:09:39.120> so<00:09:39.440> essentially 00:09:40.310 --> 00:09:40.320 align:start position:0% a contrary situation and so essentially 00:09:40.320 --> 00:09:42.829 align:start position:0% a contrary situation and so essentially the<00:09:40.480> prover<00:09:40.920> can<00:09:41.200> use<00:09:41.480> the<00:09:41.600> Oracle<00:09:42.120> by<00:09:42.240> sending 00:09:42.829 --> 00:09:42.839 align:start position:0% the prover can use the Oracle by sending 00:09:42.839 --> 00:09:45.509 align:start position:0% the prover can use the Oracle by sending big<00:09:43.000> large<00:09:43.279> message<00:09:43.720> to<00:09:44.000> it<00:09:44.800> and<00:09:45.000> the<00:09:45.079> Oracle 00:09:45.509 --> 00:09:45.519 align:start position:0% big large message to it and the Oracle 00:09:45.519 --> 00:09:47.110 align:start position:0% big large message to it and the Oracle will<00:09:45.680> just<00:09:45.920> remember<00:09:46.360> and<00:09:46.519> notify<00:09:46.959> the 00:09:47.110 --> 00:09:47.120 align:start position:0% will just remember and notify the 00:09:47.120 --> 00:09:49.750 align:start position:0% will just remember and notify the verifier<00:09:47.720> that<00:09:47.959> hey<00:09:48.560> uh<00:09:48.680> the<00:09:48.839> pr<00:09:49.240> did<00:09:49.440> is<00:09:49.600> part 00:09:49.750 --> 00:09:49.760 align:start position:0% verifier that hey uh the pr did is part 00:09:49.760 --> 00:09:52.470 align:start position:0% verifier that hey uh the pr did is part of<00:09:49.880> the<00:09:50.040> work<00:09:50.279> you<00:09:50.399> can<00:09:50.560> ask<00:09:51.040> question<00:09:52.040> and<00:09:52.320> so 00:09:52.470 --> 00:09:52.480 align:start position:0% of the work you can ask question and so 00:09:52.480 --> 00:09:55.269 align:start position:0% of the work you can ask question and so the<00:09:52.600> verifier<00:09:53.079> can<00:09:53.360> ask<00:09:53.760> questions<00:09:54.760> and<00:09:55.079> the 00:09:55.269 --> 00:09:55.279 align:start position:0% the verifier can ask questions and the 00:09:55.279 --> 00:09:57.550 align:start position:0% the verifier can ask questions and the Oracle<00:09:55.720> respond<00:09:56.079> to<00:09:56.240> the<00:09:56.440> question<00:09:57.200> without 00:09:57.550 --> 00:09:57.560 align:start position:0% Oracle respond to the question without 00:09:57.560 --> 00:09:59.470 align:start position:0% Oracle respond to the question without needing<00:09:57.880> to<00:09:58.040> do<00:09:58.200> any<00:09:58.399> computation<00:09:58.920> it's<00:09:59.079> like 00:09:59.470 --> 00:09:59.480 align:start position:0% needing to do any computation it's like 00:09:59.480 --> 00:10:01.110 align:start position:0% needing to do any computation it's like a<00:09:59.600> god-like 00:10:01.110 --> 00:10:01.120 align:start position:0% a god-like 00:10:01.120 --> 00:10:03.710 align:start position:0% a god-like entity<00:10:02.120> uh<00:10:02.320> and<00:10:02.480> it<00:10:02.600> is<00:10:02.760> always 00:10:03.710 --> 00:10:03.720 align:start position:0% entity uh and it is always 00:10:03.720 --> 00:10:06.110 align:start position:0% entity uh and it is always honest<00:10:04.720> so<00:10:04.880> you<00:10:05.000> don't<00:10:05.240> have<00:10:05.360> to<00:10:05.519> worry<00:10:05.800> about 00:10:06.110 --> 00:10:06.120 align:start position:0% honest so you don't have to worry about 00:10:06.120 --> 00:10:08.110 align:start position:0% honest so you don't have to worry about him 00:10:08.110 --> 00:10:08.120 align:start position:0% him 00:10:08.120 --> 00:10:12.870 align:start position:0% him lying<00:10:09.120> so<00:10:09.959> uh<00:10:10.959> as<00:10:11.079> I<00:10:11.240> mentioned<00:10:11.959> the<00:10:12.160> prover 00:10:12.870 --> 00:10:12.880 align:start position:0% lying so uh as I mentioned the prover 00:10:12.880 --> 00:10:15.670 align:start position:0% lying so uh as I mentioned the prover the<00:10:13.040> verifier<00:10:13.800> and<00:10:13.920> the<00:10:14.040> orle<00:10:14.640> can<00:10:15.360> send 00:10:15.670 --> 00:10:15.680 align:start position:0% the verifier and the orle can send 00:10:15.680 --> 00:10:18.870 align:start position:0% the verifier and the orle can send messages<00:10:16.160> to<00:10:16.360> each<00:10:16.839> other<00:10:17.839> uh<00:10:18.160> and<00:10:18.440> here<00:10:18.640> comes 00:10:18.870 --> 00:10:18.880 align:start position:0% messages to each other uh and here comes 00:10:18.880 --> 00:10:20.630 align:start position:0% messages to each other uh and here comes the<00:10:19.040> first<00:10:19.360> primitive<00:10:19.839> of<00:10:19.959> the<00:10:20.120> framework 00:10:20.630 --> 00:10:20.640 align:start position:0% the first primitive of the framework 00:10:20.640 --> 00:10:23.150 align:start position:0% the first primitive of the framework which<00:10:20.760> is<00:10:20.920> what<00:10:21.040> we<00:10:21.200> call<00:10:21.959> uh<00:10:22.120> colons<00:10:22.959> so 00:10:23.150 --> 00:10:23.160 align:start position:0% which is what we call uh colons so 00:10:23.160 --> 00:10:26.230 align:start position:0% which is what we call uh colons so colons<00:10:23.680> can<00:10:23.880> be<00:10:24.240> of<00:10:24.519> any<00:10:24.760> sort<00:10:25.600> we<00:10:25.839> have<00:10:26.120> what 00:10:26.230 --> 00:10:26.240 align:start position:0% colons can be of any sort we have what 00:10:26.240 --> 00:10:28.389 align:start position:0% colons can be of any sort we have what we<00:10:26.399> call<00:10:26.760> commitment<00:10:27.360> committed<00:10:27.800> colon 00:10:28.389 --> 00:10:28.399 align:start position:0% we call commitment committed colon 00:10:28.399 --> 00:10:30.590 align:start position:0% we call commitment committed colon committed<00:10:28.839> colon<00:10:29.120> means<00:10:29.320> means<00:10:29.680> it<00:10:29.839> is<00:10:30.000> sent 00:10:30.590 --> 00:10:30.600 align:start position:0% committed colon means means it is sent 00:10:30.600 --> 00:10:32.069 align:start position:0% committed colon means means it is sent to<00:10:31.000> the 00:10:32.069 --> 00:10:32.079 align:start position:0% to the 00:10:32.079 --> 00:10:35.269 align:start position:0% to the Oracle<00:10:33.079> uh<00:10:33.720> and<00:10:33.959> basically<00:10:34.320> being<00:10:34.519> sent<00:10:34.800> to 00:10:35.269 --> 00:10:35.279 align:start position:0% Oracle uh and basically being sent to 00:10:35.279 --> 00:10:38.389 align:start position:0% Oracle uh and basically being sent to the<00:10:35.440> Oracle<00:10:36.160> means<00:10:37.160> uh<00:10:37.560> that<00:10:37.839> the<00:10:38.000> prover 00:10:38.389 --> 00:10:38.399 align:start position:0% the Oracle means uh that the prover 00:10:38.399 --> 00:10:40.230 align:start position:0% the Oracle means uh that the prover cannot<00:10:38.639> change<00:10:38.959> its<00:10:39.160> mind<00:10:39.519> about<00:10:39.839> what<00:10:40.079> was 00:10:40.230 --> 00:10:40.240 align:start position:0% cannot change its mind about what was 00:10:40.240 --> 00:10:42.230 align:start position:0% cannot change its mind about what was sent<00:10:40.519> to<00:10:40.639> the<00:10:40.760> orle<00:10:41.120> you<00:10:41.200> can<00:10:41.360> only<00:10:41.600> send 00:10:42.230 --> 00:10:42.240 align:start position:0% sent to the orle you can only send 00:10:42.240 --> 00:10:44.430 align:start position:0% sent to the orle you can only send something<00:10:42.720> once<00:10:43.000> to<00:10:43.160> the<00:10:43.279> orle<00:10:43.920> otherwise 00:10:44.430 --> 00:10:44.440 align:start position:0% something once to the orle otherwise 00:10:44.440 --> 00:10:45.710 align:start position:0% something once to the orle otherwise you're 00:10:45.710 --> 00:10:45.720 align:start position:0% you're 00:10:45.720 --> 00:10:48.069 align:start position:0% you're cheating<00:10:46.720> uh<00:10:46.839> and<00:10:47.000> the<00:10:47.200> protocol<00:10:47.639> will<00:10:47.800> always 00:10:48.069 --> 00:10:48.079 align:start position:0% cheating uh and the protocol will always 00:10:48.079 --> 00:10:49.550 align:start position:0% cheating uh and the protocol will always ensure 00:10:49.550 --> 00:10:49.560 align:start position:0% ensure 00:10:49.560 --> 00:10:52.110 align:start position:0% ensure that<00:10:50.560> uh<00:10:50.720> but<00:10:50.920> on<00:10:51.079> top<00:10:51.279> of<00:10:51.440> that<00:10:51.639> we<00:10:51.800> have<00:10:52.000> what 00:10:52.110 --> 00:10:52.120 align:start position:0% that uh but on top of that we have what 00:10:52.120 --> 00:10:53.790 align:start position:0% that uh but on top of that we have what we<00:10:52.279> call<00:10:52.519> pre-computed<00:10:53.279> colon<00:10:53.639> so 00:10:53.790 --> 00:10:53.800 align:start position:0% we call pre-computed colon so 00:10:53.800 --> 00:10:56.670 align:start position:0% we call pre-computed colon so precomputed<00:10:54.440> colons<00:10:55.279> are<00:10:56.160> they<00:10:56.279> can<00:10:56.440> be<00:10:56.560> of 00:10:56.670 --> 00:10:56.680 align:start position:0% precomputed colons are they can be of 00:10:56.680 --> 00:10:57.870 align:start position:0% precomputed colons are they can be of two<00:10:56.839> types<00:10:57.040> they<00:10:57.160> can<00:10:57.279> be<00:10:57.399> sent<00:10:57.639> to<00:10:57.720> the 00:10:57.870 --> 00:10:57.880 align:start position:0% two types they can be sent to the 00:10:57.880 --> 00:11:00.389 align:start position:0% two types they can be sent to the verifier<00:10:58.360> or<00:10:58.519> sent<00:10:58.760> to<00:10:58.880> the 00:11:00.389 --> 00:11:00.399 align:start position:0% verifier or sent to the 00:11:00.399 --> 00:11:03.110 align:start position:0% verifier or sent to the and<00:11:01.399> uh<00:11:01.560> they<00:11:01.680> are<00:11:01.839> known<00:11:02.240> beforehand<00:11:02.880> so 00:11:03.110 --> 00:11:03.120 align:start position:0% and uh they are known beforehand so 00:11:03.120 --> 00:11:04.949 align:start position:0% and uh they are known beforehand so that's<00:11:03.360> something<00:11:04.120> that<00:11:04.279> is<00:11:04.480> part<00:11:04.680> of<00:11:04.800> the 00:11:04.949 --> 00:11:04.959 align:start position:0% that's something that is part of the 00:11:04.959 --> 00:11:06.470 align:start position:0% that's something that is part of the protocol<00:11:05.440> description<00:11:05.959> actually<00:11:06.320> they 00:11:06.470 --> 00:11:06.480 align:start position:0% protocol description actually they 00:11:06.480 --> 00:11:08.350 align:start position:0% protocol description actually they always<00:11:06.760> have<00:11:06.920> the<00:11:07.040> same<00:11:07.360> values<00:11:08.000> you<00:11:08.160> can 00:11:08.350 --> 00:11:08.360 align:start position:0% always have the same values you can 00:11:08.360 --> 00:11:11.310 align:start position:0% always have the same values you can think<00:11:08.760> of<00:11:09.000> for<00:11:09.200> instance<00:11:09.560> the<00:11:10.120> plun<00:11:11.120> uh 00:11:11.310 --> 00:11:11.320 align:start position:0% think of for instance the plun uh 00:11:11.320 --> 00:11:13.310 align:start position:0% think of for instance the plun uh circuit<00:11:12.000> description<00:11:13.000> which<00:11:13.120> is 00:11:13.310 --> 00:11:13.320 align:start position:0% circuit description which is 00:11:13.320 --> 00:11:15.550 align:start position:0% circuit description which is instantiated<00:11:14.040> by<00:11:14.200> several<00:11:14.639> polinomial<00:11:15.360> we're 00:11:15.550 --> 00:11:15.560 align:start position:0% instantiated by several polinomial we're 00:11:15.560 --> 00:11:17.269 align:start position:0% instantiated by several polinomial we're going<00:11:15.760> to<00:11:15.959> see<00:11:16.200> how<00:11:16.360> we<00:11:16.440> can<00:11:16.600> Implement<00:11:17.000> plun 00:11:17.269 --> 00:11:17.279 align:start position:0% going to see how we can Implement plun 00:11:17.279 --> 00:11:20.389 align:start position:0% going to see how we can Implement plun in<00:11:17.399> 10<00:11:17.560> minute<00:11:18.560> uh<00:11:18.639> so<00:11:18.839> I'm<00:11:19.040> just<00:11:19.720> uh<00:11:19.959> pting 00:11:20.389 --> 00:11:20.399 align:start position:0% in 10 minute uh so I'm just uh pting 00:11:20.399 --> 00:11:23.150 align:start position:0% in 10 minute uh so I'm just uh pting myself<00:11:20.680> forward<00:11:21.079> a<00:11:21.200> little<00:11:21.440> bit<00:11:22.320> uh<00:11:22.519> you<00:11:22.680> need 00:11:23.150 --> 00:11:23.160 align:start position:0% myself forward a little bit uh you need 00:11:23.160 --> 00:11:25.750 align:start position:0% myself forward a little bit uh you need uh<00:11:23.360> those<00:11:23.560> colons<00:11:24.560> to<00:11:25.040> uh<00:11:25.160> as<00:11:25.360> part<00:11:25.519> of<00:11:25.639> the 00:11:25.750 --> 00:11:25.760 align:start position:0% uh those colons to uh as part of the 00:11:25.760 --> 00:11:28.069 align:start position:0% uh those colons to uh as part of the proving<00:11:26.120> keys<00:11:26.639> and<00:11:26.800> they<00:11:27.000> describe<00:11:27.399> the<00:11:27.480> plum 00:11:28.069 --> 00:11:28.079 align:start position:0% proving keys and they describe the plum 00:11:28.079 --> 00:11:30.750 align:start position:0% proving keys and they describe the plum circuits<00:11:29.079> and<00:11:29.320> on<00:11:29.399> top<00:11:29.560> of<00:11:29.720> that<00:11:29.839> you<00:11:30.000> can<00:11:30.399> send 00:11:30.750 --> 00:11:30.760 align:start position:0% circuits and on top of that you can send 00:11:30.760 --> 00:11:33.269 align:start position:0% circuits and on top of that you can send proofs<00:11:31.399> and<00:11:31.560> proofs<00:11:31.959> means<00:11:32.560> a<00:11:32.760> message<00:11:33.160> that 00:11:33.269 --> 00:11:33.279 align:start position:0% proofs and proofs means a message that 00:11:33.279 --> 00:11:35.509 align:start position:0% proofs and proofs means a message that is<00:11:33.440> sent<00:11:33.880> directly<00:11:34.279> to<00:11:34.440> the<00:11:34.600> verifier<00:11:35.399> and 00:11:35.509 --> 00:11:35.519 align:start position:0% is sent directly to the verifier and 00:11:35.519 --> 00:11:37.629 align:start position:0% is sent directly to the verifier and there<00:11:35.680> are<00:11:35.880> other<00:11:36.200> types<00:11:36.880> actually<00:11:37.279> we<00:11:37.440> have 00:11:37.629 --> 00:11:37.639 align:start position:0% there are other types actually we have 00:11:37.639 --> 00:11:41.190 align:start position:0% there are other types actually we have eight<00:11:37.920> types<00:11:38.440> of<00:11:38.720> different<00:11:39.639> variant<00:11:40.639> of 00:11:41.190 --> 00:11:41.200 align:start position:0% eight types of different variant of 00:11:41.200 --> 00:11:44.030 align:start position:0% eight types of different variant of colon<00:11:41.639> type<00:11:42.000> so<00:11:42.200> col<00:11:42.560> also<00:11:42.880> have<00:11:43.079> a<00:11:43.279> predefined 00:11:44.030 --> 00:11:44.040 align:start position:0% colon type so col also have a predefined 00:11:44.040 --> 00:11:48.430 align:start position:0% colon type so col also have a predefined size<00:11:44.920> can<00:11:45.079> be<00:11:45.360> one<00:11:45.959> it<00:11:46.519> has<00:11:47.240> b<00:11:47.440> a<00:11:47.600> power<00:11:47.839> of<00:11:48.000> two 00:11:48.430 --> 00:11:48.440 align:start position:0% size can be one it has b a power of two 00:11:48.440 --> 00:11:51.069 align:start position:0% size can be one it has b a power of two it's<00:11:48.680> due<00:11:48.880> to<00:11:49.040> a<00:11:49.480> limitation<00:11:50.480> uh<00:11:50.639> aurent 00:11:51.069 --> 00:11:51.079 align:start position:0% it's due to a limitation uh aurent 00:11:51.079 --> 00:11:52.590 align:start position:0% it's due to a limitation uh aurent limitation<00:11:51.519> in<00:11:51.639> the 00:11:52.590 --> 00:11:52.600 align:start position:0% limitation in the 00:11:52.600 --> 00:11:55.389 align:start position:0% limitation in the framework<00:11:53.600> uh<00:11:54.000> and<00:11:54.279> they<00:11:54.480> have<00:11:54.720> a<00:11:54.959> r 00:11:55.389 --> 00:11:55.399 align:start position:0% framework uh and they have a r 00:11:55.399 --> 00:11:59.670 align:start position:0% framework uh and they have a r assignment<00:11:56.040> and<00:11:56.200> the<00:11:56.360> r<00:11:57.079> uh<00:11:57.480> number<00:11:58.480> is 00:11:59.670 --> 00:11:59.680 align:start position:0% assignment and the r uh number is 00:11:59.680 --> 00:12:02.710 align:start position:0% assignment and the r uh number is essentially<00:12:00.200> describing<00:12:00.920> at<00:12:01.160> which<00:12:01.440> round<00:12:01.760> of 00:12:02.710 --> 00:12:02.720 align:start position:0% essentially describing at which round of 00:12:02.720 --> 00:12:08.110 align:start position:0% essentially describing at which round of interaction<00:12:03.720> the<00:12:03.920> colon<00:12:04.600> is<00:12:05.560> sated<00:12:06.360> by<00:12:06.480> the 00:12:08.110 --> 00:12:08.120 align:start position:0% interaction the colon is sated by the 00:12:08.120 --> 00:12:12.269 align:start position:0% interaction the colon is sated by the prover<00:12:09.120> so<00:12:09.839> that's<00:12:10.040> for<00:12:10.240> the<00:12:10.399> main<00:12:10.920> part<00:12:11.920> um 00:12:12.269 --> 00:12:12.279 align:start position:0% prover so that's for the main part um 00:12:12.279 --> 00:12:14.990 align:start position:0% prover so that's for the main part um and<00:12:12.440> then<00:12:12.680> as<00:12:12.839> I<00:12:13.040> said<00:12:13.800> uh<00:12:14.000> so<00:12:14.199> for<00:12:14.399> some<00:12:14.639> colon 00:12:14.990 --> 00:12:15.000 align:start position:0% and then as I said uh so for some colon 00:12:15.000 --> 00:12:17.069 align:start position:0% and then as I said uh so for some colon that<00:12:15.120> are<00:12:15.279> sent<00:12:15.519> to<00:12:15.680> the<00:12:15.800> Oracle<00:12:16.519> or<00:12:16.680> for<00:12:16.880> some 00:12:17.069 --> 00:12:17.079 align:start position:0% that are sent to the Oracle or for some 00:12:17.079 --> 00:12:19.069 align:start position:0% that are sent to the Oracle or for some groups<00:12:17.360> of<00:12:17.519> colons<00:12:17.839> that<00:12:17.959> are<00:12:18.079> sent<00:12:18.279> to<00:12:18.440> the 00:12:19.069 --> 00:12:19.079 align:start position:0% groups of colons that are sent to the 00:12:19.079 --> 00:12:22.069 align:start position:0% groups of colons that are sent to the Oracle<00:12:20.079> the<00:12:20.480> verifier<00:12:21.079> can<00:12:21.320> ask<00:12:21.600> questions 00:12:22.069 --> 00:12:22.079 align:start position:0% Oracle the verifier can ask questions 00:12:22.079 --> 00:12:25.790 align:start position:0% Oracle the verifier can ask questions about<00:12:22.360> these<00:12:22.560> colons<00:12:23.399> to<00:12:23.760> the<00:12:24.440> Oracle<00:12:25.440> so 00:12:25.790 --> 00:12:25.800 align:start position:0% about these colons to the Oracle so 00:12:25.800 --> 00:12:28.430 align:start position:0% about these colons to the Oracle so that's<00:12:26.000> what<00:12:26.160> we<00:12:26.279> call<00:12:26.720> queries<00:12:27.720> it's<00:12:28.240> the 00:12:28.430 --> 00:12:28.440 align:start position:0% that's what we call queries it's the 00:12:28.440 --> 00:12:31.269 align:start position:0% that's what we call queries it's the common<00:12:28.720> term<00:12:28.920> used<00:12:29.279> in<00:12:29.920> Academia<00:12:30.920> uh<00:12:31.079> if<00:12:31.160> you 00:12:31.269 --> 00:12:31.279 align:start position:0% common term used in Academia uh if you 00:12:31.279 --> 00:12:33.710 align:start position:0% common term used in Academia uh if you know<00:12:31.480> about<00:12:31.720> fries<00:12:32.160> they<00:12:32.320> do<00:12:33.040> uh<00:12:33.160> random 00:12:33.710 --> 00:12:33.720 align:start position:0% know about fries they do uh random 00:12:33.720 --> 00:12:35.590 align:start position:0% know about fries they do uh random position<00:12:34.160> opening<00:12:34.560> query<00:12:35.000> so<00:12:35.199> that's<00:12:35.440> what 00:12:35.590 --> 00:12:35.600 align:start position:0% position opening query so that's what 00:12:35.600 --> 00:12:37.710 align:start position:0% position opening query so that's what they<00:12:35.720> mean<00:12:36.000> when<00:12:36.240> they<00:12:36.720> mean<00:12:36.920> query<00:12:37.480> in 00:12:37.710 --> 00:12:37.720 align:start position:0% they mean when they mean query in 00:12:37.720 --> 00:12:40.269 align:start position:0% they mean when they mean query in polinomial<00:12:38.320> IOP<00:12:38.760> protocol<00:12:39.320> that<00:12:39.440> would<00:12:39.600> be 00:12:40.269 --> 00:12:40.279 align:start position:0% polinomial IOP protocol that would be 00:12:40.279 --> 00:12:44.189 align:start position:0% polinomial IOP protocol that would be univariate<00:12:41.360> openings<00:12:42.360> in<00:12:42.480> our<00:12:42.720> framework<00:12:43.639> we 00:12:44.189 --> 00:12:44.199 align:start position:0% univariate openings in our framework we 00:12:44.199 --> 00:12:47.069 align:start position:0% univariate openings in our framework we query<00:12:44.880> stands<00:12:45.440> for<00:12:46.079> at<00:12:46.240> the<00:12:46.360> same<00:12:46.600> time 00:12:47.069 --> 00:12:47.079 align:start position:0% query stands for at the same time 00:12:47.079 --> 00:12:49.590 align:start position:0% query stands for at the same time constraints<00:12:48.079> so<00:12:48.560> that<00:12:48.760> would<00:12:48.920> be<00:12:49.199> questions 00:12:49.590 --> 00:12:49.600 align:start position:0% constraints so that would be questions 00:12:49.600 --> 00:12:52.550 align:start position:0% constraints so that would be questions that<00:12:49.800> have<00:12:49.959> a<00:12:50.120> yes<00:12:50.279> or<00:12:50.480> no<00:12:50.720> answer<00:12:51.519> like<00:12:52.120> is 00:12:52.550 --> 00:12:52.560 align:start position:0% that have a yes or no answer like is 00:12:52.560 --> 00:12:54.310 align:start position:0% that have a yes or no answer like is this<00:12:52.839> value<00:12:53.199> the<00:12:53.360> square<00:12:53.639> of<00:12:53.800> this<00:12:53.959> other 00:12:54.310 --> 00:12:54.320 align:start position:0% this value the square of this other 00:12:54.320 --> 00:12:56.990 align:start position:0% this value the square of this other value<00:12:54.680> the<00:12:54.839> answer<00:12:55.199> can<00:12:55.760> always<00:12:56.040> be<00:12:56.240> yes<00:12:56.399> or<00:12:56.560> no 00:12:56.990 --> 00:12:57.000 align:start position:0% value the answer can always be yes or no 00:12:57.000 --> 00:13:01.189 align:start position:0% value the answer can always be yes or no most<00:12:57.199> of<00:12:57.360> the<00:12:57.560> time<00:12:58.000> it<00:12:58.120> is<00:12:58.639> sough<00:12:59.360> as<00:12:59.480> a 00:13:01.189 --> 00:13:01.199 align:start position:0% most of the time it is sough as a 00:13:01.199 --> 00:13:04.269 align:start position:0% most of the time it is sough as a constraint<00:13:02.199> uh<00:13:02.480> and<00:13:02.720> here<00:13:02.959> we<00:13:03.600> describe<00:13:04.040> it<00:13:04.160> as 00:13:04.269 --> 00:13:04.279 align:start position:0% constraint uh and here we describe it as 00:13:04.279 --> 00:13:05.110 align:start position:0% constraint uh and here we describe it as a 00:13:05.110 --> 00:13:05.120 align:start position:0% a 00:13:05.120 --> 00:13:08.670 align:start position:0% a query<00:13:06.120> and<00:13:06.399> and<00:13:06.519> so<00:13:06.720> we<00:13:06.880> and<00:13:07.000> we<00:13:07.160> also<00:13:07.680> have 00:13:08.670 --> 00:13:08.680 align:start position:0% query and and so we and we also have 00:13:08.680 --> 00:13:11.110 align:start position:0% query and and so we and we also have open<00:13:09.399> questions<00:13:09.920> that<00:13:10.079> are<00:13:10.320> like<00:13:10.600> polinomial 00:13:11.110 --> 00:13:11.120 align:start position:0% open questions that are like polinomial 00:13:11.120 --> 00:13:14.670 align:start position:0% open questions that are like polinomial opening<00:13:11.639> position<00:13:12.279> opening<00:13:13.279> uh<00:13:13.399> and<00:13:13.560> so<00:13:13.839> these 00:13:14.670 --> 00:13:14.680 align:start position:0% opening position opening uh and so these 00:13:14.680 --> 00:13:17.590 align:start position:0% opening position opening uh and so these have<00:13:15.680> uh<00:13:16.000> expect<00:13:16.279> a<00:13:16.519> response<00:13:17.040> for<00:13:17.279> from<00:13:17.440> the 00:13:17.590 --> 00:13:17.600 align:start position:0% have uh expect a response for from the 00:13:17.600 --> 00:13:21.470 align:start position:0% have uh expect a response for from the orle<00:13:18.079> that<00:13:18.199> is<00:13:18.399> other<00:13:18.720> than<00:13:18.959> yes<00:13:19.079> or<00:13:19.760> no<00:13:20.760> um<00:13:21.279> so 00:13:21.470 --> 00:13:21.480 align:start position:0% orle that is other than yes or no um so 00:13:21.480 --> 00:13:23.710 align:start position:0% orle that is other than yes or no um so we<00:13:21.639> support<00:13:22.240> many<00:13:22.639> many<00:13:22.959> different<00:13:23.360> types<00:13:23.600> of 00:13:23.710 --> 00:13:23.720 align:start position:0% we support many many different types of 00:13:23.720 --> 00:13:27.189 align:start position:0% we support many many different types of query<00:13:24.160> it<00:13:24.279> can<00:13:24.480> be<00:13:24.639> lcaps<00:13:25.199> it<00:13:25.320> can<00:13:25.600> be<00:13:26.600> uh<00:13:27.040> it 00:13:27.189 --> 00:13:27.199 align:start position:0% query it can be lcaps it can be uh it 00:13:27.199 --> 00:13:30.509 align:start position:0% query it can be lcaps it can be uh it can<00:13:27.320> be<00:13:27.519> univarate<00:13:28.279> evaluation<00:13:29.279> it<00:13:29.440> can<00:13:29.680> be<00:13:30.240> uh 00:13:30.509 --> 00:13:30.519 align:start position:0% can be univarate evaluation it can be uh 00:13:30.519 --> 00:13:33.030 align:start position:0% can be univarate evaluation it can be uh inner<00:13:30.920> product<00:13:31.399> between<00:13:31.680> several<00:13:32.079> colons<00:13:32.760> so 00:13:33.030 --> 00:13:33.040 align:start position:0% inner product between several colons so 00:13:33.040 --> 00:13:35.189 align:start position:0% inner product between several colons so essentially<00:13:33.920> uh<00:13:34.079> most<00:13:34.279> of<00:13:34.399> the<00:13:34.519> folklore<00:13:35.040> is 00:13:35.189 --> 00:13:35.199 align:start position:0% essentially uh most of the folklore is 00:13:35.199 --> 00:13:38.030 align:start position:0% essentially uh most of the folklore is there<00:13:35.920> and<00:13:36.360> because<00:13:36.880> and<00:13:37.199> we<00:13:37.360> implemented<00:13:37.839> it 00:13:38.030 --> 00:13:38.040 align:start position:0% there and because and we implemented it 00:13:38.040 --> 00:13:40.350 align:start position:0% there and because and we implemented it because<00:13:38.279> we<00:13:38.399> needed<00:13:38.720> it<00:13:38.920> for<00:13:39.800> the<00:13:39.959> concrete 00:13:40.350 --> 00:13:40.360 align:start position:0% because we needed it for the concrete 00:13:40.360 --> 00:13:42.910 align:start position:0% because we needed it for the concrete implementation<00:13:41.079> of<00:13:41.279> Vortex<00:13:41.800> and<00:13:42.440> linear 00:13:42.910 --> 00:13:42.920 align:start position:0% implementation of Vortex and linear 00:13:42.920 --> 00:13:44.910 align:start position:0% implementation of Vortex and linear arithmetization 00:13:44.910 --> 00:13:44.920 align:start position:0% arithmetization 00:13:44.920 --> 00:13:48.509 align:start position:0% arithmetization all<00:13:46.040> right<00:13:47.040> uh<00:13:47.240> so<00:13:47.519> as<00:13:47.639> I<00:13:47.800> said<00:13:48.040> once<00:13:48.240> you<00:13:48.399> have 00:13:48.509 --> 00:13:48.519 align:start position:0% all right uh so as I said once you have 00:13:48.519 --> 00:13:49.829 align:start position:0% all right uh so as I said once you have a<00:13:48.800> protocol 00:13:49.829 --> 00:13:49.839 align:start position:0% a protocol 00:13:49.839 --> 00:13:51.990 align:start position:0% a protocol description<00:13:50.839> uh<00:13:51.199> the<00:13:51.320> only<00:13:51.560> thing<00:13:51.720> you<00:13:51.839> need 00:13:51.990 --> 00:13:52.000 align:start position:0% description uh the only thing you need 00:13:52.000 --> 00:13:54.910 align:start position:0% description uh the only thing you need to<00:13:52.160> do<00:13:52.480> is<00:13:52.600> to<00:13:52.839> describe<00:13:53.399> how<00:13:53.519> you<00:13:53.639> want<00:13:53.839> to<00:13:54.560> go 00:13:54.910 --> 00:13:54.920 align:start position:0% to do is to describe how you want to go 00:13:54.920 --> 00:13:57.189 align:start position:0% to do is to describe how you want to go from<00:13:55.399> this<00:13:55.680> description<00:13:56.160> in<00:13:56.320> an<00:13:56.519> Ideal<00:13:56.880> World 00:13:57.189 --> 00:13:57.199 align:start position:0% from this description in an Ideal World 00:13:57.199 --> 00:14:00.030 align:start position:0% from this description in an Ideal World with<00:13:57.440> ideal<00:13:57.839> Oracle<00:13:58.680> into<00:13:59.199> concrete<00:13:59.560> protocol 00:14:00.030 --> 00:14:00.040 align:start position:0% with ideal Oracle into concrete protocol 00:14:00.040 --> 00:14:02.590 align:start position:0% with ideal Oracle into concrete protocol that<00:14:00.160> is<00:14:00.279> secure<00:14:00.680> in<00:14:00.800> the<00:14:00.920> standard<00:14:01.440> model<00:14:02.440> uh 00:14:02.590 --> 00:14:02.600 align:start position:0% that is secure in the standard model uh 00:14:02.600 --> 00:14:05.910 align:start position:0% that is secure in the standard model uh so<00:14:02.880> here<00:14:03.040> is<00:14:03.560> the<00:14:03.959> base<00:14:04.959> uh<00:14:05.160> description<00:14:05.759> that 00:14:05.910 --> 00:14:05.920 align:start position:0% so here is the base uh description that 00:14:05.920 --> 00:14:09.110 align:start position:0% so here is the base uh description that allow<00:14:06.160> us<00:14:06.320> to<00:14:06.480> go<00:14:06.720> from<00:14:07.720> uh<00:14:07.880> without<00:14:08.279> IOP<00:14:08.720> to 00:14:09.110 --> 00:14:09.120 align:start position:0% allow us to go from uh without IOP to 00:14:09.120 --> 00:14:12.189 align:start position:0% allow us to go from uh without IOP to polinomial<00:14:09.720> IOP<00:14:10.199> at<00:14:10.320> the<00:14:10.600> end<00:14:11.600> uh<00:14:11.800> but<00:14:12.000> in 00:14:12.189 --> 00:14:12.199 align:start position:0% polinomial IOP at the end uh but in 00:14:12.199 --> 00:14:13.749 align:start position:0% polinomial IOP at the end uh but in practice<00:14:12.519> this<00:14:12.680> would<00:14:12.880> not<00:14:13.040> be<00:14:13.199> sufficient<00:14:13.639> we 00:14:13.749 --> 00:14:13.759 align:start position:0% practice this would not be sufficient we 00:14:13.759 --> 00:14:15.470 align:start position:0% practice this would not be sufficient we would<00:14:13.920> also<00:14:14.160> need<00:14:14.320> a<00:14:14.519> polinomial<00:14:15.079> commitment 00:14:15.470 --> 00:14:15.480 align:start position:0% would also need a polinomial commitment 00:14:15.480 --> 00:14:18.629 align:start position:0% would also need a polinomial commitment to<00:14:15.639> turn<00:14:15.959> this<00:14:16.199> into<00:14:16.680> a<00:14:16.880> concrete<00:14:17.480> protocol<00:14:18.480> uh 00:14:18.629 --> 00:14:18.639 align:start position:0% to turn this into a concrete protocol uh 00:14:18.639 --> 00:14:20.470 align:start position:0% to turn this into a concrete protocol uh so<00:14:18.959> in<00:14:19.199> this<00:14:19.399> part<00:14:19.600> of<00:14:19.720> the<00:14:19.880> code<00:14:20.120> does<00:14:20.279> not 00:14:20.470 --> 00:14:20.480 align:start position:0% so in this part of the code does not 00:14:20.480 --> 00:14:22.870 align:start position:0% so in this part of the code does not describe<00:14:20.920> how<00:14:21.120> we<00:14:21.560> do<00:14:21.759> the<00:14:21.920> pomal<00:14:22.440> commitment 00:14:22.870 --> 00:14:22.880 align:start position:0% describe how we do the pomal commitment 00:14:22.880 --> 00:14:27.670 align:start position:0% describe how we do the pomal commitment but<00:14:23.079> how<00:14:23.240> we<00:14:23.440> go<00:14:24.399> to<00:14:24.600> this 00:14:27.670 --> 00:14:27.680 align:start position:0% 00:14:27.680 --> 00:14:30.749 align:start position:0% point<00:14:28.680> um<00:14:28.880> okay<00:14:29.160> okay<00:14:29.320> so<00:14:29.639> now<00:14:30.000> let's<00:14:30.279> get<00:14:30.440> onto 00:14:30.749 --> 00:14:30.759 align:start position:0% point um okay okay so now let's get onto 00:14:30.759 --> 00:14:34.590 align:start position:0% point um okay okay so now let's get onto a<00:14:30.959> practical<00:14:31.560> example<00:14:32.560> uh<00:14:32.680> so<00:14:33.079> here<00:14:33.360> is<00:14:34.240> uh<00:14:34.360> the 00:14:34.590 --> 00:14:34.600 align:start position:0% a practical example uh so here is uh the 00:14:34.600 --> 00:14:38.470 align:start position:0% a practical example uh so here is uh the plun<00:14:35.480> uh<00:14:35.920> constraints<00:14:36.920> um<00:14:37.399> description<00:14:38.160> so<00:14:38.360> we 00:14:38.470 --> 00:14:38.480 align:start position:0% plun uh constraints um description so we 00:14:38.480 --> 00:14:41.509 align:start position:0% plun uh constraints um description so we have<00:14:38.639> a<00:14:38.759> set<00:14:39.000> of<00:14:39.279> colums<00:14:40.279> Q's<00:14:40.720> are<00:14:40.920> describing 00:14:41.509 --> 00:14:41.519 align:start position:0% have a set of colums Q's are describing 00:14:41.519 --> 00:14:45.189 align:start position:0% have a set of colums Q's are describing a<00:14:41.800> PL<00:14:42.120> circuit<00:14:43.120> x<00:14:43.440> a<00:14:43.639> XB<00:14:44.040> XC<00:14:44.440> are<00:14:44.600> describing 00:14:45.189 --> 00:14:45.199 align:start position:0% a PL circuit x a XB XC are describing 00:14:45.199 --> 00:14:48.790 align:start position:0% a PL circuit x a XB XC are describing the<00:14:45.600> witness<00:14:46.600> uh<00:14:46.880> and<00:14:47.279> also<00:14:47.800> usually<00:14:48.199> we<00:14:48.320> add 00:14:48.790 --> 00:14:48.800 align:start position:0% the witness uh and also usually we add 00:14:48.800 --> 00:14:51.030 align:start position:0% the witness uh and also usually we add another<00:14:49.120> colon<00:14:49.480> on<00:14:49.600> the<00:14:50.040> right<00:14:50.560> that<00:14:50.720> is<00:14:50.880> for 00:14:51.030 --> 00:14:51.040 align:start position:0% another colon on the right that is for 00:14:51.040 --> 00:14:52.749 align:start position:0% another colon on the right that is for the<00:14:51.199> public<00:14:51.519> inputs<00:14:52.079> and<00:14:52.240> that<00:14:52.360> we<00:14:52.480> are<00:14:52.600> going 00:14:52.749 --> 00:14:52.759 align:start position:0% the public inputs and that we are going 00:14:52.759 --> 00:14:55.550 align:start position:0% the public inputs and that we are going to<00:14:52.920> use<00:14:53.560> on<00:14:53.759> top<00:14:53.920> of<00:14:54.040> that<00:14:54.240> plun<00:14:54.600> has<00:14:54.720> some<00:14:54.920> copy 00:14:55.550 --> 00:14:55.560 align:start position:0% to use on top of that plun has some copy 00:14:55.560 --> 00:14:58.269 align:start position:0% to use on top of that plun has some copy constraints<00:14:56.560> uh<00:14:56.880> which<00:14:57.279> are<00:14:57.959> can<00:14:58.120> be 00:14:58.269 --> 00:14:58.279 align:start position:0% constraints uh which are can be 00:14:58.279 --> 00:15:01.430 align:start position:0% constraints uh which are can be instantiated<00:14:59.240> by<00:15:00.240> um<00:15:00.639> a<00:15:00.839> permutation 00:15:01.430 --> 00:15:01.440 align:start position:0% instantiated by um a permutation 00:15:01.440 --> 00:15:03.189 align:start position:0% instantiated by um a permutation argument<00:15:01.920> which<00:15:02.079> I'm<00:15:02.199> going<00:15:02.399> to<00:15:02.560> show<00:15:02.800> you<00:15:03.040> how 00:15:03.189 --> 00:15:03.199 align:start position:0% argument which I'm going to show you how 00:15:03.199 --> 00:15:05.710 align:start position:0% argument which I'm going to show you how to<00:15:03.360> do<00:15:04.199> okay<00:15:04.320> so<00:15:04.480> let's<00:15:04.680> Implement 00:15:05.710 --> 00:15:05.720 align:start position:0% to do okay so let's Implement 00:15:05.720 --> 00:15:08.389 align:start position:0% to do okay so let's Implement plun<00:15:06.720> uh<00:15:07.000> so<00:15:07.199> as<00:15:07.279> I<00:15:07.440> mentioned<00:15:07.839> we<00:15:07.920> need<00:15:08.120> to 00:15:08.389 --> 00:15:08.399 align:start position:0% plun uh so as I mentioned we need to 00:15:08.399 --> 00:15:10.870 align:start position:0% plun uh so as I mentioned we need to Define<00:15:08.720> our<00:15:08.959> protocol<00:15:09.920> then<00:15:10.120> we<00:15:10.279> can<00:15:10.519> compile 00:15:10.870 --> 00:15:10.880 align:start position:0% Define our protocol then we can compile 00:15:10.880 --> 00:15:12.910 align:start position:0% Define our protocol then we can compile it<00:15:11.079> and<00:15:11.240> after<00:15:11.480> we<00:15:11.600> can<00:15:11.839> run<00:15:12.399> run<00:15:12.600> it<00:15:12.759> so 00:15:12.910 --> 00:15:12.920 align:start position:0% it and after we can run run it so 00:15:12.920 --> 00:15:14.670 align:start position:0% it and after we can run run it so running<00:15:13.199> the<00:15:13.360> prover<00:15:13.680> and<00:15:13.839> verifying<00:15:14.320> it<00:15:14.600> we 00:15:14.670 --> 00:15:14.680 align:start position:0% running the prover and verifying it we 00:15:14.680 --> 00:15:16.829 align:start position:0% running the prover and verifying it we can<00:15:14.839> also<00:15:15.240> recurse<00:15:15.759> automatically<00:15:16.360> recurse 00:15:16.829 --> 00:15:16.839 align:start position:0% can also recurse automatically recurse 00:15:16.839 --> 00:15:19.590 align:start position:0% can also recurse automatically recurse it<00:15:17.240> but<00:15:17.399> we're<00:15:17.600> not<00:15:17.759> going<00:15:17.920> to<00:15:18.120> cover<00:15:18.560> that 00:15:19.590 --> 00:15:19.600 align:start position:0% it but we're not going to cover that 00:15:19.600 --> 00:15:22.430 align:start position:0% it but we're not going to cover that today<00:15:20.600> all 00:15:22.430 --> 00:15:22.440 align:start position:0% today all 00:15:22.440 --> 00:15:25.629 align:start position:0% today all right<00:15:23.440> okay<00:15:23.639> so<00:15:24.079> first<00:15:24.279> of<00:15:24.440> all<00:15:25.000> defining<00:15:25.480> the 00:15:25.629 --> 00:15:25.639 align:start position:0% right okay so first of all defining the 00:15:25.639 --> 00:15:27.629 align:start position:0% right okay so first of all defining the protocol<00:15:26.160> this<00:15:26.320> is<00:15:26.440> done<00:15:26.680> by<00:15:26.880> specifying<00:15:27.480> a 00:15:27.629 --> 00:15:27.639 align:start position:0% protocol this is done by specifying a 00:15:27.639 --> 00:15:30.430 align:start position:0% protocol this is done by specifying a function<00:15:28.079> so<00:15:28.360> the<00:15:28.600> whole<00:15:29.000> framework<00:15:29.399> is<00:15:29.519> in<00:15:29.720> go 00:15:30.430 --> 00:15:30.440 align:start position:0% function so the whole framework is in go 00:15:30.440 --> 00:15:33.110 align:start position:0% function so the whole framework is in go uh<00:15:30.560> most<00:15:30.720> of<00:15:30.839> the<00:15:31.000> prover<00:15:31.360> stack<00:15:32.199> of<00:15:32.399> linear<00:15:32.839> is 00:15:33.110 --> 00:15:33.120 align:start position:0% uh most of the prover stack of linear is 00:15:33.120 --> 00:15:36.470 align:start position:0% uh most of the prover stack of linear is using<00:15:33.480> KN<00:15:34.160> and<00:15:34.560> the<00:15:34.800> linear<00:15:35.319> prover<00:15:36.079> is<00:15:36.240> also 00:15:36.470 --> 00:15:36.480 align:start position:0% using KN and the linear prover is also 00:15:36.480 --> 00:15:39.309 align:start position:0% using KN and the linear prover is also implemented<00:15:37.000> Ino<00:15:37.720> as<00:15:37.880> it<00:15:38.000> is<00:15:38.160> also<00:15:38.480> relying<00:15:39.120> on 00:15:39.309 --> 00:15:39.319 align:start position:0% implemented Ino as it is also relying on 00:15:39.319 --> 00:15:40.389 align:start position:0% implemented Ino as it is also relying on GAR 00:15:40.389 --> 00:15:40.399 align:start position:0% GAR 00:15:40.399 --> 00:15:42.749 align:start position:0% GAR implementation<00:15:41.399> so<00:15:41.959> uh<00:15:42.120> the<00:15:42.279> defined 00:15:42.749 --> 00:15:42.759 align:start position:0% implementation so uh the defined 00:15:42.759 --> 00:15:46.990 align:start position:0% implementation so uh the defined function<00:15:43.560> uh<00:15:43.759> has<00:15:44.000> this<00:15:44.240> simple<00:15:45.240> uh<00:15:46.240> signature 00:15:46.990 --> 00:15:47.000 align:start position:0% function uh has this simple uh signature 00:15:47.000 --> 00:15:48.629 align:start position:0% function uh has this simple uh signature and<00:15:47.199> the<00:15:47.319> Builder<00:15:47.720> is<00:15:47.839> an<00:15:48.040> object<00:15:48.360> that<00:15:48.519> is 00:15:48.629 --> 00:15:48.639 align:start position:0% and the Builder is an object that is 00:15:48.639 --> 00:15:51.949 align:start position:0% and the Builder is an object that is going<00:15:48.839> to<00:15:49.000> store<00:15:49.639> everything<00:15:50.480> we<00:15:50.800> said<00:15:51.440> to 00:15:51.949 --> 00:15:51.959 align:start position:0% going to store everything we said to 00:15:51.959 --> 00:15:54.110 align:start position:0% going to store everything we said to declare<00:15:52.720> an<00:15:52.880> entity<00:15:53.279> in<00:15:53.360> the<00:15:53.519> protocol<00:15:53.959> so 00:15:54.110 --> 00:15:54.120 align:start position:0% declare an entity in the protocol so 00:15:54.120 --> 00:15:57.590 align:start position:0% declare an entity in the protocol so either<00:15:54.480> queries<00:15:55.160> colums<00:15:55.639> or<00:15:55.800> so<00:15:56.319> on<00:15:57.319> and<00:15:57.480> we 00:15:57.590 --> 00:15:57.600 align:start position:0% either queries colums or so on and we 00:15:57.600 --> 00:16:00.110 align:start position:0% either queries colums or so on and we can<00:15:57.800> also<00:15:58.240> specify<00:15:59.240> checks<00:15:59.560> to<00:15:59.680> be<00:15:59.800> done<00:16:00.000> by 00:16:00.110 --> 00:16:00.120 align:start position:0% can also specify checks to be done by 00:16:00.120 --> 00:16:04.470 align:start position:0% can also specify checks to be done by the<00:16:00.240> verifier<00:16:00.880> so<00:16:01.600> let's<00:16:01.759> go<00:16:01.920> into 00:16:04.470 --> 00:16:04.480 align:start position:0% 00:16:04.480 --> 00:16:08.670 align:start position:0% there<00:16:05.480> okay<00:16:05.680> so<00:16:06.319> here<00:16:06.560> are<00:16:06.839> the<00:16:07.079> colon<00:16:07.959> uh 00:16:08.670 --> 00:16:08.680 align:start position:0% there okay so here are the colon uh 00:16:08.680 --> 00:16:11.430 align:start position:0% there okay so here are the colon uh description<00:16:09.680> uh<00:16:09.839> so<00:16:10.079> you<00:16:10.240> can<00:16:10.440> recognize<00:16:11.319> uh 00:16:11.430 --> 00:16:11.440 align:start position:0% description uh so you can recognize uh 00:16:11.440 --> 00:16:14.509 align:start position:0% description uh so you can recognize uh the<00:16:11.639> plun<00:16:12.480> uh<00:16:12.639> colon<00:16:13.160> that<00:16:13.600> we<00:16:13.720> saw<00:16:14.000> at<00:16:14.120> the 00:16:14.509 --> 00:16:14.519 align:start position:0% the plun uh colon that we saw at the 00:16:14.519 --> 00:16:17.150 align:start position:0% the plun uh colon that we saw at the beginning<00:16:15.519> uh<00:16:15.639> so<00:16:15.920> the<00:16:16.120> cu's<00:16:16.519> colon<00:16:16.839> are<00:16:17.000> for 00:16:17.150 --> 00:16:17.160 align:start position:0% beginning uh so the cu's colon are for 00:16:17.160 --> 00:16:19.790 align:start position:0% beginning uh so the cu's colon are for the<00:16:17.319> circuit<00:16:17.759> description<00:16:18.720> they<00:16:18.880> should<00:16:19.199> be 00:16:19.790 --> 00:16:19.800 align:start position:0% the circuit description they should be 00:16:19.800 --> 00:16:21.670 align:start position:0% the circuit description they should be the<00:16:19.959> same<00:16:20.240> no<00:16:20.399> matter<00:16:20.720> what<00:16:20.839> we<00:16:21.000> try<00:16:21.240> to<00:16:21.360> prove 00:16:21.670 --> 00:16:21.680 align:start position:0% the same no matter what we try to prove 00:16:21.680 --> 00:16:23.670 align:start position:0% the same no matter what we try to prove so<00:16:22.040> they<00:16:22.199> go<00:16:22.399> into 00:16:23.670 --> 00:16:23.680 align:start position:0% so they go into 00:16:23.680 --> 00:16:27.910 align:start position:0% so they go into precomputed<00:16:24.680> uh<00:16:25.240> the<00:16:25.600> XX<00:16:26.079> bxc<00:16:27.079> are<00:16:27.639> a 00:16:27.910 --> 00:16:27.920 align:start position:0% precomputed uh the XX bxc are a 00:16:27.920 --> 00:16:30.710 align:start position:0% precomputed uh the XX bxc are a commitment<00:16:28.920> have<00:16:29.079> to<00:16:29.160> be<00:16:29.240> sent<00:16:29.480> to<00:16:29.639> the<00:16:29.759> Oracle 00:16:30.710 --> 00:16:30.720 align:start position:0% commitment have to be sent to the Oracle 00:16:30.720 --> 00:16:34.470 align:start position:0% commitment have to be sent to the Oracle and<00:16:31.079> Pi<00:16:31.759> the<00:16:31.880> public<00:16:32.360> input<00:16:33.360> is<00:16:33.680> inserted<00:16:34.160> as<00:16:34.279> a 00:16:34.470 --> 00:16:34.480 align:start position:0% and Pi the public input is inserted as a 00:16:34.480 --> 00:16:35.829 align:start position:0% and Pi the public input is inserted as a proof<00:16:34.759> object<00:16:35.079> because<00:16:35.319> it<00:16:35.440> has<00:16:35.560> to<00:16:35.680> be 00:16:35.829 --> 00:16:35.839 align:start position:0% proof object because it has to be 00:16:35.839 --> 00:16:38.110 align:start position:0% proof object because it has to be revealed<00:16:36.480> to<00:16:36.680> the<00:16:36.880> prover<00:16:37.519> so<00:16:37.680> it's<00:16:37.800> a<00:16:37.959> bit 00:16:38.110 --> 00:16:38.120 align:start position:0% revealed to the prover so it's a bit 00:16:38.120 --> 00:16:40.309 align:start position:0% revealed to the prover so it's a bit cont<00:16:38.480> inuitive<00:16:39.040> that<00:16:39.199> we<00:16:39.519> call<00:16:39.800> that<00:16:39.959> proof 00:16:40.309 --> 00:16:40.319 align:start position:0% cont inuitive that we call that proof 00:16:40.319 --> 00:16:43.069 align:start position:0% cont inuitive that we call that proof but<00:16:40.600> proof<00:16:40.920> means<00:16:41.240> a<00:16:41.399> message<00:16:41.800> sent<00:16:42.279> to<00:16:42.440> the<00:16:42.600> pr 00:16:43.069 --> 00:16:43.079 align:start position:0% but proof means a message sent to the pr 00:16:43.079 --> 00:16:45.829 align:start position:0% but proof means a message sent to the pr it<00:16:43.240> is<00:16:43.440> part<00:16:43.600> of<00:16:43.759> the<00:16:44.079> proof<00:16:45.079> even<00:16:45.360> if<00:16:45.519> it's<00:16:45.639> a 00:16:45.829 --> 00:16:45.839 align:start position:0% it is part of the proof even if it's a 00:16:45.839 --> 00:16:48.189 align:start position:0% it is part of the proof even if it's a nonsense<00:16:46.319> from<00:16:46.519> an<00:16:46.720> Academia<00:16:47.360> perspective 00:16:48.189 --> 00:16:48.199 align:start position:0% nonsense from an Academia perspective 00:16:48.199 --> 00:16:50.670 align:start position:0% nonsense from an Academia perspective and<00:16:48.360> also<00:16:48.600> a<00:16:48.720> number<00:16:48.959> of<00:16:49.120> public<00:16:49.480> inputs<00:16:50.480> uh 00:16:50.670 --> 00:16:50.680 align:start position:0% and also a number of public inputs uh 00:16:50.680 --> 00:16:53.829 align:start position:0% and also a number of public inputs uh because<00:16:51.399> the<00:16:51.639> pi<00:16:52.199> is<00:16:52.600> po<00:16:53.000> colon<00:16:53.319> is<00:16:53.480> larger 00:16:53.829 --> 00:16:53.839 align:start position:0% because the pi is po colon is larger 00:16:53.839 --> 00:16:55.389 align:start position:0% because the pi is po colon is larger than<00:16:54.000> the<00:16:54.120> actual<00:16:54.399> number<00:16:54.639> of<00:16:54.800> public<00:16:55.079> input 00:16:55.389 --> 00:16:55.399 align:start position:0% than the actual number of public input 00:16:55.399 --> 00:16:56.870 align:start position:0% than the actual number of public input is<00:16:55.600> because<00:16:55.839> every<00:16:56.040> colon<00:16:56.360> should<00:16:56.560> have<00:16:56.759> the 00:16:56.870 --> 00:16:56.880 align:start position:0% is because every colon should have the 00:16:56.880 --> 00:16:59.710 align:start position:0% is because every colon should have the same<00:16:57.120> size 00:16:59.710 --> 00:16:59.720 align:start position:0% same size 00:16:59.720 --> 00:17:01.790 align:start position:0% same size so<00:17:00.240> and<00:17:00.360> that's<00:17:00.680> the<00:17:00.800> value<00:17:01.040> of<00:17:01.160> the<00:17:01.279> CU<00:17:01.600> should 00:17:01.790 --> 00:17:01.800 align:start position:0% so and that's the value of the CU should 00:17:01.800 --> 00:17:03.749 align:start position:0% so and that's the value of the CU should be<00:17:01.959> known<00:17:02.279> beforehand<00:17:02.880> of<00:17:03.000> course<00:17:03.360> because<00:17:03.600> of 00:17:03.749 --> 00:17:03.759 align:start position:0% be known beforehand of course because of 00:17:03.759 --> 00:17:07.510 align:start position:0% be known beforehand of course because of the<00:17:03.880> circuit 00:17:07.510 --> 00:17:07.520 align:start position:0% 00:17:07.520 --> 00:17:10.270 align:start position:0% description<00:17:08.520> okay<00:17:08.919> so<00:17:09.160> now<00:17:09.520> we<00:17:09.640> can<00:17:09.880> declare 00:17:10.270 --> 00:17:10.280 align:start position:0% description okay so now we can declare 00:17:10.280 --> 00:17:13.630 align:start position:0% description okay so now we can declare the<00:17:10.880> queries<00:17:11.880> uh<00:17:12.079> so<00:17:12.720> on<00:17:12.880> your<00:17:13.120> right<00:17:13.319> you<00:17:13.439> have 00:17:13.630 --> 00:17:13.640 align:start position:0% the queries uh so on your right you have 00:17:13.640 --> 00:17:15.510 align:start position:0% the queries uh so on your right you have the<00:17:13.959> a<00:17:14.120> global<00:17:14.480> constraint<00:17:15.039> which<00:17:15.160> is<00:17:15.280> an 00:17:15.510 --> 00:17:15.520 align:start position:0% the a global constraint which is an 00:17:15.520 --> 00:17:18.909 align:start position:0% the a global constraint which is an arithmetic<00:17:16.520> expression<00:17:17.039> that<00:17:17.319> has<00:17:17.480> to<00:17:17.919> vanish 00:17:18.909 --> 00:17:18.919 align:start position:0% arithmetic expression that has to vanish 00:17:18.919 --> 00:17:21.990 align:start position:0% arithmetic expression that has to vanish uh<00:17:19.360> on<00:17:20.039> the<00:17:20.240> all<00:17:20.439> the<00:17:20.600> rows<00:17:21.000> of<00:17:21.319> every<00:17:21.600> colon 00:17:21.990 --> 00:17:22.000 align:start position:0% uh on the all the rows of every colon 00:17:22.000 --> 00:17:24.270 align:start position:0% uh on the all the rows of every colon that<00:17:22.120> is<00:17:22.319> touching<00:17:23.319> we<00:17:23.439> can<00:17:23.640> recognize<00:17:24.120> the 00:17:24.270 --> 00:17:24.280 align:start position:0% that is touching we can recognize the 00:17:24.280 --> 00:17:26.510 align:start position:0% that is touching we can recognize the equation<00:17:24.720> of<00:17:25.160> the<00:17:25.400> pl<00:17:25.720> gate<00:17:25.959> constraint<00:17:26.400> at 00:17:26.510 --> 00:17:26.520 align:start position:0% equation of the pl gate constraint at 00:17:26.520 --> 00:17:30.310 align:start position:0% equation of the pl gate constraint at the<00:17:26.640> beginning<00:17:27.360> and<00:17:27.480> we<00:17:27.679> have<00:17:27.959> a<00:17:28.160> fixed<00:17:28.439> permut 00:17:30.310 --> 00:17:30.320 align:start position:0% the beginning and we have a fixed permut 00:17:30.320 --> 00:17:33.190 align:start position:0% the beginning and we have a fixed permut which<00:17:30.720> is<00:17:31.039> instantiated<00:17:31.880> by<00:17:32.039> some<00:17:32.280> forc 00:17:33.190 --> 00:17:33.200 align:start position:0% which is instantiated by some forc 00:17:33.200 --> 00:17:36.549 align:start position:0% which is instantiated by some forc permutation<00:17:34.120> that<00:17:34.760> has<00:17:35.760> the<00:17:35.880> concatenation 00:17:36.549 --> 00:17:36.559 align:start position:0% permutation that has the concatenation 00:17:36.559 --> 00:17:37.669 align:start position:0% permutation that has the concatenation of<00:17:36.720> XA 00:17:37.669 --> 00:17:37.679 align:start position:0% of XA 00:17:37.679 --> 00:17:40.909 align:start position:0% of XA xbxc<00:17:38.679> uh<00:17:38.840> invariant<00:17:39.480> and<00:17:39.600> that's<00:17:39.840> how<00:17:40.080> PL 00:17:40.909 --> 00:17:40.919 align:start position:0% xbxc uh invariant and that's how PL 00:17:40.919 --> 00:17:46.029 align:start position:0% xbxc uh invariant and that's how PL proves<00:17:41.919> uh<00:17:42.160> the<00:17:42.360> copy 00:17:46.029 --> 00:17:46.039 align:start position:0% 00:17:46.039 --> 00:17:48.789 align:start position:0% constraints<00:17:47.039> uh<00:17:47.280> then<00:17:47.520> finally<00:17:48.280> uh<00:17:48.440> we<00:17:48.600> need 00:17:48.789 --> 00:17:48.799 align:start position:0% constraints uh then finally uh we need 00:17:48.799 --> 00:17:50.669 align:start position:0% constraints uh then finally uh we need to<00:17:48.960> add<00:17:49.120> a<00:17:49.240> verifier<00:17:49.799> check<00:17:50.280> this<00:17:50.440> is<00:17:50.559> to 00:17:50.669 --> 00:17:50.679 align:start position:0% to add a verifier check this is to 00:17:50.679 --> 00:17:53.350 align:start position:0% to add a verifier check this is to ensure<00:17:51.000> that<00:17:51.160> the<00:17:51.320> pi<00:17:52.039> that<00:17:52.160> is<00:17:52.320> sent<00:17:52.640> to<00:17:53.240> the 00:17:53.350 --> 00:17:53.360 align:start position:0% ensure that the pi that is sent to the 00:17:53.360 --> 00:17:55.149 align:start position:0% ensure that the pi that is sent to the verifier<00:17:53.840> is<00:17:54.000> well<00:17:54.200> formed<00:17:54.559> and<00:17:54.720> that<00:17:55.039> it 00:17:55.149 --> 00:17:55.159 align:start position:0% verifier is well formed and that it 00:17:55.159 --> 00:17:59.710 align:start position:0% verifier is well formed and that it should<00:17:55.400> be<00:17:55.600> paded<00:17:55.960> on<00:17:56.120> the<00:17:56.320> right<00:17:56.520> with<00:17:56.760> zeros 00:17:59.710 --> 00:17:59.720 align:start position:0% should be paded on the right with zeros 00:17:59.720 --> 00:18:02.430 align:start position:0% should be paded on the right with zeros okay<00:18:00.720> uh<00:18:00.880> so<00:18:01.120> now<00:18:01.440> once<00:18:01.600> we<00:18:01.760> have<00:18:01.919> that<00:18:02.120> we<00:18:02.240> can 00:18:02.430 --> 00:18:02.440 align:start position:0% okay uh so now once we have that we can 00:18:02.440 --> 00:18:04.310 align:start position:0% okay uh so now once we have that we can compile<00:18:02.840> that<00:18:02.960> into<00:18:03.159> an<00:18:03.320> actual<00:18:03.640> protocol<00:18:04.080> so 00:18:04.310 --> 00:18:04.320 align:start position:0% compile that into an actual protocol so 00:18:04.320 --> 00:18:07.630 align:start position:0% compile that into an actual protocol so here<00:18:04.559> I<00:18:04.760> added<00:18:05.120> the<00:18:05.360> part<00:18:05.640> that<00:18:06.480> convert<00:18:07.480> uh 00:18:07.630 --> 00:18:07.640 align:start position:0% here I added the part that convert uh 00:18:07.640 --> 00:18:11.350 align:start position:0% here I added the part that convert uh the<00:18:07.840> piop<00:18:08.840> into<00:18:09.559> uh<00:18:10.000> a<00:18:10.200> concrete<00:18:10.640> protocol 00:18:11.350 --> 00:18:11.360 align:start position:0% the piop into uh a concrete protocol 00:18:11.360 --> 00:18:13.470 align:start position:0% the piop into uh a concrete protocol because<00:18:11.600> I<00:18:11.760> added<00:18:12.039> the<00:18:12.159> vortex.<00:18:12.760> compile 00:18:13.470 --> 00:18:13.480 align:start position:0% because I added the vortex. compile 00:18:13.480 --> 00:18:15.669 align:start position:0% because I added the vortex. compile Vortex<00:18:13.919> being<00:18:14.360> the<00:18:14.520> prial<00:18:15.080> commitment<00:18:15.520> that 00:18:15.669 --> 00:18:15.679 align:start position:0% Vortex being the prial commitment that 00:18:15.679 --> 00:18:20.990 align:start position:0% Vortex being the prial commitment that we<00:18:16.159> use<00:18:17.240> and<00:18:18.240> now<00:18:18.799> uh<00:18:18.919> we<00:18:19.080> just<00:18:19.280> have<00:18:19.400> to<00:18:19.559> run 00:18:20.990 --> 00:18:21.000 align:start position:0% we use and now uh we just have to run 00:18:21.000 --> 00:18:23.870 align:start position:0% we use and now uh we just have to run it<00:18:22.000> uh<00:18:22.559> so<00:18:22.919> the<00:18:23.039> only<00:18:23.240> thing<00:18:23.400> we<00:18:23.520> need<00:18:23.679> to 00:18:23.870 --> 00:18:23.880 align:start position:0% it uh so the only thing we need to 00:18:23.880 --> 00:18:26.870 align:start position:0% it uh so the only thing we need to specify<00:18:24.440> is<00:18:24.880> how<00:18:25.480> concretely<00:18:26.480> uh<00:18:26.640> we<00:18:26.760> are 00:18:26.870 --> 00:18:26.880 align:start position:0% specify is how concretely uh we are 00:18:26.880 --> 00:18:29.149 align:start position:0% specify is how concretely uh we are going<00:18:27.080> to<00:18:27.280> assign<00:18:27.919> uh<00:18:28.039> our<00:18:28.280> colons<00:18:28.880> because 00:18:29.149 --> 00:18:29.159 align:start position:0% going to assign uh our colons because 00:18:29.159 --> 00:18:30.710 align:start position:0% going to assign uh our colons because this<00:18:29.320> is<00:18:29.440> the<00:18:29.559> only<00:18:29.760> thing<00:18:30.000> that<00:18:30.120> is<00:18:30.320> unknown 00:18:30.710 --> 00:18:30.720 align:start position:0% this is the only thing that is unknown 00:18:30.720 --> 00:18:33.750 align:start position:0% this is the only thing that is unknown at<00:18:30.880> this<00:18:31.080> stage<00:18:31.880> after<00:18:32.159> reading<00:18:32.480> the<00:18:32.679> protocol 00:18:33.750 --> 00:18:33.760 align:start position:0% at this stage after reading the protocol 00:18:33.760 --> 00:18:36.029 align:start position:0% at this stage after reading the protocol description<00:18:34.760> uh<00:18:34.880> so<00:18:35.159> yeah<00:18:35.360> we<00:18:35.520> just<00:18:35.720> provide 00:18:36.029 --> 00:18:36.039 align:start position:0% description uh so yeah we just provide 00:18:36.039 --> 00:18:39.270 align:start position:0% description uh so yeah we just provide it<00:18:36.200> and<00:18:36.320> we<00:18:36.480> assign<00:18:36.799> it<00:18:36.960> it's<00:18:37.120> for<00:18:37.320> lines<00:18:37.559> of 00:18:39.270 --> 00:18:39.280 align:start position:0% it and we assign it it's for lines of 00:18:39.280 --> 00:18:42.310 align:start position:0% it and we assign it it's for lines of code<00:18:40.280> uh<00:18:40.640> and<00:18:40.840> so<00:18:41.080> yeah<00:18:41.320> now<00:18:41.559> so<00:18:41.799> we<00:18:41.919> have<00:18:42.080> some 00:18:42.310 --> 00:18:42.320 align:start position:0% code uh and so yeah now so we have some 00:18:42.320 --> 00:18:44.190 align:start position:0% code uh and so yeah now so we have some things<00:18:42.600> that<00:18:42.799> allow<00:18:43.120> us<00:18:43.320> to<00:18:43.520> write<00:18:43.840> PL 00:18:44.190 --> 00:18:44.200 align:start position:0% things that allow us to write PL 00:18:44.200 --> 00:18:47.630 align:start position:0% things that allow us to write PL constraints<00:18:45.440> manually<00:18:46.440> uh<00:18:46.679> but<00:18:47.120> write<00:18:47.559> I 00:18:47.630 --> 00:18:47.640 align:start position:0% constraints manually uh but write I 00:18:47.640 --> 00:18:49.590 align:start position:0% constraints manually uh but write I don't<00:18:47.840> know<00:18:48.000> if<00:18:48.120> you<00:18:48.280> have<00:18:48.440> tried<00:18:48.799> writing<00:18:49.360> a 00:18:49.590 --> 00:18:49.600 align:start position:0% don't know if you have tried writing a 00:18:49.600 --> 00:18:51.710 align:start position:0% don't know if you have tried writing a PL<00:18:49.919> Circuit<00:18:50.320> by<00:18:50.480> hand<00:18:50.760> but<00:18:50.880> it<00:18:51.000> is<00:18:51.240> really 00:18:51.710 --> 00:18:51.720 align:start position:0% PL Circuit by hand but it is really 00:18:51.720 --> 00:18:54.350 align:start position:0% PL Circuit by hand but it is really difficult<00:18:52.640> uh<00:18:53.000> and<00:18:53.159> it<00:18:53.280> turns<00:18:53.559> out<00:18:53.799> that<00:18:53.960> garx 00:18:54.350 --> 00:18:54.360 align:start position:0% difficult uh and it turns out that garx 00:18:54.360 --> 00:18:56.029 align:start position:0% difficult uh and it turns out that garx offers<00:18:54.679> a<00:18:54.799> very<00:18:55.000> nice<00:18:55.200> front<00:18:55.440> end<00:18:55.679> to<00:18:55.840> WR 00:18:56.029 --> 00:18:56.039 align:start position:0% offers a very nice front end to WR 00:18:56.039 --> 00:18:58.870 align:start position:0% offers a very nice front end to WR circuit<00:18:56.640> so<00:18:56.880> let's<00:18:57.080> just<00:18:57.520> write<00:18:57.880> a<00:18:58.120> wrapper<00:18:58.600> of 00:18:58.870 --> 00:18:58.880 align:start position:0% circuit so let's just write a wrapper of 00:18:58.880 --> 00:19:01.990 align:start position:0% circuit so let's just write a wrapper of what<00:18:59.000> we<00:18:59.240> just<00:18:59.840> root<00:19:00.840> uh<00:19:00.960> using<00:19:01.360> Gar<00:19:01.720> so<00:19:01.840> that 00:19:01.990 --> 00:19:02.000 align:start position:0% what we just root uh using Gar so that 00:19:02.000 --> 00:19:04.870 align:start position:0% what we just root uh using Gar so that we<00:19:02.120> can<00:19:02.320> use<00:19:02.799> a<00:19:03.000> gar<00:19:03.360> circuit 00:19:04.870 --> 00:19:04.880 align:start position:0% we can use a gar circuit 00:19:04.880 --> 00:19:07.029 align:start position:0% we can use a gar circuit description<00:19:05.880> so<00:19:06.200> I<00:19:06.640> I<00:19:06.760> did<00:19:06.919> the 00:19:07.029 --> 00:19:07.039 align:start position:0% description so I I did the 00:19:07.039 --> 00:19:09.430 align:start position:0% description so I I did the implementation<00:19:07.720> it<00:19:07.840> was<00:19:08.000> a<00:19:08.159> bit<00:19:08.320> longer<00:19:09.000> than 00:19:09.430 --> 00:19:09.440 align:start position:0% implementation it was a bit longer than 00:19:09.440 --> 00:19:12.270 align:start position:0% implementation it was a bit longer than 100<00:19:09.760> lines<00:19:10.120> but<00:19:10.960> it<00:19:11.080> was<00:19:11.400> essentially<00:19:11.919> a<00:19:12.039> few 00:19:12.270 --> 00:19:12.280 align:start position:0% 100 lines but it was essentially a few 00:19:12.280 --> 00:19:15.630 align:start position:0% 100 lines but it was essentially a few automated 00:19:15.630 --> 00:19:15.640 align:start position:0% 00:19:15.640 --> 00:19:18.789 align:start position:0% stuff<00:19:16.640> okay<00:19:16.840> so<00:19:17.120> let's<00:19:17.320> do<00:19:17.880> a<00:19:18.039> circuit<00:19:18.480> so 00:19:18.789 --> 00:19:18.799 align:start position:0% stuff okay so let's do a circuit so 00:19:18.799 --> 00:19:22.310 align:start position:0% stuff okay so let's do a circuit so let's<00:19:18.960> use<00:19:19.720> uh<00:19:20.039> Fibonacci<00:19:20.679> as<00:19:20.760> a<00:19:20.919> use<00:19:21.240> case<00:19:22.120> uh 00:19:22.310 --> 00:19:22.320 align:start position:0% let's use uh Fibonacci as a use case uh 00:19:22.320 --> 00:19:25.590 align:start position:0% let's use uh Fibonacci as a use case uh so<00:19:22.840> my<00:19:23.039> circuit<00:19:23.559> you<00:19:23.840> have<00:19:24.080> two<00:19:24.360> values<00:19:24.720> U<00:19:25.200> U1 00:19:25.590 --> 00:19:25.600 align:start position:0% so my circuit you have two values U U1 00:19:25.600 --> 00:19:28.510 align:start position:0% so my circuit you have two values U U1 as<00:19:25.799> input<00:19:26.480> and<00:19:26.600> you<00:19:26.720> want<00:19:26.919> to<00:19:27.159> have<00:19:27.840> the<00:19:28.039> 50th 00:19:28.510 --> 00:19:28.520 align:start position:0% as input and you want to have the 50th 00:19:28.520 --> 00:19:30.270 align:start position:0% as input and you want to have the 50th number<00:19:28.720> number<00:19:29.000> of<00:19:29.120> the<00:19:29.280> Fibonacci<00:19:29.840> sequence 00:19:30.270 --> 00:19:30.280 align:start position:0% number number of the Fibonacci sequence 00:19:30.280 --> 00:19:34.350 align:start position:0% number number of the Fibonacci sequence generated<00:19:30.880> by<00:19:31.120> U<00:19:31.600> and<00:19:31.760> U1<00:19:32.679> U<00:19:33.159> and<00:19:33.320> U1<00:19:33.720> being 00:19:34.350 --> 00:19:34.360 align:start position:0% generated by U and U1 U and U1 being 00:19:34.360 --> 00:19:35.909 align:start position:0% generated by U and U1 U and U1 being public 00:19:35.909 --> 00:19:35.919 align:start position:0% public 00:19:35.919 --> 00:19:38.510 align:start position:0% public parameters<00:19:36.919> uh<00:19:37.080> so<00:19:37.320> on<00:19:37.480> your<00:19:37.679> right<00:19:37.840> you<00:19:38.039> have 00:19:38.510 --> 00:19:38.520 align:start position:0% parameters uh so on your right you have 00:19:38.520 --> 00:19:40.710 align:start position:0% parameters uh so on your right you have uh<00:19:38.679> the<00:19:38.840> circuit<00:19:39.240> writing<00:19:39.559> in<00:19:39.840> KN<00:19:40.200> you<00:19:40.320> can<00:19:40.440> see 00:19:40.710 --> 00:19:40.720 align:start position:0% uh the circuit writing in KN you can see 00:19:40.720 --> 00:19:43.350 align:start position:0% uh the circuit writing in KN you can see that<00:19:40.919> it's<00:19:41.360> fairly<00:19:41.840> easy<00:19:42.480> and<00:19:42.679> much<00:19:42.880> simpler 00:19:43.350 --> 00:19:43.360 align:start position:0% that it's fairly easy and much simpler 00:19:43.360 --> 00:19:46.669 align:start position:0% that it's fairly easy and much simpler than<00:19:43.880> writing<00:19:44.240> a<00:19:44.400> circuit<00:19:44.840> by<00:19:45.360> hand<00:19:46.360> and<00:19:46.559> then 00:19:46.669 --> 00:19:46.679 align:start position:0% than writing a circuit by hand and then 00:19:46.679 --> 00:19:49.669 align:start position:0% than writing a circuit by hand and then we<00:19:46.840> just<00:19:47.039> have<00:19:47.159> to<00:19:47.280> run<00:19:47.520> it<00:19:48.000> and<00:19:48.440> that's<00:19:48.640> it<00:19:48.880> you 00:19:49.669 --> 00:19:49.679 align:start position:0% we just have to run it and that's it you 00:19:49.679 --> 00:19:52.470 align:start position:0% we just have to run it and that's it you just<00:19:50.679> create<00:19:51.039> your<00:19:51.280> proof<00:19:51.559> function<00:19:52.080> that<00:19:52.240> is 00:19:52.470 --> 00:19:52.480 align:start position:0% just create your proof function that is 00:19:52.480 --> 00:19:54.710 align:start position:0% just create your proof function that is explaining<00:19:53.000> how<00:19:53.120> to<00:19:53.280> assign<00:19:53.559> the<00:19:53.720> colon<00:19:54.520> you 00:19:54.710 --> 00:19:54.720 align:start position:0% explaining how to assign the colon you 00:19:54.720 --> 00:19:57.750 align:start position:0% explaining how to assign the colon you run<00:19:54.960> with.<00:19:55.559> proof<00:19:55.919> and<00:19:56.120> is<00:19:56.320> going<00:19:56.559> to<00:19:57.360> generate 00:19:57.750 --> 00:19:57.760 align:start position:0% run with. proof and is going to generate 00:19:57.760 --> 00:19:59.270 align:start position:0% run with. proof and is going to generate a<00:19:57.919> proof<00:19:58.159> for<00:19:58.320> you 00:19:59.270 --> 00:19:59.280 align:start position:0% a proof for you 00:19:59.280 --> 00:20:00.630 align:start position:0% a proof for you using<00:19:59.600> vertex<00:19:59.919> of<00:20:00.039> the<00:20:00.159> polinomial 00:20:00.630 --> 00:20:00.640 align:start position:0% using vertex of the polinomial 00:20:00.640 --> 00:20:02.310 align:start position:0% using vertex of the polinomial commitment<00:20:01.080> and<00:20:01.200> you<00:20:01.320> can<00:20:01.520> verify<00:20:01.960> that<00:20:02.120> in 00:20:02.310 --> 00:20:02.320 align:start position:0% commitment and you can verify that in 00:20:02.320 --> 00:20:03.590 align:start position:0% commitment and you can verify that in one 00:20:03.590 --> 00:20:03.600 align:start position:0% one 00:20:03.600 --> 00:20:06.470 align:start position:0% one line<00:20:04.600> all<00:20:04.760> right<00:20:05.320> I<00:20:05.480> have<00:20:05.640> six<00:20:05.880> seconds<00:20:06.240> for 00:20:06.470 --> 00:20:06.480 align:start position:0% line all right I have six seconds for 00:20:06.480 --> 00:20:09.390 align:start position:0% line all right I have six seconds for the<00:20:06.919> uh<00:20:07.520> future<00:20:07.919> Improvement<00:20:08.400> so<00:20:09.000> we<00:20:09.120> want<00:20:09.240> to 00:20:09.390 --> 00:20:09.400 align:start position:0% the uh future Improvement so we want to 00:20:09.400 --> 00:20:11.230 align:start position:0% the uh future Improvement so we want to add<00:20:09.559> more<00:20:09.720> queries<00:20:10.159> and<00:20:10.559> we<00:20:10.679> think<00:20:10.919> we<00:20:11.039> can 00:20:11.230 --> 00:20:11.240 align:start position:0% add more queries and we think we can 00:20:11.240 --> 00:20:14.190 align:start position:0% add more queries and we think we can also<00:20:11.520> remove<00:20:11.880> the<00:20:12.080> necessity<00:20:12.600> for<00:20:12.880> runs<00:20:13.679> in<00:20:13.960> to 00:20:14.190 --> 00:20:14.200 align:start position:0% also remove the necessity for runs in to 00:20:14.200 --> 00:20:16.190 align:start position:0% also remove the necessity for runs in to specify<00:20:14.679> runs<00:20:15.080> in<00:20:15.200> the<00:20:15.360> protocol<00:20:15.960> as<00:20:16.080> it 00:20:16.190 --> 00:20:16.200 align:start position:0% specify runs in the protocol as it 00:20:16.200 --> 00:20:17.470 align:start position:0% specify runs in the protocol as it should<00:20:16.360> be<00:20:16.480> inferred 00:20:17.470 --> 00:20:17.480 align:start position:0% should be inferred 00:20:17.480 --> 00:20:20.510 align:start position:0% should be inferred automatically<00:20:18.480> right<00:20:18.760> that's<00:20:19.240> it<00:20:20.240> you<00:20:20.360> can 00:20:20.510 --> 00:20:20.520 align:start position:0% automatically right that's it you can 00:20:20.520 --> 00:20:22.310 align:start position:0% automatically right that's it you can check<00:20:20.720> out<00:20:20.919> the<00:20:21.080> code 00:20:22.310 --> 00:20:22.320 align:start position:0% check out the code 00:20:22.320 --> 00:20:25.830 align:start position:0% check out the code here 00:20:25.830 --> 00:20:25.840 align:start position:0% 00:20:25.840 --> 00:20:29.430 align:start position:0% yeah<00:20:26.840> amazing<00:20:27.480> alexand<00:20:28.400> thanks<00:20:28.760> so<00:20:28.880> much<00:20:29.080> for 00:20:29.430 --> 00:20:29.440 align:start position:0% yeah amazing alexand thanks so much for 00:20:29.440 --> 00:20:32.390 align:start position:0% yeah amazing alexand thanks so much for for<00:20:29.640> the<00:20:29.799> great<00:20:30.000> introduction<00:20:30.440> of<00:20:30.919> wizard<00:20:31.919> so 00:20:32.390 --> 00:20:32.400 align:start position:0% for the great introduction of wizard so 00:20:32.400 --> 00:20:34.549 align:start position:0% for the great introduction of wizard so uh<00:20:32.600> reminder<00:20:33.159> that<00:20:33.320> if<00:20:33.440> you<00:20:33.600> scan<00:20:33.840> the<00:20:33.960> QR<00:20:34.280> code 00:20:34.549 --> 00:20:34.559 align:start position:0% uh reminder that if you scan the QR code 00:20:34.559 --> 00:20:36.149 align:start position:0% uh reminder that if you scan the QR code you<00:20:34.679> will<00:20:34.960> attend<00:20:35.240> the<00:20:35.360> session<00:20:35.840> and<00:20:35.919> you<00:20:36.000> can 00:20:36.149 --> 00:20:36.159 align:start position:0% you will attend the session and you can 00:20:36.159 --> 00:20:38.029 align:start position:0% you will attend the session and you can ask<00:20:36.360> questions<00:20:36.840> and<00:20:37.000> you<00:20:37.240> can<00:20:37.400> also<00:20:37.600> claim<00:20:37.880> an 00:20:38.029 --> 00:20:38.039 align:start position:0% ask questions and you can also claim an 00:20:38.039 --> 00:20:40.909 align:start position:0% ask questions and you can also claim an nft<00:20:38.880> so<00:20:39.159> and<00:20:39.320> you<00:20:39.400> can<00:20:39.559> also<00:20:39.799> vote<00:20:40.240> so<00:20:40.440> if<00:20:40.559> you 00:20:40.909 --> 00:20:40.919 align:start position:0% nft so and you can also vote so if you 00:20:40.919 --> 00:20:42.430 align:start position:0% nft so and you can also vote so if you have<00:20:41.080> a<00:20:41.240> question<00:20:41.520> that<00:20:41.640> you<00:20:41.799> really<00:20:42.000> want<00:20:42.280> it 00:20:42.430 --> 00:20:42.440 align:start position:0% have a question that you really want it 00:20:42.440 --> 00:20:44.310 align:start position:0% have a question that you really want it to<00:20:42.559> be<00:20:42.760> answered<00:20:43.320> uh<00:20:43.440> vote<00:20:43.640> for<00:20:43.799> them<00:20:44.039> so<00:20:44.200> let's 00:20:44.310 --> 00:20:44.320 align:start position:0% to be answered uh vote for them so let's 00:20:44.320 --> 00:20:46.390 align:start position:0% to be answered uh vote for them so let's start<00:20:44.520> with<00:20:44.640> the<00:20:44.799> top<00:20:45.000> one<00:20:45.799> uh<00:20:45.919> does<00:20:46.080> wizard 00:20:46.390 --> 00:20:46.400 align:start position:0% start with the top one uh does wizard 00:20:46.400 --> 00:20:48.950 align:start position:0% start with the top one uh does wizard support<00:20:46.679> local<00:20:47.240> tables<00:20:48.080> and<00:20:48.400> can<00:20:48.520> it<00:20:48.640> be<00:20:48.720> used 00:20:48.950 --> 00:20:48.960 align:start position:0% support local tables and can it be used 00:20:48.960 --> 00:20:51.070 align:start position:0% support local tables and can it be used to<00:20:49.039> implement<00:20:49.760> uh<00:20:49.880> local<00:20:50.200> tables<00:20:50.520> based<00:20:50.760> on 00:20:51.070 --> 00:20:51.080 align:start position:0% to implement uh local tables based on 00:20:51.080 --> 00:20:54.230 align:start position:0% to implement uh local tables based on ckvm<00:20:52.080> uh<00:20:52.200> absolutely<00:20:53.159> so<00:20:53.679> uh<00:20:53.799> the<00:20:53.960> way<00:20:54.120> you 00:20:54.230 --> 00:20:54.240 align:start position:0% ckvm uh absolutely so uh the way you 00:20:54.240 --> 00:20:56.909 align:start position:0% ckvm uh absolutely so uh the way you would<00:20:54.440> do<00:20:54.600> it<00:20:54.840> is<00:20:55.000> for<00:20:55.200> instance<00:20:55.679> say<00:20:56.400> um<00:20:56.640> so 00:20:56.909 --> 00:20:56.919 align:start position:0% would do it is for instance say um so 00:20:56.919 --> 00:20:58.710 align:start position:0% would do it is for instance say um so what<00:20:57.039> you<00:20:57.159> can<00:20:57.320> do<00:20:57.520> first<00:20:57.720> of<00:20:57.840> all<00:20:58.159> if<00:20:58.280> you<00:20:58.400> want 00:20:58.710 --> 00:20:58.720 align:start position:0% what you can do first of all if you want 00:20:58.720 --> 00:21:00.990 align:start position:0% what you can do first of all if you want to<00:20:58.840> do<00:20:59.000> range<00:20:59.360> checks<00:20:59.720> so<00:21:00.000> that's<00:21:00.320> a<00:21:00.480> big<00:21:00.640> use 00:21:00.990 --> 00:21:01.000 align:start position:0% to do range checks so that's a big use 00:21:01.000 --> 00:21:02.909 align:start position:0% to do range checks so that's a big use case<00:21:01.120> for<00:21:01.320> lookup<00:21:01.679> table<00:21:02.200> you<00:21:02.360> already<00:21:02.640> have<00:21:02.799> a 00:21:02.909 --> 00:21:02.919 align:start position:0% case for lookup table you already have a 00:21:02.919 --> 00:21:05.149 align:start position:0% case for lookup table you already have a range<00:21:03.200> query<00:21:03.679> so<00:21:04.039> you<00:21:04.200> just<00:21:04.400> take<00:21:04.600> one<00:21:04.799> colon 00:21:05.149 --> 00:21:05.159 align:start position:0% range query so you just take one colon 00:21:05.159 --> 00:21:07.430 align:start position:0% range query so you just take one colon and<00:21:05.280> you<00:21:05.440> say<00:21:06.000> I<00:21:06.159> have<00:21:06.320> this<00:21:06.559> query<00:21:07.039> that<00:21:07.200> just 00:21:07.430 --> 00:21:07.440 align:start position:0% and you say I have this query that just 00:21:07.440 --> 00:21:09.230 align:start position:0% and you say I have this query that just enforce<00:21:07.880> the<00:21:08.000> whole<00:21:08.240> colon<00:21:08.520> to<00:21:08.640> be<00:21:08.840> within 00:21:09.230 --> 00:21:09.240 align:start position:0% enforce the whole colon to be within 00:21:09.240 --> 00:21:13.029 align:start position:0% enforce the whole colon to be within Bond<00:21:10.240> and<00:21:10.440> that's<00:21:10.600> all<00:21:10.799> you<00:21:11.320> do<00:21:12.320> uh<00:21:12.480> a<00:21:12.640> second 00:21:13.029 --> 00:21:13.039 align:start position:0% Bond and that's all you do uh a second 00:21:13.039 --> 00:21:14.870 align:start position:0% Bond and that's all you do uh a second way<00:21:13.279> if<00:21:13.360> you<00:21:13.480> want<00:21:13.600> to<00:21:13.720> do<00:21:13.880> more<00:21:14.080> complicated<00:21:14.640> R 00:21:14.870 --> 00:21:14.880 align:start position:0% way if you want to do more complicated R 00:21:14.880 --> 00:21:17.149 align:start position:0% way if you want to do more complicated R checks<00:21:15.240> likeor<00:21:16.120> for<00:21:16.279> instance<00:21:16.919> then<00:21:17.080> you 00:21:17.149 --> 00:21:17.159 align:start position:0% checks likeor for instance then you 00:21:17.159 --> 00:21:19.070 align:start position:0% checks likeor for instance then you would<00:21:17.360> have<00:21:17.480> to<00:21:17.679> specify<00:21:18.200> three<00:21:18.440> colons<00:21:18.880> for 00:21:19.070 --> 00:21:19.080 align:start position:0% would have to specify three colons for 00:21:19.080 --> 00:21:22.029 align:start position:0% would have to specify three colons for your<00:21:19.279> exor<00:21:19.799> one<00:21:20.039> colon<00:21:20.440> for<00:21:20.919> the<00:21:21.159> left<00:21:21.480> side 00:21:22.029 --> 00:21:22.039 align:start position:0% your exor one colon for the left side 00:21:22.039 --> 00:21:24.190 align:start position:0% your exor one colon for the left side the<00:21:22.320> hand<00:21:22.919> the<00:21:23.080> right<00:21:23.320> side<00:21:23.480> and<00:21:23.640> one<00:21:23.799> for<00:21:24.000> the 00:21:24.190 --> 00:21:24.200 align:start position:0% the hand the right side and one for the 00:21:24.200 --> 00:21:26.909 align:start position:0% the hand the right side and one for the result<00:21:24.799> and<00:21:25.000> in<00:21:25.200> this<00:21:25.400> colon<00:21:25.799> you<00:21:26.120> put<00:21:26.400> all<00:21:26.600> the 00:21:26.909 --> 00:21:26.919 align:start position:0% result and in this colon you put all the 00:21:26.919 --> 00:21:30.510 align:start position:0% result and in this colon you put all the possible<00:21:27.679> uh<00:21:27.880> all<00:21:28.039> the<00:21:28.159> possib<00:21:28.960> ities<00:21:29.960> uh<00:21:30.159> so 00:21:30.510 --> 00:21:30.520 align:start position:0% possible uh all the possib ities uh so 00:21:30.520 --> 00:21:33.269 align:start position:0% possible uh all the possib ities uh so maybe<00:21:30.919> say<00:21:31.159> for<00:21:31.520> 8<00:21:31.799> Bits<00:21:32.039> to<00:21:32.200> 8<00:21:32.440> Bits<00:21:32.880> you<00:21:33.000> would 00:21:33.269 --> 00:21:33.279 align:start position:0% maybe say for 8 Bits to 8 Bits you would 00:21:33.279 --> 00:21:35.549 align:start position:0% maybe say for 8 Bits to 8 Bits you would have<00:21:33.559> a<00:21:33.760> Col<00:21:34.120> you<00:21:34.240> would<00:21:34.440> have<00:21:34.600> two<00:21:34.760> to<00:21:34.919> the<00:21:35.120> 16 00:21:35.549 --> 00:21:35.559 align:start position:0% have a Col you would have two to the 16 00:21:35.559 --> 00:21:37.470 align:start position:0% have a Col you would have two to the 16 possibility<00:21:36.400> so<00:21:36.600> you<00:21:36.720> write<00:21:36.960> down<00:21:37.159> all<00:21:37.320> of 00:21:37.470 --> 00:21:37.480 align:start position:0% possibility so you write down all of 00:21:37.480 --> 00:21:40.549 align:start position:0% possibility so you write down all of that<00:21:37.640> in<00:21:37.760> your<00:21:38.000> table<00:21:38.640> and<00:21:38.840> then<00:21:39.080> you<00:21:39.799> create<00:21:40.360> a 00:21:40.549 --> 00:21:40.559 align:start position:0% that in your table and then you create a 00:21:40.559 --> 00:21:43.310 align:start position:0% that in your table and then you create a lookup<00:21:41.200> constraints<00:21:41.840> between<00:21:42.559> this<00:21:42.799> table 00:21:43.310 --> 00:21:43.320 align:start position:0% lookup constraints between this table 00:21:43.320 --> 00:21:45.310 align:start position:0% lookup constraints between this table and<00:21:43.640> a<00:21:43.799> tri<00:21:44.039> plate<00:21:44.240> of<00:21:44.400> color<00:21:44.840> for<00:21:45.039> which<00:21:45.200> you 00:21:45.310 --> 00:21:45.320 align:start position:0% and a tri plate of color for which you 00:21:45.320 --> 00:21:50.789 align:start position:0% and a tri plate of color for which you want<00:21:45.440> to<00:21:45.640> enforce<00:21:46.640> exor<00:21:48.000> uh<00:21:49.000> uh<00:21:49.799> constraint 00:21:50.789 --> 00:21:50.799 align:start position:0% want to enforce exor uh uh constraint 00:21:50.799 --> 00:21:52.990 align:start position:0% want to enforce exor uh uh constraint and<00:21:50.919> you<00:21:51.039> can<00:21:51.240> also<00:21:51.640> add<00:21:52.200> a<00:21:52.679> conditional 00:21:52.990 --> 00:21:53.000 align:start position:0% and you can also add a conditional 00:21:53.000 --> 00:21:55.190 align:start position:0% and you can also add a conditional lookups<00:21:53.679> you<00:21:53.799> can<00:21:53.960> have<00:21:54.080> a<00:21:54.200> force<00:21:54.520> colon<00:21:54.880> that 00:21:55.190 --> 00:21:55.200 align:start position:0% lookups you can have a force colon that 00:21:55.200 --> 00:21:58.630 align:start position:0% lookups you can have a force colon that say<00:21:56.200> that<00:21:56.320> contains<00:21:56.720> zeros<00:21:57.159> or<00:21:57.400> one<00:21:57.960> and<00:21:58.120> that 00:21:58.630 --> 00:21:58.640 align:start position:0% say that contains zeros or one and that 00:21:58.640 --> 00:22:01.710 align:start position:0% say that contains zeros or one and that activate<00:21:59.279> the<00:21:59.640> the<00:21:59.840> exort<00:22:00.279> constraints<00:22:00.720> or 00:22:01.710 --> 00:22:01.720 align:start position:0% activate the the exort constraints or 00:22:01.720 --> 00:22:04.390 align:start position:0% activate the the exort constraints or not<00:22:02.720> great<00:22:03.000> thanks<00:22:03.159> for<00:22:03.360> the<00:22:03.480> answer<00:22:04.000> the<00:22:04.159> next 00:22:04.390 --> 00:22:04.400 align:start position:0% not great thanks for the answer the next 00:22:04.400 --> 00:22:05.750 align:start position:0% not great thanks for the answer the next question<00:22:04.640> is<00:22:04.840> can<00:22:04.960> you<00:22:05.080> create<00:22:05.400> different 00:22:05.750 --> 00:22:05.760 align:start position:0% question is can you create different 00:22:05.760 --> 00:22:08.029 align:start position:0% question is can you create different custom<00:22:06.120> Gates<00:22:06.799> and<00:22:07.159> at<00:22:07.320> which<00:22:07.559> instance<00:22:07.960> do 00:22:08.029 --> 00:22:08.039 align:start position:0% custom Gates and at which instance do 00:22:08.039 --> 00:22:09.750 align:start position:0% custom Gates and at which instance do you<00:22:08.240> decide<00:22:08.600> which<00:22:08.720> roow<00:22:09.000> corresponds<00:22:09.559> to 00:22:09.750 --> 00:22:09.760 align:start position:0% you decide which roow corresponds to 00:22:09.760 --> 00:22:11.149 align:start position:0% you decide which roow corresponds to each<00:22:10.080> kind<00:22:10.279> of 00:22:11.149 --> 00:22:11.159 align:start position:0% each kind of 00:22:11.159 --> 00:22:14.510 align:start position:0% each kind of gate<00:22:12.159> um<00:22:12.279> so<00:22:12.480> when<00:22:12.640> you<00:22:12.840> generate<00:22:13.520> a<00:22:13.720> global 00:22:14.510 --> 00:22:14.520 align:start position:0% gate um so when you generate a global 00:22:14.520 --> 00:22:17.190 align:start position:0% gate um so when you generate a global constraint<00:22:15.520> this<00:22:15.760> is<00:22:16.000> essentially<00:22:16.720> what<00:22:17.039> is 00:22:17.190 --> 00:22:17.200 align:start position:0% constraint this is essentially what is 00:22:17.200 --> 00:22:19.390 align:start position:0% constraint this is essentially what is your<00:22:17.440> custom<00:22:17.799> gate<00:22:18.600> uh<00:22:18.720> then<00:22:18.880> it's<00:22:19.080> going<00:22:19.240> to 00:22:19.390 --> 00:22:19.400 align:start position:0% your custom gate uh then it's going to 00:22:19.400 --> 00:22:22.789 align:start position:0% your custom gate uh then it's going to apply<00:22:19.679> over<00:22:20.200> everything<00:22:21.200> um<00:22:21.480> but<00:22:22.279> the<00:22:22.480> wiard 00:22:22.789 --> 00:22:22.799 align:start position:0% apply over everything um but the wiard 00:22:22.799 --> 00:22:24.950 align:start position:0% apply over everything um but the wiard framework<00:22:23.200> is<00:22:23.320> more<00:22:23.480> abstract<00:22:23.919> than<00:22:24.120> this<00:22:24.840> uh 00:22:24.950 --> 00:22:24.960 align:start position:0% framework is more abstract than this uh 00:22:24.960 --> 00:22:27.029 align:start position:0% framework is more abstract than this uh essentially<00:22:25.880> there<00:22:25.960> is<00:22:26.279> a<00:22:26.360> general<00:22:26.720> technique 00:22:27.029 --> 00:22:27.039 align:start position:0% essentially there is a general technique 00:22:27.039 --> 00:22:29.190 align:start position:0% essentially there is a general technique to<00:22:27.159> do<00:22:27.320> it<00:22:28.200> uh<00:22:28.320> which<00:22:28.520> which<00:22:28.640> is<00:22:28.760> to<00:22:28.840> say<00:22:29.039> that 00:22:29.190 --> 00:22:29.200 align:start position:0% to do it uh which which is to say that 00:22:29.200 --> 00:22:31.230 align:start position:0% to do it uh which which is to say that you<00:22:29.360> add<00:22:29.640> a<00:22:29.799> selectors<00:22:30.360> colon<00:22:30.760> that<00:22:30.880> says 00:22:31.230 --> 00:22:31.240 align:start position:0% you add a selectors colon that says 00:22:31.240 --> 00:22:33.909 align:start position:0% you add a selectors colon that says which<00:22:31.440> constraint<00:22:31.840> is<00:22:32.000> going<00:22:32.159> to<00:22:32.640> apply<00:22:33.640> uh 00:22:33.909 --> 00:22:33.919 align:start position:0% which constraint is going to apply uh 00:22:33.919 --> 00:22:38.669 align:start position:0% which constraint is going to apply uh for<00:22:34.200> each<00:22:34.520> and<00:22:34.720> you<00:22:35.679> have<00:22:36.159> a<00:22:36.480> some<00:22:36.880> product<00:22:37.880> of 00:22:38.669 --> 00:22:38.679 align:start position:0% for each and you have a some product of 00:22:38.679 --> 00:22:41.710 align:start position:0% for each and you have a some product of your<00:22:39.200> constraint<00:22:40.200> custom<00:22:40.559> Gates<00:22:40.919> expression 00:22:41.710 --> 00:22:41.720 align:start position:0% your constraint custom Gates expression 00:22:41.720 --> 00:22:45.630 align:start position:0% your constraint custom Gates expression multiplied<00:22:42.480> by<00:22:43.360> uh<00:22:43.559> an<00:22:43.799> indicative<00:22:44.559> that<00:22:45.200> ask 00:22:45.630 --> 00:22:45.640 align:start position:0% multiplied by uh an indicative that ask 00:22:45.640 --> 00:22:47.310 align:start position:0% multiplied by uh an indicative that ask whether<00:22:45.960> this<00:22:46.120> constraint<00:22:46.520> is<00:22:46.720> active<00:22:47.080> here 00:22:47.310 --> 00:22:47.320 align:start position:0% whether this constraint is active here 00:22:47.320 --> 00:22:49.549 align:start position:0% whether this constraint is active here or<00:22:47.520> not<00:22:48.320> and<00:22:48.520> you<00:22:48.640> would<00:22:48.840> merge<00:22:49.200> everything 00:22:49.549 --> 00:22:49.559 align:start position:0% or not and you would merge everything 00:22:49.559 --> 00:22:51.269 align:start position:0% or not and you would merge everything into<00:22:49.760> a<00:22:49.919> single<00:22:50.240> Global<00:22:50.559> constraint<00:22:51.000> in<00:22:51.120> the 00:22:51.269 --> 00:22:51.279 align:start position:0% into a single Global constraint in the 00:22:51.279 --> 00:22:53.029 align:start position:0% into a single Global constraint in the end<00:22:51.600> so<00:22:51.799> yes<00:22:51.960> you<00:22:52.080> could<00:22:52.240> Implement<00:22:52.679> custom 00:22:53.029 --> 00:22:53.039 align:start position:0% end so yes you could Implement custom 00:22:53.039 --> 00:22:55.590 align:start position:0% end so yes you could Implement custom gaug<00:22:53.320> actually<00:22:53.679> that's<00:22:54.520> uh<00:22:54.760> what<00:22:55.159> they<00:22:55.279> do<00:22:55.480> all 00:22:55.590 --> 00:22:55.600 align:start position:0% gaug actually that's uh what they do all 00:22:55.600 --> 00:22:59.510 align:start position:0% gaug actually that's uh what they do all the<00:22:55.799> time<00:22:56.279> uh<00:22:56.440> when<00:22:56.640> they<00:22:56.880> specify<00:22:57.440> the<00:22:57.600> evm 00:22:59.510 --> 00:22:59.520 align:start position:0% the time uh when they specify the evm 00:22:59.520 --> 00:23:01.510 align:start position:0% the time uh when they specify the evm great<00:23:00.240> the<00:23:00.400> next<00:23:00.679> question<00:23:00.919> is<00:23:01.120> about 00:23:01.510 --> 00:23:01.520 align:start position:0% great the next question is about 00:23:01.520 --> 00:23:03.510 align:start position:0% great the next question is about recursion<00:23:02.240> so<00:23:02.400> is<00:23:02.559> recursion<00:23:03.039> something<00:23:03.360> that 00:23:03.510 --> 00:23:03.520 align:start position:0% recursion so is recursion something that 00:23:03.520 --> 00:23:06.070 align:start position:0% recursion so is recursion something that would<00:23:03.679> be<00:23:03.840> implemented<00:23:04.760> in<00:23:04.960> Wizard<00:23:05.600> or<00:23:05.880> would 00:23:06.070 --> 00:23:06.080 align:start position:0% would be implemented in Wizard or would 00:23:06.080 --> 00:23:08.909 align:start position:0% would be implemented in Wizard or would it<00:23:06.240> be<00:23:06.480> separately<00:23:07.000> like<00:23:07.320> a<00:23:07.480> commitment<00:23:08.440> uh<00:23:08.600> so 00:23:08.909 --> 00:23:08.919 align:start position:0% it be separately like a commitment uh so 00:23:08.919 --> 00:23:11.430 align:start position:0% it be separately like a commitment uh so there<00:23:09.039> is<00:23:09.279> separate<00:23:09.919> where<00:23:10.159> you<00:23:10.279> can<00:23:10.480> do<00:23:10.720> a 00:23:11.430 --> 00:23:11.440 align:start position:0% there is separate where you can do a 00:23:11.440 --> 00:23:14.510 align:start position:0% there is separate where you can do a recursion<00:23:12.440> uh<00:23:12.679> so<00:23:13.039> we<00:23:13.200> do<00:23:13.400> it<00:23:13.840> inside<00:23:14.159> of<00:23:14.320> the 00:23:14.510 --> 00:23:14.520 align:start position:0% recursion uh so we do it inside of the 00:23:14.520 --> 00:23:17.269 align:start position:0% recursion uh so we do it inside of the wiard<00:23:15.000> at<00:23:15.159> at<00:23:15.279> the<00:23:15.400> same<00:23:15.679> time<00:23:16.240> and 00:23:17.269 --> 00:23:17.279 align:start position:0% wiard at at the same time and 00:23:17.279 --> 00:23:21.510 align:start position:0% wiard at at the same time and outside<00:23:18.640> uh<00:23:19.640> so<00:23:20.279> the<00:23:20.440> first<00:23:20.720> way<00:23:21.080> we<00:23:21.200> have<00:23:21.360> a 00:23:21.510 --> 00:23:21.520 align:start position:0% outside uh so the first way we have a 00:23:21.520 --> 00:23:23.149 align:start position:0% outside uh so the first way we have a compilation<00:23:22.039> steps<00:23:22.360> that<00:23:22.559> is<00:23:22.679> called<00:23:22.880> self 00:23:23.149 --> 00:23:23.159 align:start position:0% compilation steps that is called self 00:23:23.159 --> 00:23:25.070 align:start position:0% compilation steps that is called self recur<00:23:23.760> that<00:23:23.919> usually<00:23:24.279> goes<00:23:24.559> just<00:23:24.720> after 00:23:25.070 --> 00:23:25.080 align:start position:0% recur that usually goes just after 00:23:25.080 --> 00:23:27.669 align:start position:0% recur that usually goes just after Vortex<00:23:25.799> that<00:23:26.000> text<00:23:26.200> a<00:23:26.360> Vortex<00:23:26.679> proof<00:23:26.960> and<00:23:27.120> rear 00:23:27.669 --> 00:23:27.679 align:start position:0% Vortex that text a Vortex proof and rear 00:23:27.679 --> 00:23:30.190 align:start position:0% Vortex that text a Vortex proof and rear matize<00:23:28.080> it<00:23:28.840> and<00:23:29.000> we<00:23:29.120> can<00:23:29.240> do<00:23:29.440> proofs<00:23:29.760> of<00:23:29.960> that 00:23:30.190 --> 00:23:30.200 align:start position:0% matize it and we can do proofs of that 00:23:30.200 --> 00:23:32.029 align:start position:0% matize it and we can do proofs of that again<00:23:30.400> and<00:23:30.520> we<00:23:30.720> repeat<00:23:31.279> and<00:23:31.440> we<00:23:31.520> can<00:23:31.640> shrink 00:23:32.029 --> 00:23:32.039 align:start position:0% again and we repeat and we can shrink 00:23:32.039 --> 00:23:34.630 align:start position:0% again and we repeat and we can shrink the<00:23:32.200> proof<00:23:32.720> that's<00:23:32.960> because<00:23:33.240> vertex<00:23:34.120> uh<00:23:34.360> as<00:23:34.520> a 00:23:34.630 --> 00:23:34.640 align:start position:0% the proof that's because vertex uh as a 00:23:34.640 --> 00:23:36.110 align:start position:0% the proof that's because vertex uh as a single<00:23:35.000> polinomial<00:23:35.440> commitment<00:23:35.880> has<00:23:36.000> a 00:23:36.110 --> 00:23:36.120 align:start position:0% single polinomial commitment has a 00:23:36.120 --> 00:23:38.870 align:start position:0% single polinomial commitment has a square<00:23:36.320> root<00:23:36.919> verifier<00:23:37.559> time<00:23:38.080> but<00:23:38.520> applying 00:23:38.870 --> 00:23:38.880 align:start position:0% square root verifier time but applying 00:23:38.880 --> 00:23:41.510 align:start position:0% square root verifier time but applying log<00:23:39.159> login<00:23:39.640> application<00:23:40.279> of<00:23:40.520> self<00:23:40.880> retion<00:23:41.400> you 00:23:41.510 --> 00:23:41.520 align:start position:0% log login application of self retion you 00:23:41.520 --> 00:23:44.909 align:start position:0% log login application of self retion you get<00:23:41.720> constant<00:23:42.120> size<00:23:42.880> proof<00:23:43.880> great<00:23:44.640> and<00:23:44.760> the 00:23:44.909 --> 00:23:44.919 align:start position:0% get constant size proof great and the 00:23:44.919 --> 00:23:46.190 align:start position:0% get constant size proof great and the last<00:23:45.120> question<00:23:45.320> that<00:23:45.440> we<00:23:45.600> have<00:23:45.760> in<00:23:45.840> the<00:23:46.000> queue 00:23:46.190 --> 00:23:46.200 align:start position:0% last question that we have in the queue 00:23:46.200 --> 00:23:48.750 align:start position:0% last question that we have in the queue at<00:23:46.279> least<00:23:46.440> for<00:23:46.600> now<00:23:47.279> is<00:23:47.880> uh<00:23:48.039> that<00:23:48.200> it's<00:23:48.400> great 00:23:48.750 --> 00:23:48.760 align:start position:0% at least for now is uh that it's great 00:23:48.760 --> 00:23:51.430 align:start position:0% at least for now is uh that it's great that<00:23:49.039> you<00:23:49.320> can<00:23:49.559> define<00:23:49.919> an<00:23:50.159> ideal<00:23:50.919> protocol 00:23:51.430 --> 00:23:51.440 align:start position:0% that you can define an ideal protocol 00:23:51.440 --> 00:23:53.110 align:start position:0% that you can define an ideal protocol programmatically<00:23:52.240> and<00:23:52.400> it<00:23:52.559> seems<00:23:52.760> that<00:23:52.960> that 00:23:53.110 --> 00:23:53.120 align:start position:0% programmatically and it seems that that 00:23:53.120 --> 00:23:55.110 align:start position:0% programmatically and it seems that that does<00:23:53.400> make<00:23:53.520> it<00:23:53.720> easy<00:23:54.320> would<00:23:54.559> would<00:23:54.760> does<00:23:54.919> that 00:23:55.110 --> 00:23:55.120 align:start position:0% does make it easy would would does that 00:23:55.120 --> 00:23:57.269 align:start position:0% does make it easy would would does that make<00:23:55.240> it<00:23:55.440> easy<00:23:56.120> or<00:23:56.400> possible<00:23:56.760> to<00:23:56.880> support 00:23:57.269 --> 00:23:57.279 align:start position:0% make it easy or possible to support 00:23:57.279 --> 00:23:59.950 align:start position:0% make it easy or possible to support automated<00:23:57.760> formal<00:23:58.120> verif<00:23:58.520> ification<00:23:59.440> or<00:23:59.760> you 00:23:59.950 --> 00:23:59.960 align:start position:0% automated formal verif ification or you 00:23:59.960 --> 00:24:01.390 align:start position:0% automated formal verif ification or you see<00:24:00.200> proofs<00:24:00.559> of 00:24:01.390 --> 00:24:01.400 align:start position:0% see proofs of 00:24:01.400 --> 00:24:04.230 align:start position:0% see proofs of security<00:24:02.400> um 00:24:04.230 --> 00:24:04.240 align:start position:0% security um 00:24:04.240 --> 00:24:07.630 align:start position:0% security um so<00:24:05.240> I'm<00:24:05.400> not<00:24:05.600> too<00:24:05.799> sure<00:24:06.679> what<00:24:06.799> it<00:24:06.919> would<00:24:07.159> entail 00:24:07.630 --> 00:24:07.640 align:start position:0% so I'm not too sure what it would entail 00:24:07.640 --> 00:24:10.149 align:start position:0% so I'm not too sure what it would entail exactly<00:24:08.080> to<00:24:08.679> formally<00:24:09.240> verify<00:24:09.640> so<00:24:09.840> we<00:24:09.960> could 00:24:10.149 --> 00:24:10.159 align:start position:0% exactly to formally verify so we could 00:24:10.159 --> 00:24:12.830 align:start position:0% exactly to formally verify so we could formally<00:24:10.679> verify<00:24:11.679> uh<00:24:11.799> like<00:24:11.960> the<00:24:12.159> standard<00:24:12.600> set 00:24:12.830 --> 00:24:12.840 align:start position:0% formally verify uh like the standard set 00:24:12.840 --> 00:24:14.830 align:start position:0% formally verify uh like the standard set of<00:24:13.000> compilers<00:24:13.559> that<00:24:13.720> we<00:24:13.880> have<00:24:14.200> I<00:24:14.400> think<00:24:14.679> this 00:24:14.830 --> 00:24:14.840 align:start position:0% of compilers that we have I think this 00:24:14.840 --> 00:24:16.950 align:start position:0% of compilers that we have I think this is<00:24:15.279> at<00:24:15.400> least<00:24:15.559> a<00:24:15.760> necessity<00:24:16.520> but<00:24:16.679> then<00:24:16.840> there 00:24:16.950 --> 00:24:16.960 align:start position:0% is at least a necessity but then there 00:24:16.960 --> 00:24:19.269 align:start position:0% is at least a necessity but then there is<00:24:17.080> a<00:24:17.240> protocol<00:24:17.720> description<00:24:18.200> it<00:24:18.279> should<00:24:18.520> be 00:24:19.269 --> 00:24:19.279 align:start position:0% is a protocol description it should be 00:24:19.279 --> 00:24:22.390 align:start position:0% is a protocol description it should be formally<00:24:19.840> verified<00:24:20.840> this<00:24:21.120> I<00:24:21.240> don't<00:24:21.440> know<00:24:22.000> how 00:24:22.390 --> 00:24:22.400 align:start position:0% formally verified this I don't know how 00:24:22.400 --> 00:24:24.909 align:start position:0% formally verified this I don't know how how<00:24:22.600> to<00:24:22.799> do<00:24:22.960> it<00:24:23.520> I<00:24:23.679> don't<00:24:23.880> know<00:24:24.400> and<00:24:24.600> I<00:24:24.720> can't 00:24:24.909 --> 00:24:24.919 align:start position:0% how to do it I don't know and I can't 00:24:24.919 --> 00:24:26.710 align:start position:0% how to do it I don't know and I can't tell<00:24:25.080> you<00:24:25.279> how<00:24:25.399> to<00:24:25.559> make<00:24:25.679> it<00:24:25.840> easy<00:24:26.440> but<00:24:26.600> that 00:24:26.710 --> 00:24:26.720 align:start position:0% tell you how to make it easy but that 00:24:26.720 --> 00:24:29.029 align:start position:0% tell you how to make it easy but that would<00:24:26.840> be<00:24:26.960> a<00:24:27.080> great<00:24:27.279> use<00:24:27.559> case<00:24:28.039> I<00:24:28.159> agree 00:24:29.029 --> 00:24:29.039 align:start position:0% would be a great use case I agree 00:24:29.039 --> 00:24:31.070 align:start position:0% would be a great use case I agree yeah<00:24:29.240> it<00:24:29.320> will<00:24:29.440> be<00:24:29.600> great<00:24:29.840> maybe<00:24:30.320> after<00:24:30.799> have 00:24:31.070 --> 00:24:31.080 align:start position:0% yeah it will be great maybe after have 00:24:31.080 --> 00:24:33.720 align:start position:0% yeah it will be great maybe after have the<00:24:31.200> conversation