WEBVTT Kind: captions Language: en 00:00:00.000 --> 00:00:04.350 align:start position:0% foreign 00:00:04.350 --> 00:00:04.360 align:start position:0% 00:00:04.360 --> 00:00:13.749 align:start position:0% [Music] 00:00:13.749 --> 00:00:13.759 align:start position:0% 00:00:13.759 --> 00:00:16.970 align:start position:0% math<00:00:14.759> this<00:00:15.059> is<00:00:15.240> also<00:00:15.540> developing<00:00:16.139> this<00:00:16.859> is 00:00:16.970 --> 00:00:16.980 align:start position:0% math this is also developing this is 00:00:16.980 --> 00:00:18.890 align:start position:0% math this is also developing this is also<00:00:17.220> tooling<00:00:17.520> for<00:00:17.699> developers<00:00:18.119> so<00:00:18.600> today<00:00:18.720> I'm 00:00:18.890 --> 00:00:18.900 align:start position:0% also tooling for developers so today I'm 00:00:18.900 --> 00:00:20.810 align:start position:0% also tooling for developers so today I'm going<00:00:19.020> to<00:00:19.140> present<00:00:19.320> Socrates<00:00:19.800> I'm<00:00:20.460> going<00:00:20.640> to 00:00:20.810 --> 00:00:20.820 align:start position:0% going to present Socrates I'm going to 00:00:20.820 --> 00:00:22.429 align:start position:0% going to present Socrates I'm going to give<00:00:20.939> a<00:00:21.180> quick<00:00:21.300> introduction<00:00:21.720> to<00:00:21.960> what<00:00:22.140> it<00:00:22.260> is 00:00:22.429 --> 00:00:22.439 align:start position:0% give a quick introduction to what it is 00:00:22.439 --> 00:00:25.550 align:start position:0% give a quick introduction to what it is for<00:00:23.160> those<00:00:23.460> of<00:00:23.640> you<00:00:24.000> who<00:00:24.300> don't<00:00:24.420> know<00:00:24.600> it<00:00:24.840> and 00:00:25.550 --> 00:00:25.560 align:start position:0% for those of you who don't know it and 00:00:25.560 --> 00:00:27.470 align:start position:0% for those of you who don't know it and then<00:00:25.740> I<00:00:25.920> will<00:00:26.160> present<00:00:26.760> a<00:00:27.000> few<00:00:27.119> things<00:00:27.240> that 00:00:27.470 --> 00:00:27.480 align:start position:0% then I will present a few things that 00:00:27.480 --> 00:00:28.730 align:start position:0% then I will present a few things that we've<00:00:27.720> been<00:00:27.840> working<00:00:28.019> on<00:00:28.199> and<00:00:28.380> that<00:00:28.619> I'm 00:00:28.730 --> 00:00:28.740 align:start position:0% we've been working on and that I'm 00:00:28.740 --> 00:00:31.970 align:start position:0% we've been working on and that I'm excited<00:00:29.099> to<00:00:29.220> share<00:00:29.939> so<00:00:30.359> what<00:00:30.539> is<00:00:30.660> Socrates<00:00:31.080> if 00:00:31.970 --> 00:00:31.980 align:start position:0% excited to share so what is Socrates if 00:00:31.980 --> 00:00:34.910 align:start position:0% excited to share so what is Socrates if you<00:00:32.040> want<00:00:32.220> to<00:00:32.340> program<00:00:32.960> snarks<00:00:33.960> today 00:00:34.910 --> 00:00:34.920 align:start position:0% you want to program snarks today 00:00:34.920 --> 00:00:36.770 align:start position:0% you want to program snarks today there's<00:00:35.460> different<00:00:35.700> tools<00:00:36.180> that<00:00:36.300> you<00:00:36.480> can<00:00:36.600> use 00:00:36.770 --> 00:00:36.780 align:start position:0% there's different tools that you can use 00:00:36.780 --> 00:00:39.049 align:start position:0% there's different tools that you can use maybe<00:00:37.140> some<00:00:37.440> of<00:00:37.559> you<00:00:37.680> have<00:00:37.800> heard<00:00:38.160> of<00:00:38.579> Socrates 00:00:39.049 --> 00:00:39.059 align:start position:0% maybe some of you have heard of Socrates 00:00:39.059 --> 00:00:41.030 align:start position:0% maybe some of you have heard of Socrates and<00:00:39.840> all<00:00:40.020> those<00:00:40.200> tools<00:00:40.559> have<00:00:40.800> different 00:00:41.030 --> 00:00:41.040 align:start position:0% and all those tools have different 00:00:41.040 --> 00:00:43.430 align:start position:0% and all those tools have different trade-offs<00:00:41.820> in<00:00:42.120> terms<00:00:42.360> of<00:00:42.540> power<00:00:43.079> that<00:00:43.320> they 00:00:43.430 --> 00:00:43.440 align:start position:0% trade-offs in terms of power that they 00:00:43.440 --> 00:00:45.290 align:start position:0% trade-offs in terms of power that they give<00:00:43.620> to<00:00:43.800> developers<00:00:44.280> and<00:00:44.579> how<00:00:44.820> easy<00:00:44.940> they<00:00:45.180> are 00:00:45.290 --> 00:00:45.300 align:start position:0% give to developers and how easy they are 00:00:45.300 --> 00:00:47.330 align:start position:0% give to developers and how easy they are to<00:00:45.480> use<00:00:45.600> and<00:00:45.780> how<00:00:46.020> high<00:00:46.620> level<00:00:46.800> or<00:00:47.040> low<00:00:47.219> level 00:00:47.330 --> 00:00:47.340 align:start position:0% to use and how high level or low level 00:00:47.340 --> 00:00:49.330 align:start position:0% to use and how high level or low level they<00:00:47.640> are<00:00:47.820> Socrates 00:00:49.330 --> 00:00:49.340 align:start position:0% they are Socrates 00:00:49.340 --> 00:00:52.430 align:start position:0% they are Socrates has<00:00:50.340> a<00:00:50.520> positioning<00:00:50.940> as<00:00:51.180> a<00:00:51.480> very<00:00:51.660> high<00:00:52.260> level 00:00:52.430 --> 00:00:52.440 align:start position:0% has a positioning as a very high level 00:00:52.440 --> 00:00:55.189 align:start position:0% has a positioning as a very high level language<00:00:53.340> so<00:00:54.180> when<00:00:54.300> you<00:00:54.420> write<00:00:54.539> Socrates<00:00:54.899> it 00:00:55.189 --> 00:00:55.199 align:start position:0% language so when you write Socrates it 00:00:55.199 --> 00:00:57.229 align:start position:0% language so when you write Socrates it looks<00:00:55.559> very<00:00:55.680> similar<00:00:56.100> to<00:00:56.280> if<00:00:56.879> you<00:00:57.120> were 00:00:57.229 --> 00:00:57.239 align:start position:0% looks very similar to if you were 00:00:57.239 --> 00:00:59.510 align:start position:0% looks very similar to if you were writing<00:00:57.539> rust<00:00:58.020> or<00:00:58.379> python<00:00:58.920> or<00:00:59.100> something<00:00:59.280> like 00:00:59.510 --> 00:00:59.520 align:start position:0% writing rust or python or something like 00:00:59.520 --> 00:01:03.410 align:start position:0% writing rust or python or something like that<00:00:59.640> it<00:01:00.539> compiles<00:01:00.899> to<00:01:01.020> r1cs<00:01:01.800> so<00:01:02.399> this<00:01:02.760> is<00:01:02.940> uh 00:01:03.410 --> 00:01:03.420 align:start position:0% that it compiles to r1cs so this is uh 00:01:03.420 --> 00:01:05.570 align:start position:0% that it compiles to r1cs so this is uh the<00:01:03.600> kind<00:01:03.719> of<00:01:03.840> snarks<00:01:04.260> that<00:01:04.440> are<00:01:04.619> easy<00:01:05.220> to 00:01:05.570 --> 00:01:05.580 align:start position:0% the kind of snarks that are easy to 00:01:05.580 --> 00:01:08.330 align:start position:0% the kind of snarks that are easy to verify<00:01:06.000> today<00:01:06.540> on<00:01:07.020> ethereum<00:01:07.500> so<00:01:07.979> you<00:01:08.159> can 00:01:08.330 --> 00:01:08.340 align:start position:0% verify today on ethereum so you can 00:01:08.340 --> 00:01:10.310 align:start position:0% verify today on ethereum so you can verify<00:01:08.939> directly<00:01:09.299> in<00:01:09.479> your<00:01:09.659> smart<00:01:09.780> contracts 00:01:10.310 --> 00:01:10.320 align:start position:0% verify directly in your smart contracts 00:01:10.320 --> 00:01:13.910 align:start position:0% verify directly in your smart contracts it<00:01:11.159> uses<00:01:11.520> modular<00:01:12.320> backend<00:01:13.320> implementations 00:01:13.910 --> 00:01:13.920 align:start position:0% it uses modular backend implementations 00:01:13.920 --> 00:01:16.010 align:start position:0% it uses modular backend implementations which<00:01:14.460> means<00:01:14.700> that<00:01:14.880> rocket<00:01:15.360> is<00:01:15.540> does<00:01:15.840> not 00:01:16.010 --> 00:01:16.020 align:start position:0% which means that rocket is does not 00:01:16.020 --> 00:01:18.830 align:start position:0% which means that rocket is does not develop<00:01:16.439> a<00:01:16.979> proof<00:01:17.280> system<00:01:17.400> itself<00:01:17.939> but<00:01:18.540> rather 00:01:18.830 --> 00:01:18.840 align:start position:0% develop a proof system itself but rather 00:01:18.840 --> 00:01:20.030 align:start position:0% develop a proof system itself but rather uses 00:01:20.030 --> 00:01:20.040 align:start position:0% uses 00:01:20.040 --> 00:01:21.830 align:start position:0% uses back-end<00:01:20.759> implementations<00:01:21.299> from<00:01:21.659> the 00:01:21.830 --> 00:01:21.840 align:start position:0% back-end implementations from the 00:01:21.840 --> 00:01:25.370 align:start position:0% back-end implementations from the community<00:01:22.020> for<00:01:22.799> different<00:01:22.979> proof<00:01:23.340> systems 00:01:25.370 --> 00:01:25.380 align:start position:0% community for different proof systems 00:01:25.380 --> 00:01:27.950 align:start position:0% community for different proof systems and<00:01:25.920> just<00:01:26.040> targets<00:01:26.580> that<00:01:26.759> and<00:01:27.180> uses<00:01:27.780> those 00:01:27.950 --> 00:01:27.960 align:start position:0% and just targets that and uses those 00:01:27.960 --> 00:01:30.490 align:start position:0% and just targets that and uses those great<00:01:28.200> implementations 00:01:30.490 --> 00:01:30.500 align:start position:0% great implementations 00:01:30.500 --> 00:01:32.810 align:start position:0% great implementations in<00:01:31.500> order<00:01:31.619> to<00:01:31.860> have<00:01:32.100> such<00:01:32.400> a<00:01:32.520> high<00:01:32.640> level 00:01:32.810 --> 00:01:32.820 align:start position:0% in order to have such a high level 00:01:32.820 --> 00:01:35.510 align:start position:0% in order to have such a high level language<00:01:33.680> but<00:01:34.680> still<00:01:34.860> have<00:01:35.040> something<00:01:35.220> that's 00:01:35.510 --> 00:01:35.520 align:start position:0% language but still have something that's 00:01:35.520 --> 00:01:38.230 align:start position:0% language but still have something that's really<00:01:35.700> efficient<00:01:36.240> at<00:01:36.960> the<00:01:37.020> at<00:01:37.259> the<00:01:37.380> low<00:01:37.560> level 00:01:38.230 --> 00:01:38.240 align:start position:0% really efficient at the at the low level 00:01:38.240 --> 00:01:41.990 align:start position:0% really efficient at the at the low level zocoties<00:01:39.240> Max<00:01:39.479> use<00:01:39.780> of<00:01:40.520> optimizations<00:01:41.520> in<00:01:41.880> the 00:01:41.990 --> 00:01:42.000 align:start position:0% zocoties Max use of optimizations in the 00:01:42.000 --> 00:01:44.390 align:start position:0% zocoties Max use of optimizations in the compiler<00:01:42.900> which<00:01:43.380> is<00:01:43.500> something<00:01:43.740> that's<00:01:44.040> also 00:01:44.390 --> 00:01:44.400 align:start position:0% compiler which is something that's also 00:01:44.400 --> 00:01:46.730 align:start position:0% compiler which is something that's also different<00:01:44.520> from<00:01:44.880> some<00:01:45.060> other<00:01:45.240> tools<00:01:45.740> which 00:01:46.730 --> 00:01:46.740 align:start position:0% different from some other tools which 00:01:46.740 --> 00:01:49.249 align:start position:0% different from some other tools which give<00:01:47.220> you<00:01:47.400> a<00:01:47.640> very<00:01:47.700> low<00:01:47.939> level<00:01:48.119> access<00:01:48.720> to 00:01:49.249 --> 00:01:49.259 align:start position:0% give you a very low level access to 00:01:49.259 --> 00:01:51.670 align:start position:0% give you a very low level access to what's<00:01:49.680> going<00:01:49.920> on<00:01:50.100> on<00:01:50.579> the<00:01:50.759> constraint<00:01:51.060> level 00:01:51.670 --> 00:01:51.680 align:start position:0% what's going on on the constraint level 00:01:51.680 --> 00:01:53.690 align:start position:0% what's going on on the constraint level but<00:01:52.680> don't<00:01:52.799> really<00:01:52.979> apply<00:01:53.340> a<00:01:53.520> lot<00:01:53.640> of 00:01:53.690 --> 00:01:53.700 align:start position:0% but don't really apply a lot of 00:01:53.700 --> 00:01:55.670 align:start position:0% but don't really apply a lot of optimizations 00:01:55.670 --> 00:01:55.680 align:start position:0% optimizations 00:01:55.680 --> 00:01:58.429 align:start position:0% optimizations um so<00:01:55.920> where<00:01:56.100> does<00:01:56.280> it<00:01:56.399> run<00:01:56.579> so<00:01:57.479> the<00:01:58.200> part<00:01:58.320> of 00:01:58.429 --> 00:01:58.439 align:start position:0% um so where does it run so the part of 00:01:58.439 --> 00:02:00.770 align:start position:0% um so where does it run so the part of Socrates<00:01:58.860> uh<00:01:59.579> which<00:01:59.820> allows<00:02:00.180> you<00:02:00.240> to<00:02:00.420> compile 00:02:00.770 --> 00:02:00.780 align:start position:0% Socrates uh which allows you to compile 00:02:00.780 --> 00:02:03.649 align:start position:0% Socrates uh which allows you to compile so<00:02:01.079> the<00:02:01.259> compiler<00:02:01.680> you<00:02:02.520> can<00:02:02.579> run<00:02:02.759> it<00:02:03.000> natively 00:02:03.649 --> 00:02:03.659 align:start position:0% so the compiler you can run it natively 00:02:03.659 --> 00:02:06.050 align:start position:0% so the compiler you can run it natively on<00:02:03.960> your<00:02:04.140> machine<00:02:04.320> we<00:02:04.860> have<00:02:04.979> a<00:02:05.219> remix<00:02:05.399> plugin 00:02:06.050 --> 00:02:06.060 align:start position:0% on your machine we have a remix plugin 00:02:06.060 --> 00:02:08.330 align:start position:0% on your machine we have a remix plugin as<00:02:06.299> well<00:02:06.420> and<00:02:06.960> we<00:02:07.140> also<00:02:07.380> now<00:02:07.560> have<00:02:07.920> a 00:02:08.330 --> 00:02:08.340 align:start position:0% as well and we also now have a 00:02:08.340 --> 00:02:10.669 align:start position:0% as well and we also now have a playground<00:02:08.759> that<00:02:09.119> you<00:02:09.179> can<00:02:09.360> access<00:02:09.539> at<00:02:10.319> play 00:02:10.669 --> 00:02:10.679 align:start position:0% playground that you can access at play 00:02:10.679 --> 00:02:13.729 align:start position:0% playground that you can access at play dot<00:02:11.099> socrate.es<00:02:11.900> which<00:02:12.900> I<00:02:13.080> encourage<00:02:13.379> you<00:02:13.500> to 00:02:13.729 --> 00:02:13.739 align:start position:0% dot socrate.es which I encourage you to 00:02:13.739 --> 00:02:15.830 align:start position:0% dot socrate.es which I encourage you to to<00:02:14.160> start<00:02:14.459> that's<00:02:14.879> probably<00:02:15.120> the<00:02:15.360> easiest<00:02:15.599> way 00:02:15.830 --> 00:02:15.840 align:start position:0% to start that's probably the easiest way 00:02:15.840 --> 00:02:17.270 align:start position:0% to start that's probably the easiest way to<00:02:15.959> get<00:02:16.080> started<00:02:16.379> with<00:02:16.500> Socrates<00:02:16.860> and<00:02:17.099> just 00:02:17.270 --> 00:02:17.280 align:start position:0% to get started with Socrates and just 00:02:17.280 --> 00:02:19.309 align:start position:0% to get started with Socrates and just write<00:02:17.400> some<00:02:17.580> simple<00:02:17.819> programs 00:02:19.309 --> 00:02:19.319 align:start position:0% write some simple programs 00:02:19.319 --> 00:02:20.690 align:start position:0% write some simple programs um<00:02:19.379> in<00:02:19.620> terms<00:02:19.800> of<00:02:19.860> the<00:02:20.040> schemes<00:02:20.340> so<00:02:20.459> there's 00:02:20.690 --> 00:02:20.700 align:start position:0% um in terms of the schemes so there's 00:02:20.700 --> 00:02:22.190 align:start position:0% um in terms of the schemes so there's back-end<00:02:21.000> implementations<00:02:21.480> that<00:02:21.780> we<00:02:21.959> support 00:02:22.190 --> 00:02:22.200 align:start position:0% back-end implementations that we support 00:02:22.200 --> 00:02:24.949 align:start position:0% back-end implementations that we support we<00:02:23.160> currently<00:02:23.459> have<00:02:23.700> support<00:02:23.940> for<00:02:24.300> a<00:02:24.420> graph<00:02:24.660> 16 00:02:24.949 --> 00:02:24.959 align:start position:0% we currently have support for a graph 16 00:02:24.959 --> 00:02:29.470 align:start position:0% we currently have support for a graph 16 which<00:02:25.739> is<00:02:26.420> some<00:02:27.420> of<00:02:27.599> you<00:02:27.660> may<00:02:27.959> know<00:02:28.200> the<00:02:28.620> the 00:02:29.470 --> 00:02:29.480 align:start position:0% which is some of you may know the the 00:02:29.480 --> 00:02:31.970 align:start position:0% which is some of you may know the the snark<00:02:30.480> that<00:02:30.720> is<00:02:30.900> the<00:02:31.080> smallest 00:02:31.970 --> 00:02:31.980 align:start position:0% snark that is the smallest 00:02:31.980 --> 00:02:35.630 align:start position:0% snark that is the smallest and<00:02:32.640> the<00:02:32.819> fastest<00:02:33.120> to<00:02:33.300> verify<00:02:34.080> for<00:02:34.500> gm17<00:02:35.220> which 00:02:35.630 --> 00:02:35.640 align:start position:0% and the fastest to verify for gm17 which 00:02:35.640 --> 00:02:37.250 align:start position:0% and the fastest to verify for gm17 which is<00:02:35.760> an<00:02:35.940> uh 00:02:37.250 --> 00:02:37.260 align:start position:0% is an uh 00:02:37.260 --> 00:02:39.530 align:start position:0% is an uh an<00:02:37.319> evolution<00:02:37.920> of<00:02:38.160> graph<00:02:38.280> 16<00:02:38.580> let's<00:02:39.000> say<00:02:39.120> for 00:02:39.530 --> 00:02:39.540 align:start position:0% an evolution of graph 16 let's say for 00:02:39.540 --> 00:02:42.070 align:start position:0% an evolution of graph 16 let's say for Moreland<00:02:40.080> which<00:02:40.319> is<00:02:40.500> a<00:02:41.040> universal<00:02:41.700> snark 00:02:42.070 --> 00:02:42.080 align:start position:0% Moreland which is a universal snark 00:02:42.080 --> 00:02:44.869 align:start position:0% Moreland which is a universal snark which<00:02:43.080> I'll<00:02:43.260> touch<00:02:43.440> on<00:02:43.620> a<00:02:43.800> bit<00:02:43.920> later 00:02:44.869 --> 00:02:44.879 align:start position:0% which I'll touch on a bit later 00:02:44.879 --> 00:02:47.390 align:start position:0% which I'll touch on a bit later and<00:02:45.300> for<00:02:45.420> Nova<00:02:45.840> which<00:02:46.080> I<00:02:46.260> also<00:02:46.500> go<00:02:46.680> into<00:02:46.860> which 00:02:47.390 --> 00:02:47.400 align:start position:0% and for Nova which I also go into which 00:02:47.400 --> 00:02:49.670 align:start position:0% and for Nova which I also go into which is<00:02:47.519> a<00:02:47.700> new<00:02:47.819> type<00:02:48.120> of<00:02:48.480> exciting<00:02:48.959> snark<00:02:49.319> that 00:02:49.670 --> 00:02:49.680 align:start position:0% is a new type of exciting snark that 00:02:49.680 --> 00:02:52.250 align:start position:0% is a new type of exciting snark that enables<00:02:50.099> new<00:02:50.400> use<00:02:50.700> cases 00:02:52.250 --> 00:02:52.260 align:start position:0% enables new use cases 00:02:52.260 --> 00:02:54.470 align:start position:0% enables new use cases for<00:02:52.980> proving<00:02:53.459> so<00:02:53.940> the<00:02:54.180> particular 00:02:54.470 --> 00:02:54.480 align:start position:0% for proving so the particular 00:02:54.480 --> 00:02:56.809 align:start position:0% for proving so the particular implementations<00:02:55.080> we<00:02:55.440> rely<00:02:55.739> on<00:02:55.920> Bellman<00:02:56.340> Arc 00:02:56.809 --> 00:02:56.819 align:start position:0% implementations we rely on Bellman Arc 00:02:56.819 --> 00:02:59.470 align:start position:0% implementations we rely on Bellman Arc Bel<00:02:57.120> person<00:02:57.360> and<00:02:57.599> also<00:02:57.840> snark.js 00:02:59.470 --> 00:02:59.480 align:start position:0% Bel person and also snark.js 00:02:59.480 --> 00:03:02.809 align:start position:0% Bel person and also snark.js I'll<00:03:00.480> also<00:03:00.720> go<00:03:00.959> into<00:03:01.379> a<00:03:01.620> bit<00:03:01.739> more<00:03:01.920> detail<00:03:02.340> on 00:03:02.809 --> 00:03:02.819 align:start position:0% I'll also go into a bit more detail on 00:03:02.819 --> 00:03:04.850 align:start position:0% I'll also go into a bit more detail on on<00:03:03.060> that<00:03:03.540> integration 00:03:04.850 --> 00:03:04.860 align:start position:0% on that integration 00:03:04.860 --> 00:03:07.729 align:start position:0% on that integration and<00:03:05.340> in<00:03:05.519> terms<00:03:05.700> of<00:03:05.760> the<00:03:05.940> verifier<00:03:06.420> we<00:03:06.840> have<00:03:07.019> you 00:03:07.729 --> 00:03:07.739 align:start position:0% and in terms of the verifier we have you 00:03:07.739 --> 00:03:09.710 align:start position:0% and in terms of the verifier we have you can<00:03:07.860> verify<00:03:08.280> in<00:03:08.580> JavaScript<00:03:09.000> or<00:03:09.239> in<00:03:09.420> this<00:03:09.480> in 00:03:09.710 --> 00:03:09.720 align:start position:0% can verify in JavaScript or in this in 00:03:09.720 --> 00:03:12.589 align:start position:0% can verify in JavaScript or in this in the<00:03:09.959> CLI<00:03:10.379> and<00:03:10.980> for<00:03:11.159> some<00:03:11.340> of<00:03:11.519> the<00:03:11.700> schemes<00:03:12.120> that 00:03:12.589 --> 00:03:12.599 align:start position:0% the CLI and for some of the schemes that 00:03:12.599 --> 00:03:15.949 align:start position:0% the CLI and for some of the schemes that are<00:03:12.720> compatible<00:03:13.080> with<00:03:13.560> devm<00:03:14.519> we<00:03:15.120> generate<00:03:15.599> a 00:03:15.949 --> 00:03:15.959 align:start position:0% are compatible with devm we generate a 00:03:15.959 --> 00:03:17.630 align:start position:0% are compatible with devm we generate a verifier<00:03:16.379> contract<00:03:16.800> so<00:03:17.220> that<00:03:17.400> you<00:03:17.519> can 00:03:17.630 --> 00:03:17.640 align:start position:0% verifier contract so that you can 00:03:17.640 --> 00:03:20.390 align:start position:0% verifier contract so that you can directly<00:03:18.120> send<00:03:18.959> your<00:03:19.140> proofs<00:03:19.500> to<00:03:19.860> your<00:03:20.220> smart 00:03:20.390 --> 00:03:20.400 align:start position:0% directly send your proofs to your smart 00:03:20.400 --> 00:03:23.030 align:start position:0% directly send your proofs to your smart contracts<00:03:20.879> and<00:03:21.060> verify<00:03:21.540> them<00:03:21.720> and<00:03:22.019> and<00:03:22.319> Link 00:03:23.030 --> 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a a program which takes two<00:03:31.980> private<00:03:32.400> inputs<00:03:32.940> A<00:03:33.180> and<00:03:33.360> B 00:03:34.309 --> 00:03:34.319 align:start position:0% two private inputs A and B 00:03:34.319 --> 00:03:38.930 align:start position:0% two private inputs A and B and<00:03:34.860> one<00:03:35.099> public<00:03:35.340> input<00:03:35.940> C<00:03:36.440> and<00:03:37.440> then<00:03:37.940> asserts 00:03:38.930 --> 00:03:38.940 align:start position:0% and one public input C and then asserts 00:03:38.940 --> 00:03:41.630 align:start position:0% and one public input C and then asserts that<00:03:39.060> a<00:03:39.300> times<00:03:39.480> B<00:03:39.840> is<00:03:40.260> equals<00:03:40.680> to<00:03:40.739> C<00:03:40.980> so 00:03:41.630 --> 00:03:41.640 align:start position:0% that a times B is equals to C so 00:03:41.640 --> 00:03:43.369 align:start position:0% that a times B is equals to C so technically<00:03:42.060> this<00:03:42.299> is<00:03:42.420> a<00:03:42.599> program<00:03:42.720> where<00:03:43.080> with 00:03:43.369 --> 00:03:43.379 align:start position:0% technically this is a program where with 00:03:43.379 --> 00:03:44.750 align:start position:0% technically this is a program where with which<00:03:43.620> you<00:03:43.799> can<00:03:43.920> prove<00:03:44.220> that<00:03:44.340> you<00:03:44.519> know<00:03:44.640> the 00:03:44.750 --> 00:03:44.760 align:start position:0% which you can prove that you know the 00:03:44.760 --> 00:03:48.350 align:start position:0% which you can prove that you know the factorization<00:03:45.360> of<00:03:46.319> a<00:03:46.500> number<00:03:47.060> the<00:03:48.060> way<00:03:48.180> you 00:03:48.350 --> 00:03:48.360 align:start position:0% factorization of a number the way you 00:03:48.360 --> 00:03:50.149 align:start position:0% factorization of a number the way you would<00:03:48.599> run<00:03:49.140> that<00:03:49.319> is<00:03:49.500> you<00:03:49.680> would<00:03:49.860> first 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then<00:03:59.340> you<00:03:59.519> could<00:03:59.700> execute<00:04:00.120> that<00:04:00.360> program<00:04:00.480> with 00:04:00.830 --> 00:04:00.840 align:start position:0% then you could execute that program with 00:04:00.840 --> 00:04:03.890 align:start position:0% then you could execute that program with an<00:04:00.959> input<00:04:01.319> here<00:04:01.620> three<00:04:02.280> three<00:04:02.519> and<00:04:02.700> nine<00:04:03.420> then 00:04:03.890 --> 00:04:03.900 align:start position:0% an input here three three and nine then 00:04:03.900 --> 00:04:06.050 align:start position:0% an input here three three and nine then you<00:04:04.019> could<00:04:04.140> generate<00:04:04.560> a<00:04:04.739> proof<00:04:05.220> using<00:04:05.760> a 00:04:06.050 --> 00:04:06.060 align:start position:0% you could generate a proof using a 00:04:06.060 --> 00:04:09.050 align:start position:0% you could generate a proof using a particular<00:04:06.360> proof<00:04:07.200> system<00:04:07.459> and<00:04:08.459> you<00:04:08.940> could 00:04:09.050 --> 00:04:09.060 align:start position:0% particular proof system and you could 00:04:09.060 --> 00:04:10.190 align:start position:0% particular proof system and you could also 00:04:10.190 --> 00:04:10.200 align:start position:0% also 00:04:10.200 --> 00:04:12.350 align:start position:0% also generate<00:04:10.920> a<00:04:11.280> verifier<00:04:11.760> that<00:04:12.000> you<00:04:12.120> can<00:04:12.239> then 00:04:12.350 --> 00:04:12.360 align:start position:0% generate a verifier that you can then 00:04:12.360 --> 00:04:14.210 align:start position:0% generate a verifier that you can then Deploy<00:04:12.720> on<00:04:12.900> the<00:04:13.019> evm 00:04:14.210 --> 00:04:14.220 align:start position:0% Deploy on the evm 00:04:14.220 --> 00:04:16.009 align:start position:0% Deploy on the evm and<00:04:14.700> then<00:04:14.819> send<00:04:15.060> you<00:04:15.239> proof<00:04:15.540> to<00:04:15.659> and<00:04:15.900> then 00:04:16.009 --> 00:04:16.019 align:start position:0% and then send you proof to and then 00:04:16.019 --> 00:04:17.949 align:start position:0% and then send you proof to and then convince<00:04:16.500> basically<00:04:16.859> convince<00:04:17.340> the<00:04:17.519> network 00:04:17.949 --> 00:04:17.959 align:start position:0% convince basically convince the network 00:04:17.959 --> 00:04:20.090 align:start position:0% convince basically convince the network that<00:04:18.959> you<00:04:19.440> actually<00:04:19.560> knew<00:04:19.979> this 00:04:20.090 --> 00:04:20.100 align:start position:0% that you actually knew this 00:04:20.100 --> 00:04:22.310 align:start position:0% that you actually knew this factorization<00:04:20.699> for<00:04:21.600> an<00:04:21.780> example<00:04:22.019> if 00:04:22.310 --> 00:04:22.320 align:start position:0% factorization for an example if 00:04:22.320 --> 00:04:23.450 align:start position:0% factorization for an example if something<00:04:22.500> that's<00:04:22.800> a<00:04:22.979> little<00:04:23.040> bit<00:04:23.220> more 00:04:23.450 --> 00:04:23.460 align:start position:0% something that's a little bit more 00:04:23.460 --> 00:04:25.730 align:start position:0% something that's a little bit more advanced<00:04:23.940> to<00:04:24.720> make<00:04:24.840> the<00:04:25.020> point<00:04:25.139> that<00:04:25.320> this<00:04:25.560> is 00:04:25.730 --> 00:04:25.740 align:start position:0% advanced to make the point that this is 00:04:25.740 --> 00:04:27.430 align:start position:0% advanced to make the point that this is actually<00:04:25.919> a<00:04:26.280> high<00:04:26.400> level<00:04:26.580> language 00:04:27.430 --> 00:04:27.440 align:start position:0% actually a high level language 00:04:27.440 --> 00:04:30.110 align:start position:0% actually a high level language here's<00:04:28.440> the<00:04:28.620> implementation<00:04:29.280> and<00:04:29.639> Socrates 00:04:30.110 --> 00:04:30.120 align:start position:0% here's the implementation and Socrates 00:04:30.120 --> 00:04:32.450 align:start position:0% here's the implementation and Socrates of<00:04:30.479> the<00:04:30.600> shot<00:04:30.780> 256<00:04:31.380> function 00:04:32.450 --> 00:04:32.460 align:start position:0% of the shot 256 function 00:04:32.460 --> 00:04:34.490 align:start position:0% of the shot 256 function so<00:04:33.000> just<00:04:33.240> to<00:04:33.419> give<00:04:33.600> you<00:04:33.720> a<00:04:33.900> few<00:04:34.020> things<00:04:34.199> that 00:04:34.490 --> 00:04:34.500 align:start position:0% so just to give you a few things that 00:04:34.500 --> 00:04:36.530 align:start position:0% so just to give you a few things that are<00:04:34.680> expected<00:04:35.340> in<00:04:35.520> high<00:04:35.699> level<00:04:35.880> language<00:04:36.120> we 00:04:36.530 --> 00:04:36.540 align:start position:0% are expected in high level language we 00:04:36.540 --> 00:04:38.450 align:start position:0% are expected in high level language we have<00:04:36.660> a<00:04:36.960> module<00:04:37.259> import<00:04:37.500> system<00:04:37.919> you<00:04:38.280> can 00:04:38.450 --> 00:04:38.460 align:start position:0% have a module import system you can 00:04:38.460 --> 00:04:41.270 align:start position:0% have a module import system you can import<00:04:38.580> constants<00:04:39.180> as<00:04:39.419> well<00:04:39.979> we<00:04:40.979> have<00:04:41.040> for 00:04:41.270 --> 00:04:41.280 align:start position:0% import constants as well we have for 00:04:41.280 --> 00:04:43.610 align:start position:0% import constants as well we have for Loops<00:04:41.639> of<00:04:41.880> course<00:04:42.000> we<00:04:42.720> have<00:04:42.840> function<00:04:43.139> calls 00:04:43.610 --> 00:04:43.620 align:start position:0% Loops of course we have function calls 00:04:43.620 --> 00:04:45.950 align:start position:0% Loops of course we have function calls and<00:04:44.160> also<00:04:44.400> one<00:04:44.759> exciting<00:04:45.360> thing<00:04:45.600> that<00:04:45.900> we 00:04:45.950 --> 00:04:45.960 align:start position:0% and also one exciting thing that we 00:04:45.960 --> 00:04:47.689 align:start position:0% and also one exciting thing that we added<00:04:46.259> kind<00:04:46.500> of<00:04:46.620> recently<00:04:46.860> and<00:04:47.040> maybe<00:04:47.220> some<00:04:47.520> of 00:04:47.689 --> 00:04:47.699 align:start position:0% added kind of recently and maybe some of 00:04:47.699 --> 00:04:49.909 align:start position:0% added kind of recently and maybe some of you<00:04:47.820> who<00:04:48.300> use<00:04:48.479> rust<00:04:48.840> are<00:04:49.080> familiar<00:04:49.560> with<00:04:49.620> that 00:04:49.909 --> 00:04:49.919 align:start position:0% you who use rust are familiar with that 00:04:49.919 --> 00:04:52.490 align:start position:0% you who use rust are familiar with that feature<00:04:50.280> is<00:04:50.639> the<00:04:50.880> notion<00:04:51.180> of<00:04:51.500> constant 00:04:52.490 --> 00:04:52.500 align:start position:0% feature is the notion of constant 00:04:52.500 --> 00:04:55.570 align:start position:0% feature is the notion of constant generics<00:04:52.919> so<00:04:53.880> in<00:04:54.000> this<00:04:54.180> case<00:04:54.300> the<00:04:54.780> shot<00:04:55.259> 25 00:04:55.570 --> 00:04:55.580 align:start position:0% generics so in this case the shot 25 00:04:55.580 --> 00:04:58.790 align:start position:0% generics so in this case the shot 25 shot<00:04:56.580> 256<00:04:57.240> function<00:04:57.660> is<00:04:58.259> a<00:04:58.380> hash<00:04:58.560> function 00:04:58.790 --> 00:04:58.800 align:start position:0% shot 256 function is a hash function 00:04:58.800 --> 00:05:00.830 align:start position:0% shot 256 function is a hash function that<00:04:59.040> can<00:04:59.280> take<00:04:59.460> an<00:05:00.000> arbitrary<00:05:00.419> number<00:05:00.660> of 00:05:00.830 --> 00:05:00.840 align:start position:0% that can take an arbitrary number of 00:05:00.840 --> 00:05:04.550 align:start position:0% that can take an arbitrary number of bytes<00:05:01.259> as<00:05:01.440> input<00:05:01.880> however<00:05:02.880> in<00:05:03.540> circuits<00:05:04.080> all 00:05:04.550 --> 00:05:04.560 align:start position:0% bytes as input however in circuits all 00:05:04.560 --> 00:05:07.430 align:start position:0% bytes as input however in circuits all the<00:05:04.680> inputs<00:05:05.040> are<00:05:05.100> always<00:05:05.280> static<00:05:06.180> so<00:05:06.960> all<00:05:07.320> of 00:05:07.430 --> 00:05:07.440 align:start position:0% the inputs are always static so all of 00:05:07.440 --> 00:05:10.370 align:start position:0% the inputs are always static so all of these<00:05:07.800> uh<00:05:08.460> the<00:05:08.759> size<00:05:08.880> of<00:05:09.120> the<00:05:09.240> input<00:05:09.600> will 00:05:10.370 --> 00:05:10.380 align:start position:0% these uh the size of the input will 00:05:10.380 --> 00:05:13.610 align:start position:0% these uh the size of the input will always<00:05:10.560> have<00:05:10.860> to<00:05:11.040> be<00:05:11.160> known<00:05:11.400> at<00:05:12.180> compile<00:05:13.020> time 00:05:13.610 --> 00:05:13.620 align:start position:0% always have to be known at compile time 00:05:13.620 --> 00:05:15.830 align:start position:0% always have to be known at compile time but<00:05:14.040> this<00:05:14.220> is<00:05:14.340> something<00:05:14.520> that<00:05:14.820> we<00:05:15.000> do<00:05:15.120> you<00:05:15.720> can 00:05:15.830 --> 00:05:15.840 align:start position:0% but this is something that we do you can 00:05:15.840 --> 00:05:18.170 align:start position:0% but this is something that we do you can still<00:05:15.960> Define<00:05:16.259> this<00:05:16.800> uh<00:05:17.400> as<00:05:17.580> something<00:05:17.820> that 00:05:18.170 --> 00:05:18.180 align:start position:0% still Define this uh as something that 00:05:18.180 --> 00:05:20.810 align:start position:0% still Define this uh as something that is<00:05:18.360> generic<00:05:18.960> over<00:05:19.199> K<00:05:19.500> and<00:05:20.040> then<00:05:20.220> have<00:05:20.400> a<00:05:20.699> number 00:05:20.810 --> 00:05:20.820 align:start position:0% is generic over K and then have a number 00:05:20.820 --> 00:05:24.350 align:start position:0% is generic over K and then have a number of<00:05:21.139> rounds<00:05:22.139> of<00:05:22.380> this<00:05:22.620> sha<00:05:22.979> round<00:05:23.160> function 00:05:24.350 --> 00:05:24.360 align:start position:0% of rounds of this sha round function 00:05:24.360 --> 00:05:25.909 align:start position:0% of rounds of this sha round function but<00:05:24.780> then<00:05:24.900> when<00:05:25.080> you<00:05:25.199> compile<00:05:25.500> your<00:05:25.740> program 00:05:25.909 --> 00:05:25.919 align:start position:0% but then when you compile your program 00:05:25.919 --> 00:05:28.010 align:start position:0% but then when you compile your program and<00:05:26.160> actually<00:05:26.460> use<00:05:26.880> the<00:05:27.120> function<00:05:27.479> the<00:05:27.840> shot 00:05:28.010 --> 00:05:28.020 align:start position:0% and actually use the function the shot 00:05:28.020 --> 00:05:29.650 align:start position:0% and actually use the function the shot five<00:05:28.380> six 00:05:29.650 --> 00:05:29.660 align:start position:0% five six 00:05:29.660 --> 00:05:33.830 align:start position:0% five six this<00:05:30.860> this<00:05:31.860> variable<00:05:32.280> K<00:05:32.639> is<00:05:33.180> going<00:05:33.300> to<00:05:33.479> have<00:05:33.660> a 00:05:33.830 --> 00:05:33.840 align:start position:0% this this variable K is going to have a 00:05:33.840 --> 00:05:36.170 align:start position:0% this this variable K is going to have a concrete<00:05:34.199> value<00:05:34.380> which<00:05:35.340> will<00:05:35.520> then<00:05:35.699> compile 00:05:36.170 --> 00:05:36.180 align:start position:0% concrete value which will then compile 00:05:36.180 --> 00:05:37.610 align:start position:0% concrete value which will then compile to<00:05:36.360> the<00:05:36.600> exact<00:05:36.840> number<00:05:37.020> of<00:05:37.199> blocks<00:05:37.440> that 00:05:37.610 --> 00:05:37.620 align:start position:0% to the exact number of blocks that 00:05:37.620 --> 00:05:39.409 align:start position:0% to the exact number of blocks that you're<00:05:37.740> hashing<00:05:38.160> and<00:05:38.699> if<00:05:38.820> you're<00:05:38.940> trying<00:05:39.180> to 00:05:39.409 --> 00:05:39.419 align:start position:0% you're hashing and if you're trying to 00:05:39.419 --> 00:05:41.749 align:start position:0% you're hashing and if you're trying to do<00:05:39.539> something<00:05:39.720> that's<00:05:40.020> Dynamic<00:05:40.860> calling<00:05:41.580> this 00:05:41.749 --> 00:05:41.759 align:start position:0% do something that's Dynamic calling this 00:05:41.759 --> 00:05:44.450 align:start position:0% do something that's Dynamic calling this function<00:05:42.060> on<00:05:42.419> something<00:05:42.960> that's<00:05:43.320> not<00:05:43.560> whose 00:05:44.450 --> 00:05:44.460 align:start position:0% function on something that's not whose 00:05:44.460 --> 00:05:46.370 align:start position:0% function on something that's not whose size<00:05:45.060> does<00:05:45.300> not<00:05:45.419> know<00:05:45.539> that<00:05:45.780> compile<00:05:46.020> time<00:05:46.199> is 00:05:46.370 --> 00:05:46.380 align:start position:0% size does not know that compile time is 00:05:46.380 --> 00:05:48.469 align:start position:0% size does not know that compile time is just<00:05:46.560> going<00:05:46.680> to<00:05:46.800> fail<00:05:46.979> at<00:05:47.220> compile<00:05:47.520> time<00:05:47.759> so<00:05:48.360> we 00:05:48.469 --> 00:05:48.479 align:start position:0% just going to fail at compile time so we 00:05:48.479 --> 00:05:50.930 align:start position:0% just going to fail at compile time so we can<00:05:48.600> have<00:05:48.720> a<00:05:48.960> very<00:05:49.100> idiomatic<00:05:50.100> implementation 00:05:50.930 --> 00:05:50.940 align:start position:0% can have a very idiomatic implementation 00:05:50.940 --> 00:05:52.310 align:start position:0% can have a very idiomatic implementation of<00:05:51.180> chapter<00:05:51.360> five<00:05:51.660> six<00:05:51.840> of<00:05:52.080> course<00:05:52.139> there's 00:05:52.310 --> 00:05:52.320 align:start position:0% of chapter five six of course there's 00:05:52.320 --> 00:05:54.770 align:start position:0% of chapter five six of course there's more<00:05:52.560> complexity<00:05:52.919> in<00:05:53.160> the<00:05:53.220> show<00:05:53.340> around<00:05:53.780> but 00:05:54.770 --> 00:05:54.780 align:start position:0% more complexity in the show around but 00:05:54.780 --> 00:05:57.529 align:start position:0% more complexity in the show around but if<00:05:55.020> you<00:05:55.080> look<00:05:55.259> at<00:05:55.380> the<00:05:55.560> code<00:05:55.740> it's 00:05:57.529 --> 00:05:57.539 align:start position:0% if you look at the code it's 00:05:57.539 --> 00:06:00.890 align:start position:0% if you look at the code it's almost<00:05:58.139> line<00:05:58.440> for<00:05:58.680> line<00:05:58.800> equivalent<00:05:59.340> to<00:05:59.699> uh<00:06:00.419> an 00:06:00.890 --> 00:06:00.900 align:start position:0% almost line for line equivalent to uh an 00:06:00.900 --> 00:06:02.510 align:start position:0% almost line for line equivalent to uh an implementation<00:06:01.380> that<00:06:01.860> you<00:06:02.039> would<00:06:02.160> see<00:06:02.340> on 00:06:02.510 --> 00:06:02.520 align:start position:0% implementation that you would see on 00:06:02.520 --> 00:06:03.890 align:start position:0% implementation that you would see on Wikipedia<00:06:03.000> for<00:06:03.120> example<00:06:03.300> as<00:06:03.539> pseudocode 00:06:03.890 --> 00:06:03.900 align:start position:0% Wikipedia for example as pseudocode 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round 00:06:15.350 --> 00:06:15.360 align:start position:0% implementation so inside the Sha round 00:06:15.360 --> 00:06:18.290 align:start position:0% implementation so inside the Sha round this<00:06:16.080> expression<00:06:16.560> needs<00:06:16.919> to<00:06:16.919> be<00:06:17.039> calculated 00:06:18.290 --> 00:06:18.300 align:start position:0% this expression needs to be calculated 00:06:18.300 --> 00:06:21.610 align:start position:0% this expression needs to be calculated a<00:06:18.720> lot<00:06:18.780> of<00:06:18.900> times<00:06:19.080> it<00:06:19.560> basically<00:06:19.860> takes<00:06:20.639> three 00:06:21.610 --> 00:06:21.620 align:start position:0% a lot of times it basically takes three 00:06:21.620 --> 00:06:24.969 align:start position:0% a lot of times it basically takes three unsigned<00:06:22.620> integers<00:06:22.979> a<00:06:23.340> b<00:06:23.460> and<00:06:23.639> c<00:06:23.819> of<00:06:24.120> 32<00:06:24.539> bits 00:06:24.969 --> 00:06:24.979 align:start position:0% unsigned integers a b and c of 32 bits 00:06:24.979 --> 00:06:29.990 align:start position:0% unsigned integers a b and c of 32 bits and<00:06:25.979> calculates<00:06:26.759> a<00:06:27.000> and<00:06:27.180> bigs<00:06:27.600> or<00:06:27.780> ancs<00:06:28.740> or<00:06:29.039> BNC 00:06:29.990 --> 00:06:30.000 align:start position:0% and calculates a and bigs or ancs or BNC 00:06:30.000 --> 00:06:31.610 align:start position:0% and calculates a and bigs or ancs or BNC and<00:06:30.600> this<00:06:30.720> is<00:06:30.840> something<00:06:31.020> that<00:06:31.259> you<00:06:31.380> can<00:06:31.500> just 00:06:31.610 --> 00:06:31.620 align:start position:0% and this is something that you can just 00:06:31.620 --> 00:06:33.290 align:start position:0% and this is something that you can just write<00:06:31.800> like<00:06:32.039> this<00:06:32.280> in<00:06:32.460> Socrates<00:06:32.880> today 00:06:33.290 --> 00:06:33.300 align:start position:0% write like this in Socrates today 00:06:33.300 --> 00:06:35.689 align:start position:0% write like this in Socrates today compile<00:06:34.020> and<00:06:34.259> it<00:06:34.440> will<00:06:34.680> translate<00:06:35.039> that<00:06:35.400> to<00:06:35.580> a 00:06:35.689 --> 00:06:35.699 align:start position:0% compile and it will translate that to a 00:06:35.699 --> 00:06:37.730 align:start position:0% compile and it will translate that to a number<00:06:35.759> of<00:06:35.940> constraints<00:06:36.419> at<00:06:36.720> the<00:06:36.840> low<00:06:36.960> level 00:06:37.730 --> 00:06:37.740 align:start position:0% number of constraints at the low level 00:06:37.740 --> 00:06:39.430 align:start position:0% number of constraints at the low level however 00:06:39.430 --> 00:06:39.440 align:start position:0% however 00:06:39.440 --> 00:06:43.730 align:start position:0% however if<00:06:40.460> you<00:06:41.460> do<00:06:41.639> the<00:06:41.819> math<00:06:41.940> and<00:06:42.180> look<00:06:42.419> at<00:06:42.720> the<00:06:43.560> let's 00:06:43.730 --> 00:06:43.740 align:start position:0% if you do the math and look at the let's 00:06:43.740 --> 00:06:45.529 align:start position:0% if you do the math and look at the let's say<00:06:43.919> the<00:06:44.160> first<00:06:44.280> bit<00:06:44.460> of<00:06:44.639> a<00:06:44.819> the<00:06:45.060> first<00:06:45.180> bit<00:06:45.360> of 00:06:45.529 --> 00:06:45.539 align:start position:0% say the first bit of a the first bit of 00:06:45.539 --> 00:06:47.710 align:start position:0% say the first bit of a the first bit of B<00:06:45.720> and<00:06:45.900> the<00:06:46.080> first<00:06:46.139> bit<00:06:46.380> of<00:06:46.800> C 00:06:47.710 --> 00:06:47.720 align:start position:0% B and the first bit of C 00:06:47.720 --> 00:06:50.510 align:start position:0% B and the first bit of C you<00:06:48.720> can<00:06:48.840> see<00:06:49.139> that<00:06:49.440> if<00:06:49.740> you<00:06:49.860> considering<00:06:50.340> them 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verifies those two equations so<00:06:58.380> you<00:06:58.800> define<00:06:59.100> or<00:06:59.759> you<00:07:00.000> constrain<00:07:00.360> a<00:07:00.660> new 00:07:00.770 --> 00:07:00.780 align:start position:0% so you define or you constrain a new 00:07:00.780 --> 00:07:03.230 align:start position:0% so you define or you constrain a new variable<00:07:01.139> BC<00:07:01.560> to<00:07:01.800> be<00:07:01.919> equals<00:07:02.280> to<00:07:02.400> equal<00:07:02.759> to<00:07:03.060> B 00:07:03.230 --> 00:07:03.240 align:start position:0% variable BC to be equals to equal to B 00:07:03.240 --> 00:07:06.230 align:start position:0% variable BC to be equals to equal to B times<00:07:03.419> C<00:07:03.720> and<00:07:04.560> here<00:07:04.979> I<00:07:05.220> just<00:07:05.520> want<00:07:05.699> to<00:07:05.819> clarify 00:07:06.230 --> 00:07:06.240 align:start position:0% times C and here I just want to clarify 00:07:06.240 --> 00:07:08.749 align:start position:0% times C and here I just want to clarify that<00:07:06.600> these<00:07:07.199> constraints<00:07:07.620> are<00:07:08.160> the<00:07:08.460> low<00:07:08.580> level 00:07:08.749 --> 00:07:08.759 align:start position:0% that these constraints are the low level 00:07:08.759 --> 00:07:10.249 align:start position:0% that these constraints are the low level constraints<00:07:09.240> that<00:07:09.360> we<00:07:09.539> deal<00:07:09.720> with<00:07:09.840> so<00:07:10.139> the 00:07:10.249 --> 00:07:10.259 align:start position:0% constraints that we deal with so the 00:07:10.259 --> 00:07:12.110 align:start position:0% constraints that we deal with so the r1cn's<00:07:10.979> constraints<00:07:11.280> they<00:07:11.520> look<00:07:11.699> like<00:07:11.880> this 00:07:12.110 --> 00:07:12.120 align:start position:0% r1cn's constraints they look like this 00:07:12.120 --> 00:07:15.170 align:start position:0% r1cn's constraints they look like this they<00:07:12.660> have<00:07:13.259> one<00:07:13.500> sign<00:07:13.740> which<00:07:14.100> is<00:07:14.220> linear<00:07:14.699> so<00:07:15.000> in 00:07:15.170 --> 00:07:15.180 align:start position:0% they have one sign which is linear so in 00:07:15.180 --> 00:07:16.969 align:start position:0% they have one sign which is linear so in this<00:07:15.539> case<00:07:15.660> it's<00:07:15.840> only<00:07:16.020> one<00:07:16.199> variable<00:07:16.560> but<00:07:16.800> you 00:07:16.969 --> 00:07:16.979 align:start position:0% this case it's only one variable but you 00:07:16.979 --> 00:07:19.790 align:start position:0% this case it's only one variable but you can<00:07:17.100> have<00:07:17.220> a<00:07:17.520> sum<00:07:17.819> of<00:07:18.660> different<00:07:18.900> variables 00:07:19.790 --> 00:07:19.800 align:start position:0% can have a sum of different variables 00:07:19.800 --> 00:07:23.629 align:start position:0% can have a sum of different variables one<00:07:20.400> side<00:07:20.699> which<00:07:21.539> is<00:07:21.720> quadratic<00:07:22.500> right<00:07:23.099> so 00:07:23.629 --> 00:07:23.639 align:start position:0% one side which is quadratic right so 00:07:23.639 --> 00:07:25.969 align:start position:0% one side which is quadratic right so this<00:07:23.880> first<00:07:24.060> one<00:07:24.300> uh<00:07:24.660> just<00:07:24.780> defines<00:07:25.259> BC<00:07:25.680> or 00:07:25.969 --> 00:07:25.979 align:start position:0% this first one uh just defines BC or 00:07:25.979 --> 00:07:27.890 align:start position:0% this first one uh just defines BC or like<00:07:26.160> constrains<00:07:26.580> a<00:07:26.759> new<00:07:26.880> variable<00:07:27.180> BC<00:07:27.539> to<00:07:27.720> be 00:07:27.890 --> 00:07:27.900 align:start position:0% like constrains a new variable BC to be 00:07:27.900 --> 00:07:30.469 align:start position:0% like constrains a new variable BC to be equal<00:07:28.080> to<00:07:28.259> B<00:07:28.440> times<00:07:28.680> C<00:07:28.979> and<00:07:29.819> then<00:07:30.000> uh 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of<00:07:48.120> what<00:07:48.419> we're<00:07:48.599> actually<00:07:48.840> trying<00:07:49.139> to<00:07:49.319> do 00:07:50.150 --> 00:07:50.160 align:start position:0% of what we're actually trying to do 00:07:50.160 --> 00:07:52.189 align:start position:0% of what we're actually trying to do than<00:07:50.699> the<00:07:50.880> compiler<00:07:51.300> does 00:07:52.189 --> 00:07:52.199 align:start position:0% than the compiler does 00:07:52.199 --> 00:07:54.950 align:start position:0% than the compiler does on<00:07:52.740> the<00:07:52.860> flip<00:07:53.099> side<00:07:53.300> here<00:07:54.300> what<00:07:54.660> we're<00:07:54.780> doing 00:07:54.950 --> 00:07:54.960 align:start position:0% on the flip side here what we're doing 00:07:54.960 --> 00:07:58.370 align:start position:0% on the flip side here what we're doing is<00:07:55.319> that<00:07:55.680> we're<00:07:56.520> introducing<00:07:57.300> a<00:07:57.900> new<00:07:58.020> variable 00:07:58.370 --> 00:07:58.380 align:start position:0% is that we're introducing a new variable 00:07:58.380 --> 00:08:00.790 align:start position:0% is that we're introducing a new variable res<00:07:58.620> and<00:07:59.160> then<00:07:59.280> constraining<00:08:00.000> it<00:08:00.120> with<00:08:00.419> this 00:08:00.790 --> 00:08:00.800 align:start position:0% res and then constraining it with this 00:08:00.800 --> 00:08:04.370 align:start position:0% res and then constraining it with this uh<00:08:01.800> with<00:08:02.099> this<00:08:02.340> equation<00:08:02.900> however<00:08:03.900> when 00:08:04.370 --> 00:08:04.380 align:start position:0% uh with this equation however when 00:08:04.380 --> 00:08:05.870 align:start position:0% uh with this equation however when you're<00:08:04.500> dealing<00:08:04.860> with<00:08:05.039> such<00:08:05.460> low<00:08:05.639> level 00:08:05.870 --> 00:08:05.880 align:start position:0% you're dealing with such low level 00:08:05.880 --> 00:08:08.510 align:start position:0% you're dealing with such low level details<00:08:06.419> in<00:08:06.720> strikes<00:08:07.199> it's<00:08:07.620> really<00:08:07.860> easy<00:08:08.099> to 00:08:08.510 --> 00:08:08.520 align:start position:0% details in strikes it's really easy to 00:08:08.520 --> 00:08:11.029 align:start position:0% details in strikes it's really easy to introduce<00:08:08.880> new<00:08:09.180> variables<00:08:09.660> but<00:08:10.560> fail<00:08:10.800> to 00:08:11.029 --> 00:08:11.039 align:start position:0% introduce new variables but fail to 00:08:11.039 --> 00:08:14.510 align:start position:0% introduce new variables but fail to constrain<00:08:11.460> them<00:08:11.699> sufficiently<00:08:12.599> so<00:08:13.319> that<00:08:13.620> you 00:08:14.510 --> 00:08:14.520 align:start position:0% constrain them sufficiently so that you 00:08:14.520 --> 00:08:17.029 align:start position:0% constrain them sufficiently so that you actually<00:08:15.120> introduce<00:08:15.680> vulnerabilities<00:08:16.680> in 00:08:17.029 --> 00:08:17.039 align:start position:0% actually introduce vulnerabilities in 00:08:17.039 --> 00:08:18.290 align:start position:0% actually introduce vulnerabilities in your<00:08:17.220> circuits 00:08:18.290 --> 00:08:18.300 align:start position:0% your circuits 00:08:18.300 --> 00:08:20.570 align:start position:0% your circuits so<00:08:18.840> this<00:08:19.020> is<00:08:19.139> something<00:08:19.319> that<00:08:19.620> Socrates<00:08:20.039> does 00:08:20.570 --> 00:08:20.580 align:start position:0% so this is something that Socrates does 00:08:20.580 --> 00:08:22.129 align:start position:0% so this is something that Socrates does not<00:08:20.759> expose<00:08:21.120> at<00:08:21.360> the<00:08:21.479> moment<00:08:21.599> to<00:08:21.960> the 00:08:22.129 --> 00:08:22.139 align:start position:0% not expose at the moment to the 00:08:22.139 --> 00:08:24.230 align:start position:0% not expose at the moment to the developer<00:08:22.560> which<00:08:23.099> means<00:08:23.340> that<00:08:23.520> you<00:08:23.819> can<00:08:24.000> only 00:08:24.230 --> 00:08:24.240 align:start position:0% developer which means that you can only 00:08:24.240 --> 00:08:27.050 align:start position:0% developer which means that you can only do<00:08:24.599> this<00:08:25.379> one<00:08:25.500> which<00:08:25.740> is<00:08:25.860> less<00:08:26.039> efficient<00:08:26.460> if 00:08:27.050 --> 00:08:27.060 align:start position:0% do this one which is less efficient if 00:08:27.060 --> 00:08:29.809 align:start position:0% do this one which is less efficient if you<00:08:27.120> look<00:08:27.300> at<00:08:27.419> more<00:08:27.780> lower<00:08:28.139> level<00:08:28.379> tools<00:08:28.919> they 00:08:29.809 --> 00:08:29.819 align:start position:0% you look at more lower level tools they 00:08:29.819 --> 00:08:32.329 align:start position:0% you look at more lower level tools they let<00:08:30.060> you<00:08:30.240> use<00:08:30.479> these<00:08:30.840> things<00:08:30.960> but<00:08:31.379> then<00:08:31.620> it's 00:08:32.329 --> 00:08:32.339 align:start position:0% let you use these things but then it's 00:08:32.339 --> 00:08:33.769 align:start position:0% let you use these things but then it's at<00:08:32.520> your<00:08:32.700> own<00:08:32.820> risk 00:08:33.769 --> 00:08:33.779 align:start position:0% at your own risk 00:08:33.779 --> 00:08:35.570 align:start position:0% at your own risk and<00:08:34.440> then<00:08:34.620> it's<00:08:34.800> likely<00:08:35.099> that<00:08:35.219> you're<00:08:35.399> going 00:08:35.570 --> 00:08:35.580 align:start position:0% and then it's likely that you're going 00:08:35.580 --> 00:08:38.029 align:start position:0% and then it's likely that you're going to<00:08:35.700> introduce<00:08:36.120> vulnerabilities 00:08:38.029 --> 00:08:38.039 align:start position:0% to introduce vulnerabilities 00:08:38.039 --> 00:08:40.670 align:start position:0% to introduce vulnerabilities so<00:08:38.339> what<00:08:38.580> I<00:08:38.700> want<00:08:38.880> to<00:08:39.000> showcase<00:08:39.360> today<00:08:39.599> is<00:08:39.959> uh 00:08:40.670 --> 00:08:40.680 align:start position:0% so what I want to showcase today is uh 00:08:40.680 --> 00:08:43.250 align:start position:0% so what I want to showcase today is uh the<00:08:41.159> addition<00:08:41.399> to<00:08:41.640> Socrates<00:08:42.060> a<00:08:42.899> way<00:08:43.080> to 00:08:43.250 --> 00:08:43.260 align:start position:0% the addition to Socrates a way to 00:08:43.260 --> 00:08:46.190 align:start position:0% the addition to Socrates a way to actually<00:08:43.440> encode<00:08:43.979> this<00:08:44.279> thing<00:08:44.399> and<00:08:45.120> have 00:08:46.190 --> 00:08:46.200 align:start position:0% actually encode this thing and have 00:08:46.200 --> 00:08:48.350 align:start position:0% actually encode this thing and have um the<00:08:46.680> performance<00:08:47.040> from<00:08:47.279> this<00:08:47.519> thing<00:08:47.700> in 00:08:48.350 --> 00:08:48.360 align:start position:0% um the performance from this thing in 00:08:48.360 --> 00:08:49.610 align:start position:0% um the performance from this thing in the<00:08:48.420> context<00:08:48.660> of<00:08:48.839> the<00:08:48.959> higher<00:08:49.200> level<00:08:49.320> language 00:08:49.610 --> 00:08:49.620 align:start position:0% the context of the higher level language 00:08:49.620 --> 00:08:52.790 align:start position:0% the context of the higher level language yeah<00:08:50.580> so<00:08:50.820> I<00:08:51.000> have<00:08:51.120> a<00:08:51.240> video<00:08:51.480> now<00:08:51.839> if<00:08:52.500> you<00:08:52.620> could 00:08:52.790 --> 00:08:52.800 align:start position:0% yeah so I have a video now if you could 00:08:52.800 --> 00:08:55.130 align:start position:0% yeah so I have a video now if you could start<00:08:52.920> the<00:08:53.100> video<00:08:53.279> right<00:08:54.000> so<00:08:54.480> this<00:08:54.660> is<00:08:54.779> using 00:08:55.130 --> 00:08:55.140 align:start position:0% start the video right so this is using 00:08:55.140 --> 00:08:58.490 align:start position:0% start the video right so this is using the<00:08:55.440> actually<00:08:55.680> the<00:08:55.920> Socrates<00:08:56.720> playground<00:08:57.720> so 00:08:58.490 --> 00:08:58.500 align:start position:0% the actually the Socrates playground so 00:08:58.500 --> 00:09:01.370 align:start position:0% the actually the Socrates playground so here<00:08:58.740> I<00:08:59.040> defined<00:08:59.600> the<00:09:00.600> default<00:09:01.080> function 00:09:01.370 --> 00:09:01.380 align:start position:0% here I defined the default function 00:09:01.380 --> 00:09:02.690 align:start position:0% here I defined the default function which<00:09:01.560> I<00:09:01.680> call<00:09:01.800> the<00:09:01.920> default<00:09:02.279> function<00:09:02.399> where 00:09:02.690 --> 00:09:02.700 align:start position:0% which I call the default function where 00:09:02.700 --> 00:09:07.250 align:start position:0% which I call the default function where I<00:09:02.940> just<00:09:03.120> I'll<00:09:03.779> just<00:09:04.019> use<00:09:04.320> the<00:09:04.560> compiler<00:09:05.519> uh<00:09:06.480> to 00:09:07.250 --> 00:09:07.260 align:start position:0% I just I'll just use the compiler uh to 00:09:07.260 --> 00:09:10.670 align:start position:0% I just I'll just use the compiler uh to generate<00:09:08.100> the<00:09:08.279> constraints<00:09:08.640> for<00:09:08.940> this<00:09:09.120> uh 00:09:10.670 --> 00:09:10.680 align:start position:0% generate the constraints for this uh 00:09:10.680 --> 00:09:13.030 align:start position:0% generate the constraints for this uh this<00:09:11.220> expression 00:09:13.030 --> 00:09:13.040 align:start position:0% this expression 00:09:13.040 --> 00:09:15.889 align:start position:0% this expression here<00:09:14.040> I'm<00:09:14.220> going<00:09:14.399> to<00:09:14.580> create<00:09:14.760> an<00:09:15.120> uh<00:09:15.300> an<00:09:15.600> entry 00:09:15.889 --> 00:09:15.899 align:start position:0% here I'm going to create an uh an entry 00:09:15.899 --> 00:09:17.509 align:start position:0% here I'm going to create an uh an entry point<00:09:16.140> for<00:09:16.440> this<00:09:16.620> program 00:09:17.509 --> 00:09:17.519 align:start position:0% point for this program 00:09:17.519 --> 00:09:20.269 align:start position:0% point for this program uh<00:09:18.120> so<00:09:18.240> taking<00:09:18.480> also<00:09:18.899> a<00:09:19.140> b<00:09:19.320> and<00:09:19.440> c<00:09:19.560> returning<00:09:20.160> a 00:09:20.269 --> 00:09:20.279 align:start position:0% uh so taking also a b and c returning a 00:09:20.279 --> 00:09:21.949 align:start position:0% uh so taking also a b and c returning a u32 00:09:21.949 --> 00:09:21.959 align:start position:0% u32 00:09:21.959 --> 00:09:24.829 align:start position:0% u32 and<00:09:22.320> I'm<00:09:22.440> just<00:09:22.620> gonna<00:09:22.860> call<00:09:23.760> the<00:09:24.300> default 00:09:24.829 --> 00:09:24.839 align:start position:0% and I'm just gonna call the default 00:09:24.839 --> 00:09:26.710 align:start position:0% and I'm just gonna call the default function<00:09:25.440> and<00:09:25.680> see<00:09:25.860> how<00:09:25.980> many<00:09:26.160> constraints 00:09:26.710 --> 00:09:26.720 align:start position:0% function and see how many constraints 00:09:26.720 --> 00:09:29.750 align:start position:0% function and see how many constraints are<00:09:27.720> created<00:09:28.260> in<00:09:28.620> the<00:09:28.740> process 00:09:29.750 --> 00:09:29.760 align:start position:0% are created in the process 00:09:29.760 --> 00:09:32.150 align:start position:0% are created in the process so<00:09:30.060> I<00:09:30.240> compile<00:09:30.600> and<00:09:31.080> then<00:09:31.200> I<00:09:31.440> get<00:09:31.560> the<00:09:31.980> result 00:09:32.150 --> 00:09:32.160 align:start position:0% so I compile and then I get the result 00:09:32.160 --> 00:09:35.449 align:start position:0% so I compile and then I get the result 260<00:09:33.000> constraints<00:09:33.540> here<00:09:34.320> and<00:09:34.920> now<00:09:35.100> what<00:09:35.279> I'm 00:09:35.449 --> 00:09:35.459 align:start position:0% 260 constraints here and now what I'm 00:09:35.459 --> 00:09:37.550 align:start position:0% 260 constraints here and now what I'm going<00:09:35.580> to<00:09:35.700> do<00:09:35.880> is<00:09:36.180> to<00:09:36.540> Define<00:09:36.779> another<00:09:37.200> version 00:09:37.550 --> 00:09:37.560 align:start position:0% going to do is to Define another version 00:09:37.560 --> 00:09:40.850 align:start position:0% going to do is to Define another version of<00:09:38.459> this<00:09:38.580> function<00:09:38.940> which<00:09:39.480> hopefully<00:09:39.899> will 00:09:40.850 --> 00:09:40.860 align:start position:0% of this function which hopefully will 00:09:40.860 --> 00:09:42.949 align:start position:0% of this function which hopefully will reduce<00:09:41.339> the<00:09:41.640> number<00:09:41.820> of<00:09:41.940> constraints<00:09:42.360> by 00:09:42.949 --> 00:09:42.959 align:start position:0% reduce the number of constraints by 00:09:42.959 --> 00:09:45.350 align:start position:0% reduce the number of constraints by leveraging<00:09:43.940> this<00:09:44.940> lower<00:09:45.120> level 00:09:45.350 --> 00:09:45.360 align:start position:0% leveraging this lower level 00:09:45.360 --> 00:09:47.509 align:start position:0% leveraging this lower level implementation<00:09:46.560> so<00:09:46.980> I<00:09:47.160> call<00:09:47.220> it<00:09:47.339> hand 00:09:47.509 --> 00:09:47.519 align:start position:0% implementation so I call it hand 00:09:47.519 --> 00:09:48.710 align:start position:0% implementation so I call it hand optimized 00:09:48.710 --> 00:09:48.720 align:start position:0% optimized 00:09:48.720 --> 00:09:51.889 align:start position:0% optimized has<00:09:49.260> the<00:09:49.440> same<00:09:49.560> signature<00:09:50.100> a<00:09:50.640> b<00:09:50.880> and<00:09:51.060> c 00:09:51.889 --> 00:09:51.899 align:start position:0% has the same signature a b and c 00:09:51.899 --> 00:09:54.050 align:start position:0% has the same signature a b and c also<00:09:52.440> return<00:09:52.560> a<00:09:52.800> u32 00:09:54.050 --> 00:09:54.060 align:start position:0% also return a u32 00:09:54.060 --> 00:09:56.030 align:start position:0% also return a u32 as<00:09:54.480> I<00:09:54.660> described<00:09:54.959> earlier<00:09:55.200> I<00:09:55.500> want<00:09:55.560> to<00:09:55.680> operate 00:09:56.030 --> 00:09:56.040 align:start position:0% as I described earlier I want to operate 00:09:56.040 --> 00:09:59.030 align:start position:0% as I described earlier I want to operate on<00:09:56.279> each<00:09:56.700> individual<00:09:57.300> bit<00:09:57.720> of<00:09:58.200> this<00:09:58.380> year<00:09:58.620> 32 00:09:59.030 --> 00:09:59.040 align:start position:0% on each individual bit of this year 32 00:09:59.040 --> 00:10:00.829 align:start position:0% on each individual bit of this year 32 so<00:09:59.399> the<00:09:59.519> first<00:09:59.640> thing<00:09:59.820> I'm<00:09:59.940> going<00:10:00.120> to<00:10:00.240> do<00:10:00.420> is 00:10:00.829 --> 00:10:00.839 align:start position:0% so the first thing I'm going to do is 00:10:00.839 --> 00:10:04.550 align:start position:0% so the first thing I'm going to do is turning<00:10:01.200> those<00:10:01.320> u32<00:10:01.980> into<00:10:02.779> an<00:10:03.779> array<00:10:04.080> of 00:10:04.550 --> 00:10:04.560 align:start position:0% turning those u32 into an array of 00:10:04.560 --> 00:10:08.030 align:start position:0% turning those u32 into an array of booleans 00:10:08.030 --> 00:10:08.040 align:start position:0% 00:10:08.040 --> 00:10:11.150 align:start position:0% we<00:10:08.940> have<00:10:09.300> sort<00:10:09.660> of<00:10:09.779> a<00:10:09.959> magic<00:10:10.200> tool<00:10:10.860> in<00:10:11.040> our 00:10:11.150 --> 00:10:11.160 align:start position:0% we have sort of a magic tool in our 00:10:11.160 --> 00:10:12.829 align:start position:0% we have sort of a magic tool in our standard<00:10:11.459> library<00:10:11.640> to<00:10:12.000> do<00:10:12.180> that<00:10:12.360> which<00:10:12.720> is 00:10:12.829 --> 00:10:12.839 align:start position:0% standard library to do that which is 00:10:12.839 --> 00:10:16.310 align:start position:0% standard library to do that which is called<00:10:13.080> the<00:10:13.200> cast<00:10:13.380> function<00:10:14.360> and<00:10:15.360> which 00:10:16.310 --> 00:10:16.320 align:start position:0% called the cast function and which 00:10:16.320 --> 00:10:19.009 align:start position:0% called the cast function and which can<00:10:16.800> do<00:10:16.980> this<00:10:17.220> conversion<00:10:17.760> for<00:10:18.000> you<00:10:18.180> and<00:10:18.839> here 00:10:19.009 --> 00:10:19.019 align:start position:0% can do this conversion for you and here 00:10:19.019 --> 00:10:20.150 align:start position:0% can do this conversion for you and here I<00:10:19.200> want<00:10:19.260> to<00:10:19.380> point<00:10:19.440> out<00:10:19.620> that<00:10:19.800> this<00:10:19.980> is 00:10:20.150 --> 00:10:20.160 align:start position:0% I want to point out that this is 00:10:20.160 --> 00:10:23.870 align:start position:0% I want to point out that this is actually<00:10:20.339> free<00:10:20.700> because<00:10:21.660> the<00:10:21.959> u32<00:10:22.620> type<00:10:23.519> is 00:10:23.870 --> 00:10:23.880 align:start position:0% actually free because the u32 type is 00:10:23.880 --> 00:10:26.630 align:start position:0% actually free because the u32 type is actually<00:10:24.000> represented<00:10:24.660> as<00:10:24.839> 32<00:10:25.320> bits<00:10:25.740> under 00:10:26.630 --> 00:10:26.640 align:start position:0% actually represented as 32 bits under 00:10:26.640 --> 00:10:28.310 align:start position:0% actually represented as 32 bits under the<00:10:26.880> hood<00:10:27.000> so<00:10:27.600> we're<00:10:27.720> not<00:10:27.899> paying<00:10:28.200> any 00:10:28.310 --> 00:10:28.320 align:start position:0% the hood so we're not paying any 00:10:28.320 --> 00:10:30.590 align:start position:0% the hood so we're not paying any constraints<00:10:28.740> for<00:10:29.040> this 00:10:30.590 --> 00:10:30.600 align:start position:0% constraints for this 00:10:30.600 --> 00:10:33.889 align:start position:0% constraints for this so<00:10:31.019> just<00:10:31.320> cast<00:10:31.440> the<00:10:31.680> three<00:10:31.860> of<00:10:31.980> them 00:10:33.889 --> 00:10:33.899 align:start position:0% so just cast the three of them 00:10:33.899 --> 00:10:35.750 align:start position:0% so just cast the three of them the<00:10:34.380> next<00:10:34.560> thing<00:10:34.740> I'm<00:10:34.920> going<00:10:35.100> to<00:10:35.220> do<00:10:35.459> is 00:10:35.750 --> 00:10:35.760 align:start position:0% the next thing I'm going to do is 00:10:35.760 --> 00:10:39.829 align:start position:0% the next thing I'm going to do is introduce<00:10:36.300> a<00:10:36.779> new<00:10:37.220> array<00:10:38.220> of<00:10:38.459> booleans 00:10:39.829 --> 00:10:39.839 align:start position:0% introduce a new array of booleans 00:10:39.839 --> 00:10:42.590 align:start position:0% introduce a new array of booleans for<00:10:40.560> the<00:10:40.860> result 00:10:42.590 --> 00:10:42.600 align:start position:0% for the result 00:10:42.600 --> 00:10:45.949 align:start position:0% for the result here<00:10:43.640> one<00:10:44.640> relatively<00:10:45.180> new<00:10:45.360> feature<00:10:45.660> we<00:10:45.839> have 00:10:45.949 --> 00:10:45.959 align:start position:0% here one relatively new feature we have 00:10:45.959 --> 00:10:47.329 align:start position:0% here one relatively new feature we have is<00:10:46.079> that<00:10:46.260> everything<00:10:46.440> is<00:10:46.680> immutable<00:10:47.100> by 00:10:47.329 --> 00:10:47.339 align:start position:0% is that everything is immutable by 00:10:47.339 --> 00:10:49.730 align:start position:0% is that everything is immutable by default<00:10:47.640> so<00:10:47.940> here<00:10:48.180> I<00:10:48.480> have<00:10:49.140> to<00:10:49.260> declare<00:10:49.560> this 00:10:49.730 --> 00:10:49.740 align:start position:0% default so here I have to declare this 00:10:49.740 --> 00:10:51.650 align:start position:0% default so here I have to declare this variable<00:10:50.040> mutable<00:10:50.459> if<00:10:50.820> I<00:10:51.000> want<00:10:51.120> to<00:10:51.240> be<00:10:51.360> able<00:10:51.480> to 00:10:51.650 --> 00:10:51.660 align:start position:0% variable mutable if I want to be able to 00:10:51.660 --> 00:10:53.389 align:start position:0% variable mutable if I want to be able to modify<00:10:52.079> it<00:10:52.200> after 00:10:53.389 --> 00:10:53.399 align:start position:0% modify it after 00:10:53.399 --> 00:10:54.769 align:start position:0% modify it after okay 00:10:54.769 --> 00:10:54.779 align:start position:0% okay 00:10:54.779 --> 00:10:57.230 align:start position:0% okay so<00:10:55.140> now<00:10:55.260> that<00:10:55.440> I<00:10:55.620> have<00:10:55.680> all<00:10:55.860> the<00:10:56.040> bits<00:10:56.339> I<00:10:56.940> can 00:10:57.230 --> 00:10:57.240 align:start position:0% so now that I have all the bits I can 00:10:57.240 --> 00:10:59.389 align:start position:0% so now that I have all the bits I can start<00:10:57.600> a<00:10:57.779> for<00:10:57.899> Loop 00:10:59.389 --> 00:10:59.399 align:start position:0% start a for Loop 00:10:59.399 --> 00:11:01.670 align:start position:0% start a for Loop so<00:11:00.000> for<00:11:00.240> I<00:11:00.660> from 00:11:01.670 --> 00:11:01.680 align:start position:0% so for I from 00:11:01.680 --> 00:11:05.150 align:start position:0% so for I from 0<00:11:02.459> to<00:11:02.880> 32 00:11:05.150 --> 00:11:05.160 align:start position:0% 0 to 32 00:11:05.160 --> 00:11:07.190 align:start position:0% 0 to 32 and<00:11:05.640> here<00:11:05.760> I'm<00:11:05.940> going<00:11:06.060> to<00:11:06.180> consider<00:11:06.540> the<00:11:06.779> if 00:11:07.190 --> 00:11:07.200 align:start position:0% and here I'm going to consider the if 00:11:07.200 --> 00:11:10.190 align:start position:0% and here I'm going to consider the if bit<00:11:07.800> of<00:11:08.579> a<00:11:08.700> b<00:11:08.880> and<00:11:09.000> c 00:11:10.190 --> 00:11:10.200 align:start position:0% bit of a b and c 00:11:10.200 --> 00:11:13.550 align:start position:0% bit of a b and c and<00:11:11.339> if<00:11:11.700> we<00:11:11.940> want<00:11:12.120> to<00:11:12.180> have<00:11:12.360> access<00:11:12.540> to<00:11:12.839> those 00:11:13.550 --> 00:11:13.560 align:start position:0% and if we want to have access to those 00:11:13.560 --> 00:11:16.250 align:start position:0% and if we want to have access to those low<00:11:13.800> level<00:11:13.980> constraints<00:11:14.839> we<00:11:15.839> need<00:11:15.959> to<00:11:16.079> reason 00:11:16.250 --> 00:11:16.260 align:start position:0% low level constraints we need to reason 00:11:16.260 --> 00:11:18.410 align:start position:0% low level constraints we need to reason at<00:11:16.860> the<00:11:16.980> level<00:11:17.100> of<00:11:17.279> field<00:11:17.459> elements<00:11:18.000> so<00:11:18.300> we 00:11:18.410 --> 00:11:18.420 align:start position:0% at the level of field elements so we 00:11:18.420 --> 00:11:20.750 align:start position:0% at the level of field elements so we need<00:11:18.540> to<00:11:18.660> turn<00:11:18.839> those<00:11:19.019> booleans<00:11:19.560> into<00:11:20.459> field 00:11:20.750 --> 00:11:20.760 align:start position:0% need to turn those booleans into field 00:11:20.760 --> 00:11:23.870 align:start position:0% need to turn those booleans into field Elements<00:11:21.300> which<00:11:21.540> is<00:11:21.660> a<00:11:21.839> lower<00:11:22.019> level 00:11:23.870 --> 00:11:23.880 align:start position:0% Elements which is a lower level 00:11:23.880 --> 00:11:25.430 align:start position:0% Elements which is a lower level representation 00:11:25.430 --> 00:11:25.440 align:start position:0% representation 00:11:25.440 --> 00:11:28.030 align:start position:0% representation for<00:11:25.800> this<00:11:25.920> I<00:11:26.100> call<00:11:26.279> this<00:11:26.399> Bluetooth<00:11:26.640> field 00:11:28.030 --> 00:11:28.040 align:start position:0% for this I call this Bluetooth field 00:11:28.040 --> 00:11:31.069 align:start position:0% for this I call this Bluetooth field function<00:11:29.040> which<00:11:29.640> I'm<00:11:29.820> going<00:11:30.060> to 00:11:31.069 --> 00:11:31.079 align:start position:0% function which I'm going to 00:11:31.079 --> 00:11:35.389 align:start position:0% function which I'm going to Define<00:11:31.740> in<00:11:32.160> a<00:11:32.279> second 00:11:35.389 --> 00:11:35.399 align:start position:0% 00:11:35.399 --> 00:11:46.850 align:start position:0% I<00:11:36.000> do<00:11:36.240> the<00:11:36.360> same<00:11:36.540> for<00:11:36.779> B<00:11:36.959> and<00:11:37.200> C 00:11:46.850 --> 00:11:46.860 align:start position:0% 00:11:46.860 --> 00:11:49.069 align:start position:0% and<00:11:47.760> here 00:11:49.069 --> 00:11:49.079 align:start position:0% and here 00:11:49.079 --> 00:11:51.230 align:start position:0% and here I'm<00:11:49.500> going<00:11:49.620> to<00:11:49.740> Define<00:11:49.860> this<00:11:50.160> function<00:11:50.459> and 00:11:51.230 --> 00:11:51.240 align:start position:0% I'm going to Define this function and 00:11:51.240 --> 00:11:53.030 align:start position:0% I'm going to Define this function and again<00:11:51.839> this<00:11:52.200> is<00:11:52.320> something<00:11:52.500> that's<00:11:52.740> going<00:11:52.980> to 00:11:53.030 --> 00:11:53.040 align:start position:0% again this is something that's going to 00:11:53.040 --> 00:11:55.130 align:start position:0% again this is something that's going to be<00:11:53.220> free<00:11:53.399> that's<00:11:53.940> not<00:11:54.240> going<00:11:54.420> to<00:11:54.540> create<00:11:54.899> any 00:11:55.130 --> 00:11:55.140 align:start position:0% be free that's not going to create any 00:11:55.140 --> 00:11:56.750 align:start position:0% be free that's not going to create any constraints<00:11:55.560> for<00:11:56.100> the<00:11:56.220> same<00:11:56.339> reason<00:11:56.519> as 00:11:56.750 --> 00:11:56.760 align:start position:0% constraints for the same reason as 00:11:56.760 --> 00:11:59.329 align:start position:0% constraints for the same reason as earlier<00:11:57.120> because<00:11:57.600> the<00:11:57.839> Boolean 00:11:59.329 --> 00:11:59.339 align:start position:0% earlier because the Boolean 00:11:59.339 --> 00:12:01.190 align:start position:0% earlier because the Boolean is<00:11:59.760> actually<00:11:59.940> presented<00:12:00.540> as<00:12:00.660> a<00:12:00.779> field<00:12:00.899> element 00:12:01.190 --> 00:12:01.200 align:start position:0% is actually presented as a field element 00:12:01.200 --> 00:12:02.990 align:start position:0% is actually presented as a field element at<00:12:01.680> the<00:12:01.800> low<00:12:01.920> level 00:12:02.990 --> 00:12:03.000 align:start position:0% at the low level 00:12:03.000 --> 00:12:05.509 align:start position:0% at the low level it's<00:12:03.300> just<00:12:03.480> that<00:12:03.600> it<00:12:03.779> can<00:12:03.899> only<00:12:04.019> be<00:12:04.320> value<00:12:05.220> 0 00:12:05.509 --> 00:12:05.519 align:start position:0% it's just that it can only be value 0 00:12:05.519 --> 00:12:11.810 align:start position:0% it's just that it can only be value 0 for<00:12:05.880> false<00:12:06.240> and<00:12:06.480> one<00:12:06.660> for<00:12:06.899> two 00:12:11.810 --> 00:12:11.820 align:start position:0% 00:12:11.820 --> 00:12:14.870 align:start position:0% so<00:12:12.480> I<00:12:12.720> can<00:12:12.899> just<00:12:13.200> return<00:12:13.800> that<00:12:14.220> using<00:12:14.640> a 00:12:14.870 --> 00:12:14.880 align:start position:0% so I can just return that using a 00:12:14.880 --> 00:12:20.030 align:start position:0% so I can just return that using a ternary<00:12:15.540> expression 00:12:20.030 --> 00:12:20.040 align:start position:0% 00:12:20.040 --> 00:12:21.889 align:start position:0% okay 00:12:21.889 --> 00:12:21.899 align:start position:0% okay 00:12:21.899 --> 00:12:26.389 align:start position:0% okay so<00:12:22.380> now<00:12:22.500> I<00:12:22.680> have<00:12:22.740> ABC<00:12:23.540> as<00:12:24.540> uh<00:12:25.019> SPL<00:12:25.500> elements 00:12:26.389 --> 00:12:26.399 align:start position:0% so now I have ABC as uh SPL elements 00:12:26.399 --> 00:12:28.550 align:start position:0% so now I have ABC as uh SPL elements now<00:12:26.880> I<00:12:27.180> have<00:12:27.300> this<00:12:27.540> first<00:12:27.660> constraint<00:12:28.140> which 00:12:28.550 --> 00:12:28.560 align:start position:0% now I have this first constraint which 00:12:28.560 --> 00:12:30.670 align:start position:0% now I have this first constraint which was<00:12:28.740> uh<00:12:29.519> BC 00:12:30.670 --> 00:12:30.680 align:start position:0% was uh BC 00:12:30.680 --> 00:12:33.829 align:start position:0% was uh BC equals<00:12:31.680> B<00:12:32.579> times<00:12:32.760> C<00:12:33.000> and<00:12:33.480> actually<00:12:33.660> this 00:12:33.829 --> 00:12:33.839 align:start position:0% equals B times C and actually this 00:12:33.839 --> 00:12:36.889 align:start position:0% equals B times C and actually this constraint<00:12:34.200> I<00:12:34.440> can<00:12:34.560> already<00:12:34.880> Define<00:12:35.880> in<00:12:36.600> in 00:12:36.889 --> 00:12:36.899 align:start position:0% constraint I can already Define in in 00:12:36.899 --> 00:12:38.569 align:start position:0% constraint I can already Define in in the<00:12:37.079> high<00:12:37.200> level<00:12:37.440> language<00:12:37.740> because<00:12:38.220> I'm 00:12:38.569 --> 00:12:38.579 align:start position:0% the high level language because I'm 00:12:38.579 --> 00:12:42.350 align:start position:0% the high level language because I'm doing<00:12:38.820> both<00:12:39.060> constraining<00:12:39.779> and<00:12:40.079> assigning<00:12:40.800> VC 00:12:42.350 --> 00:12:42.360 align:start position:0% doing both constraining and assigning VC 00:12:42.360 --> 00:12:44.150 align:start position:0% doing both constraining and assigning VC so<00:12:42.720> I<00:12:42.959> do<00:12:43.079> that<00:12:43.260> so<00:12:43.620> I<00:12:43.740> have<00:12:43.860> that<00:12:43.980> first 00:12:44.150 --> 00:12:44.160 align:start position:0% so I do that so I have that first 00:12:44.160 --> 00:12:46.670 align:start position:0% so I do that so I have that first constraint<00:12:44.519> is<00:12:44.820> done<00:12:45.000> then<00:12:45.540> I<00:12:45.720> declare<00:12:46.079> this 00:12:46.670 --> 00:12:46.680 align:start position:0% constraint is done then I declare this 00:12:46.680 --> 00:12:49.069 align:start position:0% constraint is done then I declare this result<00:12:47.100> all<00:12:47.639> again<00:12:48.000> mutable 00:12:49.069 --> 00:12:49.079 align:start position:0% result all again mutable 00:12:49.079 --> 00:12:51.889 align:start position:0% result all again mutable and<00:12:49.560> this<00:12:49.740> is<00:12:49.860> where<00:12:50.279> the<00:12:51.240> interesting<00:12:51.720> new 00:12:51.889 --> 00:12:51.899 align:start position:0% and this is where the interesting new 00:12:51.899 --> 00:12:53.990 align:start position:0% and this is where the interesting new thing<00:12:52.139> happens<00:12:52.320> I<00:12:52.680> have<00:12:52.860> this<00:12:53.220> assembly<00:12:53.760> block 00:12:53.990 --> 00:12:54.000 align:start position:0% thing happens I have this assembly block 00:12:54.000 --> 00:12:56.269 align:start position:0% thing happens I have this assembly block that<00:12:54.300> I<00:12:54.480> can<00:12:54.600> create<00:12:55.200> and<00:12:55.440> here<00:12:55.620> as<00:12:55.800> I<00:12:55.980> I<00:12:56.100> have 00:12:56.269 --> 00:12:56.279 align:start position:0% that I can create and here as I I have 00:12:56.279 --> 00:12:59.449 align:start position:0% that I can create and here as I I have access<00:12:56.459> to<00:12:56.839> and<00:12:57.839> two<00:12:58.680> special<00:12:58.860> kinds<00:12:59.339> of 00:12:59.449 --> 00:12:59.459 align:start position:0% access to and two special kinds of 00:12:59.459 --> 00:13:02.030 align:start position:0% access to and two special kinds of statements 00:13:02.030 --> 00:13:02.040 align:start position:0% statements 00:13:02.040 --> 00:13:03.710 align:start position:0% statements the<00:13:02.459> first<00:13:02.519> one<00:13:02.700> is<00:13:02.880> going<00:13:03.060> to<00:13:03.180> be<00:13:03.300> just<00:13:03.540> an 00:13:03.710 --> 00:13:03.720 align:start position:0% the first one is going to be just an 00:13:03.720 --> 00:13:06.769 align:start position:0% the first one is going to be just an assignment<00:13:04.139> so<00:13:04.380> I<00:13:04.560> introduce<00:13:05.040> I<00:13:05.820> just<00:13:06.000> assign 00:13:06.769 --> 00:13:06.779 align:start position:0% assignment so I introduce I just assign 00:13:06.779 --> 00:13:08.990 align:start position:0% assignment so I introduce I just assign the<00:13:07.440> value 00:13:08.990 --> 00:13:09.000 align:start position:0% the value 00:13:09.000 --> 00:13:11.389 align:start position:0% the value BC<00:13:09.660> minus<00:13:10.139> this<00:13:10.320> other<00:13:10.500> expression<00:13:10.980> to<00:13:11.160> Res 00:13:11.389 --> 00:13:11.399 align:start position:0% BC minus this other expression to Res 00:13:11.399 --> 00:13:13.250 align:start position:0% BC minus this other expression to Res but<00:13:11.880> I<00:13:12.060> did<00:13:12.240> not<00:13:12.360> create<00:13:12.540> any<00:13:12.839> constraints 00:13:13.250 --> 00:13:13.260 align:start position:0% but I did not create any constraints 00:13:13.260 --> 00:13:15.710 align:start position:0% but I did not create any constraints it's<00:13:13.500> purely<00:13:13.860> just<00:13:14.040> an<00:13:14.220> assignment 00:13:15.710 --> 00:13:15.720 align:start position:0% it's purely just an assignment 00:13:15.720 --> 00:13:17.509 align:start position:0% it's purely just an assignment so<00:13:16.200> this<00:13:16.380> has<00:13:16.560> no<00:13:16.740> influence<00:13:17.160> on<00:13:17.399> the 00:13:17.509 --> 00:13:17.519 align:start position:0% so this has no influence on the 00:13:17.519 --> 00:13:23.690 align:start position:0% so this has no influence on the constraint<00:13:17.760> system 00:13:23.690 --> 00:13:23.700 align:start position:0% 00:13:23.700 --> 00:13:27.050 align:start position:0% and<00:13:24.180> then<00:13:24.300> I<00:13:24.600> want<00:13:24.660> to<00:13:24.779> be<00:13:24.899> able<00:13:25.079> to<00:13:25.200> use<00:13:25.440> this 00:13:27.050 --> 00:13:27.060 align:start position:0% and then I want to be able to use this 00:13:27.060 --> 00:13:31.190 align:start position:0% and then I want to be able to use this this<00:13:27.540> res<00:13:28.160> value<00:13:29.160> later<00:13:29.519> but<00:13:30.420> to<00:13:30.720> use<00:13:30.899> it<00:13:31.019> I 00:13:31.190 --> 00:13:31.200 align:start position:0% this res value later but to use it I 00:13:31.200 --> 00:13:32.750 align:start position:0% this res value later but to use it I need<00:13:31.320> to<00:13:31.440> make<00:13:31.560> sure<00:13:31.680> that<00:13:31.920> it's<00:13:32.220> really 00:13:32.750 --> 00:13:32.760 align:start position:0% need to make sure that it's really 00:13:32.760 --> 00:13:35.329 align:start position:0% need to make sure that it's really constrained<00:13:33.360> in<00:13:33.660> the<00:13:33.779> constraint<00:13:34.079> system 00:13:35.329 --> 00:13:35.339 align:start position:0% constrained in the constraint system 00:13:35.339 --> 00:13:37.970 align:start position:0% constrained in the constraint system so<00:13:35.579> after<00:13:35.760> this<00:13:35.940> is<00:13:36.120> I<00:13:36.360> did<00:13:36.600> this<00:13:36.959> assignment<00:13:37.500> I 00:13:37.970 --> 00:13:37.980 align:start position:0% so after this is I did this assignment I 00:13:37.980 --> 00:13:41.889 align:start position:0% so after this is I did this assignment I add<00:13:38.279> actually<00:13:39.000> constrained<00:13:39.779> which 00:13:41.889 --> 00:13:41.899 align:start position:0% add actually constrained which 00:13:41.899 --> 00:13:44.569 align:start position:0% add actually constrained which which<00:13:42.899> makes<00:13:43.200> sure<00:13:43.380> that<00:13:43.560> everything 00:13:44.569 --> 00:13:44.579 align:start position:0% which makes sure that everything 00:13:44.579 --> 00:13:48.769 align:start position:0% which makes sure that everything is<00:13:45.180> uh<00:13:45.660> is<00:13:46.019> set<00:13:46.200> in<00:13:46.440> stone 00:13:48.769 --> 00:13:48.779 align:start position:0% 00:13:48.779 --> 00:13:51.470 align:start position:0% so<00:13:49.740> here<00:13:49.860> BC<00:13:50.220> minus<00:13:50.579> res<00:13:50.820> equals<00:13:51.300> this 00:13:51.470 --> 00:13:51.480 align:start position:0% so here BC minus res equals this 00:13:51.480 --> 00:13:53.170 align:start position:0% so here BC minus res equals this multiplication<00:13:51.959> you<00:13:52.380> can<00:13:52.500> see<00:13:52.620> that<00:13:52.860> again 00:13:53.170 --> 00:13:53.180 align:start position:0% multiplication you can see that again 00:13:53.180 --> 00:13:56.210 align:start position:0% multiplication you can see that again this<00:13:54.180> can<00:13:54.300> be<00:13:54.480> any<00:13:54.779> expression<00:13:55.380> here<00:13:55.620> when<00:13:56.040> I 00:13:56.210 --> 00:13:56.220 align:start position:0% this can be any expression here when I 00:13:56.220 --> 00:13:59.389 align:start position:0% this can be any expression here when I assign<00:13:56.519> but<00:13:56.820> this<00:13:57.060> has<00:13:57.300> to<00:13:57.480> be<00:13:57.800> linear<00:13:58.800> equals 00:13:59.389 --> 00:13:59.399 align:start position:0% assign but this has to be linear equals 00:13:59.399 --> 00:14:02.329 align:start position:0% assign but this has to be linear equals quadratic<00:14:00.120> right<00:14:00.779> so<00:14:01.200> here 00:14:02.329 --> 00:14:02.339 align:start position:0% quadratic right so here 00:14:02.339 --> 00:14:05.269 align:start position:0% quadratic right so here this<00:14:02.880> is<00:14:03.000> this<00:14:03.300> is<00:14:03.480> working 00:14:05.269 --> 00:14:05.279 align:start position:0% this is this is working 00:14:05.279 --> 00:14:08.569 align:start position:0% this is this is working okay<00:14:05.760> so<00:14:06.060> now<00:14:06.240> I<00:14:06.480> have<00:14:06.600> everything<00:14:06.899> set<00:14:07.500> up 00:14:08.569 --> 00:14:08.579 align:start position:0% okay so now I have everything set up 00:14:08.579 --> 00:14:10.370 align:start position:0% okay so now I have everything set up um<00:14:08.639> and<00:14:08.880> I'm<00:14:09.000> convinced<00:14:09.420> that<00:14:09.600> res<00:14:09.779> has<00:14:10.200> a 00:14:10.370 --> 00:14:10.380 align:start position:0% um and I'm convinced that res has a 00:14:10.380 --> 00:14:11.990 align:start position:0% um and I'm convinced that res has a result<00:14:10.500> that<00:14:10.860> I<00:14:11.040> need 00:14:11.990 --> 00:14:12.000 align:start position:0% result that I need 00:14:12.000 --> 00:14:13.550 align:start position:0% result that I need the<00:14:12.420> next<00:14:12.480> thing<00:14:12.600> that<00:14:12.779> I<00:14:12.899> want<00:14:13.019> to<00:14:13.079> do<00:14:13.200> is<00:14:13.380> that 00:14:13.550 --> 00:14:13.560 align:start position:0% the next thing that I want to do is that 00:14:13.560 --> 00:14:14.990 align:start position:0% the next thing that I want to do is that I<00:14:13.740> actually<00:14:13.860> want<00:14:14.040> to<00:14:14.160> have<00:14:14.279> a<00:14:14.459> Boolean<00:14:14.820> I'm 00:14:14.990 --> 00:14:15.000 align:start position:0% I actually want to have a Boolean I'm 00:14:15.000 --> 00:14:16.629 align:start position:0% I actually want to have a Boolean I'm going<00:14:15.180> to<00:14:15.240> go<00:14:15.480> the<00:14:15.600> other<00:14:15.720> way<00:14:15.959> around<00:14:16.139> and 00:14:16.629 --> 00:14:16.639 align:start position:0% going to go the other way around and 00:14:16.639 --> 00:14:19.370 align:start position:0% going to go the other way around and reconstruct<00:14:17.639> my<00:14:18.240> result<00:14:18.360> but<00:14:18.839> I<00:14:18.959> want<00:14:19.200> to<00:14:19.320> have 00:14:19.370 --> 00:14:19.380 align:start position:0% reconstruct my result but I want to have 00:14:19.380 --> 00:14:21.769 align:start position:0% reconstruct my result but I want to have a<00:14:19.500> Boolean<00:14:19.860> and<00:14:20.040> I<00:14:20.160> want<00:14:20.220> to<00:14:20.339> go<00:14:20.519> from<00:14:21.300> a<00:14:21.660> field 00:14:21.769 --> 00:14:21.779 align:start position:0% a Boolean and I want to go from a field 00:14:21.779 --> 00:14:24.530 align:start position:0% a Boolean and I want to go from a field element<00:14:22.019> to<00:14:22.320> a<00:14:22.440> Boolean<00:14:22.800> and<00:14:23.519> here<00:14:23.940> I<00:14:24.300> want<00:14:24.420> to 00:14:24.530 --> 00:14:24.540 align:start position:0% element to a Boolean and here I want to 00:14:24.540 --> 00:14:26.449 align:start position:0% element to a Boolean and here I want to make<00:14:24.660> it<00:14:24.779> really<00:14:24.899> clear<00:14:25.139> that<00:14:25.440> this<00:14:25.680> is<00:14:25.860> an 00:14:26.449 --> 00:14:26.459 align:start position:0% make it really clear that this is an 00:14:26.459 --> 00:14:28.730 align:start position:0% make it really clear that this is an unsafe<00:14:27.060> a<00:14:27.420> potentially<00:14:27.839> unsafe<00:14:28.200> operation 00:14:28.730 --> 00:14:28.740 align:start position:0% unsafe a potentially unsafe operation 00:14:28.740 --> 00:14:32.210 align:start position:0% unsafe a potentially unsafe operation because<00:14:29.660> this<00:14:30.660> res<00:14:30.899> value<00:14:31.200> I<00:14:31.560> know<00:14:31.680> that<00:14:32.040> it's 00:14:32.210 --> 00:14:32.220 align:start position:0% because this res value I know that it's 00:14:32.220 --> 00:14:35.389 align:start position:0% because this res value I know that it's 0<00:14:32.459> or<00:14:33.060> 1<00:14:33.180> because<00:14:33.360> I<00:14:33.600> I<00:14:33.779> wrote<00:14:34.079> this<00:14:34.320> but<00:14:35.040> in 00:14:35.389 --> 00:14:35.399 align:start position:0% 0 or 1 because I I wrote this but in 00:14:35.399 --> 00:14:38.389 align:start position:0% 0 or 1 because I I wrote this but in theory<00:14:35.700> it<00:14:36.060> could<00:14:36.180> be<00:14:36.360> any<00:14:37.200> value<00:14:37.500> so<00:14:38.160> I<00:14:38.279> need 00:14:38.389 --> 00:14:38.399 align:start position:0% theory it could be any value so I need 00:14:38.399 --> 00:14:42.170 align:start position:0% theory it could be any value so I need to<00:14:38.519> be<00:14:38.639> really<00:14:38.820> careful<00:14:39.120> when<00:14:39.360> I<00:14:39.480> do<00:14:39.600> this 00:14:42.170 --> 00:14:42.180 align:start position:0% 00:14:42.180 --> 00:14:44.990 align:start position:0% um but<00:14:42.540> I<00:14:42.779> can<00:14:42.959> force<00:14:43.440> uh<00:14:44.339> the<00:14:44.519> creation<00:14:44.760> of 00:14:44.990 --> 00:14:45.000 align:start position:0% um but I can force uh the creation of 00:14:45.000 --> 00:14:46.850 align:start position:0% um but I can force uh the creation of this<00:14:45.180> Boolean<00:14:45.600> with<00:14:45.899> this<00:14:46.079> value 00:14:46.850 --> 00:14:46.860 align:start position:0% this Boolean with this value 00:14:46.860 --> 00:14:50.629 align:start position:0% this Boolean with this value finally<00:14:47.519> I<00:14:48.120> reconstruct<00:14:48.660> the<00:14:49.019> u32<00:14:49.560> value<00:14:49.800> from 00:14:50.629 --> 00:14:50.639 align:start position:0% finally I reconstruct the u32 value from 00:14:50.639 --> 00:14:53.150 align:start position:0% finally I reconstruct the u32 value from the<00:14:50.820> Boolean<00:14:51.240> array 00:14:53.150 --> 00:14:53.160 align:start position:0% the Boolean array 00:14:53.160 --> 00:14:57.110 align:start position:0% the Boolean array using<00:14:53.699> this<00:14:53.820> cost<00:14:54.000> function<00:14:54.300> again 00:14:57.110 --> 00:14:57.120 align:start position:0% 00:14:57.120 --> 00:14:59.150 align:start position:0% okay<00:14:57.480> and<00:14:57.899> I<00:14:58.019> changed<00:14:58.260> my<00:14:58.380> entry<00:14:58.680> point<00:14:58.800> to<00:14:58.980> use 00:14:59.150 --> 00:14:59.160 align:start position:0% okay and I changed my entry point to use 00:14:59.160 --> 00:15:01.129 align:start position:0% okay and I changed my entry point to use the<00:14:59.279> hand<00:14:59.459> optimized<00:15:00.000> version 00:15:01.129 --> 00:15:01.139 align:start position:0% the hand optimized version 00:15:01.139 --> 00:15:05.290 align:start position:0% the hand optimized version so<00:15:01.500> we<00:15:01.680> were<00:15:01.800> at<00:15:01.980> 260<00:15:02.699> and<00:15:03.480> now<00:15:03.600> we're<00:15:03.779> at<00:15:03.899> 164. 00:15:05.290 --> 00:15:05.300 align:start position:0% so we were at 260 and now we're at 164. 00:15:05.300 --> 00:15:09.650 align:start position:0% so we were at 260 and now we're at 164. so<00:15:06.300> we<00:15:06.540> made<00:15:06.720> uh<00:15:07.620> quite<00:15:08.399> quite<00:15:08.699> a<00:15:08.820> bit<00:15:08.940> uh<00:15:09.420> dent 00:15:09.650 --> 00:15:09.660 align:start position:0% so we made uh quite quite a bit uh dent 00:15:09.660 --> 00:15:12.949 align:start position:0% so we made uh quite quite a bit uh dent in<00:15:10.199> our<00:15:10.500> constraint<00:15:10.980> count 00:15:12.949 --> 00:15:12.959 align:start position:0% in our constraint count 00:15:12.959 --> 00:15:15.050 align:start position:0% in our constraint count so<00:15:13.380> what's<00:15:13.560> the<00:15:13.800> idea<00:15:14.040> here 00:15:15.050 --> 00:15:15.060 align:start position:0% so what's the idea here 00:15:15.060 --> 00:15:15.650 align:start position:0% so what's the idea here um 00:15:15.650 --> 00:15:15.660 align:start position:0% um 00:15:15.660 --> 00:15:18.170 align:start position:0% um we<00:15:16.380> want<00:15:16.560> to<00:15:16.680> keep<00:15:16.980> all<00:15:17.399> the<00:15:17.519> guarantees<00:15:17.940> that 00:15:18.170 --> 00:15:18.180 align:start position:0% we want to keep all the guarantees that 00:15:18.180 --> 00:15:19.850 align:start position:0% we want to keep all the guarantees that we<00:15:18.300> have<00:15:18.420> from<00:15:18.720> our<00:15:18.959> higher<00:15:19.380> level<00:15:19.500> language 00:15:19.850 --> 00:15:19.860 align:start position:0% we have from our higher level language 00:15:19.860 --> 00:15:21.949 align:start position:0% we have from our higher level language we<00:15:20.279> have<00:15:20.399> types<00:15:20.820> we<00:15:21.000> have<00:15:21.120> things<00:15:21.360> we<00:15:21.779> know 00:15:21.949 --> 00:15:21.959 align:start position:0% we have types we have things we know 00:15:21.959 --> 00:15:23.870 align:start position:0% we have types we have things we know that<00:15:22.139> booleans<00:15:22.500> can<00:15:22.740> be<00:15:22.860> only<00:15:23.040> zero<00:15:23.459> one<00:15:23.579> if 00:15:23.870 --> 00:15:23.880 align:start position:0% that booleans can be only zero one if 00:15:23.880 --> 00:15:25.910 align:start position:0% that booleans can be only zero one if you<00:15:24.060> don't<00:15:24.180> write<00:15:24.300> assembly<00:15:24.779> blocks<00:15:25.199> but<00:15:25.800> at 00:15:25.910 --> 00:15:25.920 align:start position:0% you don't write assembly blocks but at 00:15:25.920 --> 00:15:27.290 align:start position:0% you don't write assembly blocks but at the<00:15:26.040> same<00:15:26.160> time<00:15:26.279> we<00:15:26.459> want<00:15:26.579> to<00:15:26.699> have<00:15:26.820> access<00:15:27.060> to 00:15:27.290 --> 00:15:27.300 align:start position:0% the same time we want to have access to 00:15:27.300 --> 00:15:29.150 align:start position:0% the same time we want to have access to this<00:15:27.480> low<00:15:27.660> level<00:15:27.839> thing<00:15:28.139> and<00:15:28.740> here<00:15:28.860> I<00:15:29.040> think 00:15:29.150 --> 00:15:29.160 align:start position:0% this low level thing and here I think 00:15:29.160 --> 00:15:31.430 align:start position:0% this low level thing and here I think there's<00:15:29.399> actually<00:15:29.699> a<00:15:29.940> parallel<00:15:30.300> with<00:15:30.540> rust<00:15:31.199> in 00:15:31.430 --> 00:15:31.440 align:start position:0% there's actually a parallel with rust in 00:15:31.440 --> 00:15:33.650 align:start position:0% there's actually a parallel with rust in a<00:15:31.560> way<00:15:31.680> which<00:15:32.220> says<00:15:32.579> okay<00:15:32.699> we<00:15:33.060> we<00:15:33.300> have<00:15:33.540> a 00:15:33.650 --> 00:15:33.660 align:start position:0% a way which says okay we we have a 00:15:33.660 --> 00:15:35.569 align:start position:0% a way which says okay we we have a compiler<00:15:34.019> that's<00:15:34.199> like<00:15:34.500> really<00:15:34.980> strict<00:15:35.279> all 00:15:35.569 --> 00:15:35.579 align:start position:0% compiler that's like really strict all 00:15:35.579 --> 00:15:36.769 align:start position:0% compiler that's like really strict all these<00:15:35.820> things<00:15:35.940> but<00:15:36.180> we<00:15:36.360> still<00:15:36.480> want<00:15:36.600> to<00:15:36.720> be 00:15:36.769 --> 00:15:36.779 align:start position:0% these things but we still want to be 00:15:36.779 --> 00:15:39.050 align:start position:0% these things but we still want to be able<00:15:36.899> to<00:15:37.079> do<00:15:37.260> all<00:15:37.500> these<00:15:37.860> lower<00:15:38.519> level<00:15:38.760> things 00:15:39.050 --> 00:15:39.060 align:start position:0% able to do all these lower level things 00:15:39.060 --> 00:15:41.930 align:start position:0% able to do all these lower level things we<00:15:39.240> want<00:15:39.480> to<00:15:39.600> disable<00:15:40.079> a<00:15:40.320> bunch<00:15:40.500> of<00:15:40.620> checks<00:15:41.399> and 00:15:41.930 --> 00:15:41.940 align:start position:0% we want to disable a bunch of checks and 00:15:41.940 --> 00:15:44.509 align:start position:0% we want to disable a bunch of checks and we<00:15:42.060> have<00:15:42.240> a<00:15:42.480> similar<00:15:42.839> approach<00:15:43.199> where<00:15:44.100> as<00:15:44.339> a 00:15:44.509 --> 00:15:44.519 align:start position:0% we have a similar approach where as a 00:15:44.519 --> 00:15:46.610 align:start position:0% we have a similar approach where as a developer<00:15:44.880> you<00:15:45.120> would<00:15:45.240> write<00:15:45.480> most<00:15:46.079> of<00:15:46.320> your 00:15:46.610 --> 00:15:46.620 align:start position:0% developer you would write most of your 00:15:46.620 --> 00:15:50.689 align:start position:0% developer you would write most of your program<00:15:47.220> in<00:15:48.180> safe<00:15:48.480> zocots<00:15:49.019> let's<00:15:49.380> say<00:15:49.699> but 00:15:50.689 --> 00:15:50.699 align:start position:0% program in safe zocots let's say but 00:15:50.699 --> 00:15:52.790 align:start position:0% program in safe zocots let's say but then<00:15:50.820> for<00:15:51.000> the<00:15:51.120> few<00:15:51.240> parts<00:15:51.480> that<00:15:52.079> need<00:15:52.380> the 00:15:52.790 --> 00:15:52.800 align:start position:0% then for the few parts that need the 00:15:52.800 --> 00:15:54.710 align:start position:0% then for the few parts that need the extra<00:15:52.980> performance<00:15:53.579> you<00:15:53.880> can<00:15:54.000> write<00:15:54.180> them<00:15:54.420> in 00:15:54.710 --> 00:15:54.720 align:start position:0% extra performance you can write them in 00:15:54.720 --> 00:15:57.769 align:start position:0% extra performance you can write them in those<00:15:54.899> ASM<00:15:55.740> blocks<00:15:56.100> and<00:15:57.060> try<00:15:57.240> to<00:15:57.420> make<00:15:57.540> those 00:15:57.769 --> 00:15:57.779 align:start position:0% those ASM blocks and try to make those 00:15:57.779 --> 00:15:59.689 align:start position:0% those ASM blocks and try to make those blocks<00:15:58.139> as<00:15:58.380> small<00:15:58.620> as<00:15:58.800> possible<00:15:59.100> so<00:15:59.399> that<00:15:59.519> when 00:15:59.689 --> 00:15:59.699 align:start position:0% blocks as small as possible so that when 00:15:59.699 --> 00:16:01.490 align:start position:0% blocks as small as possible so that when you<00:15:59.820> need<00:15:59.940> to<00:16:00.060> review<00:16:00.180> the<00:16:00.480> code<00:16:00.660> or<00:16:01.260> make<00:16:01.380> sure 00:16:01.490 --> 00:16:01.500 align:start position:0% you need to review the code or make sure 00:16:01.500 --> 00:16:03.769 align:start position:0% you need to review the code or make sure that<00:16:01.680> things<00:16:01.920> are<00:16:02.040> not<00:16:02.160> unconstrained<00:16:03.360> you 00:16:03.769 --> 00:16:03.779 align:start position:0% that things are not unconstrained you 00:16:03.779 --> 00:16:05.269 align:start position:0% that things are not unconstrained you know<00:16:03.959> exactly<00:16:04.260> where<00:16:04.380> to<00:16:04.560> look<00:16:04.740> at<00:16:04.860> and<00:16:05.040> these 00:16:05.269 --> 00:16:05.279 align:start position:0% know exactly where to look at and these 00:16:05.279 --> 00:16:08.150 align:start position:0% know exactly where to look at and these things<00:16:05.399> are<00:16:05.579> relatively<00:16:06.360> small 00:16:08.150 --> 00:16:08.160 align:start position:0% things are relatively small 00:16:08.160 --> 00:16:10.670 align:start position:0% things are relatively small um<00:16:08.220> one<00:16:08.820> side<00:16:09.120> effect<00:16:09.300> of<00:16:09.720> this<00:16:09.899> also<00:16:10.320> for<00:16:10.500> us 00:16:10.670 --> 00:16:10.680 align:start position:0% um one side effect of this also for us 00:16:10.680 --> 00:16:13.129 align:start position:0% um one side effect of this also for us as<00:16:11.040> a<00:16:11.160> compiler<00:16:11.579> team<00:16:11.760> is<00:16:12.480> that<00:16:12.660> we<00:16:12.839> can<00:16:12.959> use 00:16:13.129 --> 00:16:13.139 align:start position:0% as a compiler team is that we can use 00:16:13.139 --> 00:16:15.110 align:start position:0% as a compiler team is that we can use this<00:16:13.440> ourselves<00:16:13.920> to<00:16:14.279> reduce<00:16:14.399> the<00:16:14.699> complexity 00:16:15.110 --> 00:16:15.120 align:start position:0% this ourselves to reduce the complexity 00:16:15.120 --> 00:16:17.689 align:start position:0% this ourselves to reduce the complexity of<00:16:15.240> the<00:16:15.360> compiler<00:16:15.839> this<00:16:16.440> particular 00:16:17.689 --> 00:16:17.699 align:start position:0% of the compiler this particular 00:16:17.699 --> 00:16:21.250 align:start position:0% of the compiler this particular um<00:16:18.180> operation<00:16:18.839> and<00:16:19.079> the<00:16:19.199> shot<00:16:19.380> 256<00:16:20.180> algorithm 00:16:21.250 --> 00:16:21.260 align:start position:0% um operation and the shot 256 algorithm 00:16:21.260 --> 00:16:24.290 align:start position:0% um operation and the shot 256 algorithm we<00:16:22.260> in<00:16:22.500> the<00:16:22.680> compiler<00:16:23.160> we<00:16:23.639> have<00:16:23.820> a<00:16:24.120> special 00:16:24.290 --> 00:16:24.300 align:start position:0% we in the compiler we have a special 00:16:24.300 --> 00:16:26.210 align:start position:0% we in the compiler we have a special case<00:16:24.600> which<00:16:25.019> detects<00:16:25.500> whenever<00:16:25.860> we're<00:16:25.980> doing 00:16:26.210 --> 00:16:26.220 align:start position:0% case which detects whenever we're doing 00:16:26.220 --> 00:16:29.930 align:start position:0% case which detects whenever we're doing this<00:16:26.519> and<00:16:27.240> uses<00:16:27.720> this<00:16:28.380> exact<00:16:28.800> constraints 00:16:29.930 --> 00:16:29.940 align:start position:0% this and uses this exact constraints 00:16:29.940 --> 00:16:32.030 align:start position:0% this and uses this exact constraints but<00:16:30.540> now<00:16:30.779> potentially<00:16:31.260> using<00:16:31.620> assembly 00:16:32.030 --> 00:16:32.040 align:start position:0% but now potentially using assembly 00:16:32.040 --> 00:16:34.629 align:start position:0% but now potentially using assembly blocks<00:16:32.399> what<00:16:32.639> we<00:16:32.760> can<00:16:32.880> do<00:16:33.060> is<00:16:33.300> rewriting 00:16:34.629 --> 00:16:34.639 align:start position:0% blocks what we can do is rewriting 00:16:34.639 --> 00:16:36.530 align:start position:0% blocks what we can do is rewriting some<00:16:35.639> of 00:16:36.530 --> 00:16:36.540 align:start position:0% some of 00:16:36.540 --> 00:16:38.389 align:start position:0% some of the<00:16:37.019> internals<00:16:37.440> of<00:16:37.560> the<00:16:37.680> compiler<00:16:38.100> to 00:16:38.389 --> 00:16:38.399 align:start position:0% the internals of the compiler to 00:16:38.399 --> 00:16:40.249 align:start position:0% the internals of the compiler to actually<00:16:38.579> use<00:16:38.940> these<00:16:39.300> things 00:16:40.249 --> 00:16:40.259 align:start position:0% actually use these things 00:16:40.259 --> 00:16:42.769 align:start position:0% actually use these things which<00:16:40.980> then<00:16:41.339> reduce<00:16:41.639> the<00:16:42.000> size<00:16:42.360> of<00:16:42.600> the 00:16:42.769 --> 00:16:42.779 align:start position:0% which then reduce the size of the 00:16:42.779 --> 00:16:44.569 align:start position:0% which then reduce the size of the compiler<00:16:43.320> code<00:16:43.440> base<00:16:43.620> and<00:16:43.860> makes<00:16:43.980> it<00:16:44.220> easier 00:16:44.569 --> 00:16:44.579 align:start position:0% compiler code base and makes it easier 00:16:44.579 --> 00:16:47.449 align:start position:0% compiler code base and makes it easier to<00:16:44.820> reason<00:16:45.000> about<00:16:45.300> an<00:16:45.600> audit<00:16:46.380> the<00:16:47.220> next<00:16:47.339> thing 00:16:47.449 --> 00:16:47.459 align:start position:0% to reason about an audit the next thing 00:16:47.459 --> 00:16:50.210 align:start position:0% to reason about an audit the next thing that<00:16:47.639> I<00:16:47.759> want<00:16:47.880> to<00:16:48.000> talk<00:16:48.180> about<00:16:48.360> which<00:16:49.079> is<00:16:49.320> uh 00:16:50.210 --> 00:16:50.220 align:start position:0% that I want to talk about which is uh 00:16:50.220 --> 00:16:52.370 align:start position:0% that I want to talk about which is uh unrelated<00:16:50.699> to<00:16:50.940> this<00:16:51.120> is<00:16:51.839> the<00:16:52.139> fact<00:16:52.259> that 00:16:52.370 --> 00:16:52.380 align:start position:0% unrelated to this is the fact that 00:16:52.380 --> 00:16:54.110 align:start position:0% unrelated to this is the fact that Socrates<00:16:52.800> is<00:16:52.980> not<00:16:53.160> compatible<00:16:53.519> with<00:16:53.699> with 00:16:54.110 --> 00:16:54.120 align:start position:0% Socrates is not compatible with with 00:16:54.120 --> 00:16:57.530 align:start position:0% Socrates is not compatible with with snot<00:16:54.660> JS<00:16:55.019> so<00:16:55.500> snog<00:16:55.860> JS<00:16:56.160> is<00:16:56.639> a<00:16:57.000> JavaScript 00:16:57.530 --> 00:16:57.540 align:start position:0% snot JS so snog JS is a JavaScript 00:16:57.540 --> 00:17:00.949 align:start position:0% snot JS so snog JS is a JavaScript library<00:16:57.899> for<00:16:58.500> snorix<00:16:59.040> from<00:16:59.579> the<00:17:00.540> identity 00:17:00.949 --> 00:17:00.959 align:start position:0% library for snorix from the identity 00:17:00.959 --> 00:17:03.949 align:start position:0% library for snorix from the identity team<00:17:01.259> from<00:17:01.740> the<00:17:01.860> circum<00:17:02.220> team<00:17:02.660> which<00:17:03.660> has<00:17:03.839> a 00:17:03.949 --> 00:17:03.959 align:start position:0% team from the circum team which has a 00:17:03.959 --> 00:17:06.169 align:start position:0% team from the circum team which has a bunch<00:17:04.079> of<00:17:04.199> tools<00:17:04.500> allowing<00:17:04.919> you<00:17:05.100> to<00:17:05.579> work<00:17:06.000> with 00:17:06.169 --> 00:17:06.179 align:start position:0% bunch of tools allowing you to work with 00:17:06.179 --> 00:17:08.689 align:start position:0% bunch of tools allowing you to work with snarks<00:17:06.660> in<00:17:07.199> a<00:17:07.319> JavaScript<00:17:07.740> context 00:17:08.689 --> 00:17:08.699 align:start position:0% snarks in a JavaScript context 00:17:08.699 --> 00:17:11.990 align:start position:0% snarks in a JavaScript context what<00:17:09.240> we<00:17:09.419> have<00:17:09.600> now<00:17:09.900> available<00:17:10.260> today<00:17:10.679> is<00:17:11.640> uh 00:17:11.990 --> 00:17:12.000 align:start position:0% what we have now available today is uh 00:17:12.000 --> 00:17:14.210 align:start position:0% what we have now available today is uh if<00:17:12.240> you<00:17:12.360> start<00:17:12.540> from<00:17:12.839> your<00:17:13.199> your<00:17:13.500> zocoties 00:17:14.210 --> 00:17:14.220 align:start position:0% if you start from your your zocoties 00:17:14.220 --> 00:17:16.309 align:start position:0% if you start from your your zocoties program<00:17:14.400> and<00:17:15.059> you<00:17:15.179> run<00:17:15.360> the<00:17:15.720> compilation 00:17:16.309 --> 00:17:16.319 align:start position:0% program and you run the compilation 00:17:16.319 --> 00:17:18.530 align:start position:0% program and you run the compilation currently 00:17:18.530 --> 00:17:18.540 align:start position:0% currently 00:17:18.540 --> 00:17:21.289 align:start position:0% currently um it<00:17:19.199> returns<00:17:19.679> an<00:17:19.799> output<00:17:20.160> which<00:17:20.520> is<00:17:20.699> the<00:17:21.120> low 00:17:21.289 --> 00:17:21.299 align:start position:0% um it returns an output which is the low 00:17:21.299 --> 00:17:23.569 align:start position:0% um it returns an output which is the low level<00:17:21.480> zocchi's<00:17:22.260> representation<00:17:22.620> but<00:17:23.459> you 00:17:23.569 --> 00:17:23.579 align:start position:0% level zocchi's representation but you 00:17:23.579 --> 00:17:27.169 align:start position:0% level zocchi's representation but you can<00:17:23.699> also<00:17:24.000> optionally<00:17:24.540> return<00:17:25.260> and<00:17:25.980> Dot<00:17:26.459> r1cs 00:17:27.169 --> 00:17:27.179 align:start position:0% can also optionally return and Dot r1cs 00:17:27.179 --> 00:17:29.990 align:start position:0% can also optionally return and Dot r1cs file<00:17:27.540> which<00:17:27.780> is<00:17:27.959> uh<00:17:28.439> the<00:17:29.040> format<00:17:29.400> that<00:17:29.760> is 00:17:29.990 --> 00:17:30.000 align:start position:0% file which is uh the format that is 00:17:30.000 --> 00:17:33.110 align:start position:0% file which is uh the format that is accepted<00:17:30.540> by<00:17:30.900> it's<00:17:31.799> not<00:17:31.980> Js 00:17:33.110 --> 00:17:33.120 align:start position:0% accepted by it's not Js 00:17:33.120 --> 00:17:36.110 align:start position:0% accepted by it's not Js and<00:17:33.840> then<00:17:34.140> if<00:17:34.740> you<00:17:34.860> want<00:17:35.039> to<00:17:35.160> execute<00:17:35.880> your 00:17:36.110 --> 00:17:36.120 align:start position:0% and then if you want to execute your 00:17:36.120 --> 00:17:40.490 align:start position:0% and then if you want to execute your program<00:17:36.299> you<00:17:37.200> take<00:17:37.440> your<00:17:38.280> input<00:17:38.780> and<00:17:39.780> uh<00:17:40.260> and 00:17:40.490 --> 00:17:40.500 align:start position:0% program you take your input and uh and 00:17:40.500 --> 00:17:43.190 align:start position:0% program you take your input and uh and the<00:17:40.620> program<00:17:40.740> itself<00:17:41.220> and<00:17:42.059> you<00:17:42.240> can<00:17:42.299> create 00:17:43.190 --> 00:17:43.200 align:start position:0% the program itself and you can create 00:17:43.200 --> 00:17:45.529 align:start position:0% the program itself and you can create a<00:17:43.799> witness<00:17:44.100> file<00:17:44.460> which<00:17:44.760> is<00:17:44.880> also<00:17:45.120> compatible 00:17:45.529 --> 00:17:45.539 align:start position:0% a witness file which is also compatible 00:17:45.539 --> 00:17:48.049 align:start position:0% a witness file which is also compatible with<00:17:45.780> with<00:17:46.080> snot<00:17:46.740> Js 00:17:48.049 --> 00:17:48.059 align:start position:0% with with snot Js 00:17:48.059 --> 00:17:51.529 align:start position:0% with with snot Js and<00:17:48.539> from<00:17:48.780> this<00:17:48.960> point<00:17:49.140> on<00:17:49.700> your<00:17:50.700> Instagram<00:17:51.000> JS 00:17:51.529 --> 00:17:51.539 align:start position:0% and from this point on your Instagram JS 00:17:51.539 --> 00:17:53.630 align:start position:0% and from this point on your Instagram JS lens<00:17:51.840> so<00:17:51.960> you<00:17:52.140> can<00:17:52.200> do<00:17:52.380> whatever<00:17:52.620> snog<00:17:53.400> JS 00:17:53.630 --> 00:17:53.640 align:start position:0% lens so you can do whatever snog JS 00:17:53.640 --> 00:17:56.270 align:start position:0% lens so you can do whatever snog JS enables<00:17:54.059> you<00:17:54.240> to<00:17:54.360> do<00:17:54.559> using<00:17:55.559> different<00:17:55.919> proof 00:17:56.270 --> 00:17:56.280 align:start position:0% enables you to do using different proof 00:17:56.280 --> 00:17:58.850 align:start position:0% enables you to do using different proof systems<00:17:56.760> uh<00:17:57.600> using<00:17:57.900> a<00:17:58.080> powersoft<00:17:58.500> Tau 00:17:58.850 --> 00:17:58.860 align:start position:0% systems uh using a powersoft Tau 00:17:58.860 --> 00:18:00.350 align:start position:0% systems uh using a powersoft Tau ceremony 00:18:00.350 --> 00:18:00.360 align:start position:0% ceremony 00:18:00.360 --> 00:18:01.010 align:start position:0% ceremony um 00:18:01.010 --> 00:18:01.020 align:start position:0% um 00:18:01.020 --> 00:18:04.430 align:start position:0% um uh<00:18:01.799> and<00:18:02.520> run<00:18:02.880> your<00:18:03.360> verifier<00:18:03.780> in<00:18:03.900> the<00:18:04.020> browser 00:18:04.430 --> 00:18:04.440 align:start position:0% uh and run your verifier in the browser 00:18:04.440 --> 00:18:05.990 align:start position:0% uh and run your verifier in the browser etc<00:18:04.860> etc 00:18:05.990 --> 00:18:06.000 align:start position:0% etc etc 00:18:06.000 --> 00:18:08.270 align:start position:0% etc etc so<00:18:06.419> any<00:18:06.660> tooling<00:18:07.260> that's<00:18:07.380> compatible<00:18:07.860> with 00:18:08.270 --> 00:18:08.280 align:start position:0% so any tooling that's compatible with 00:18:08.280 --> 00:18:10.310 align:start position:0% so any tooling that's compatible with these<00:18:09.000> formats<00:18:09.480> can<00:18:09.720> now<00:18:09.840> be<00:18:10.080> used<00:18:10.200> with 00:18:10.310 --> 00:18:10.320 align:start position:0% these formats can now be used with 00:18:10.320 --> 00:18:11.870 align:start position:0% these formats can now be used with circuses<00:18:10.860> as<00:18:11.039> well 00:18:11.870 --> 00:18:11.880 align:start position:0% circuses as well 00:18:11.880 --> 00:18:15.169 align:start position:0% circuses as well another<00:18:12.419> topic<00:18:12.840> that<00:18:12.960> I<00:18:13.140> wanted<00:18:13.200> to<00:18:13.380> touch<00:18:13.620> on 00:18:15.169 --> 00:18:15.179 align:start position:0% another topic that I wanted to touch on 00:18:15.179 --> 00:18:18.289 align:start position:0% another topic that I wanted to touch on quickly<00:18:15.900> is<00:18:16.799> the 00:18:18.289 --> 00:18:18.299 align:start position:0% quickly is the 00:18:18.299 --> 00:18:20.690 align:start position:0% quickly is the is<00:18:18.840> incrementally<00:18:19.700> incrementally 00:18:20.690 --> 00:18:20.700 align:start position:0% is incrementally incrementally 00:18:20.700 --> 00:18:22.789 align:start position:0% is incrementally incrementally verifiable<00:18:21.360> computation<00:18:21.840> so<00:18:22.380> this<00:18:22.559> is<00:18:22.679> a 00:18:22.789 --> 00:18:22.799 align:start position:0% verifiable computation so this is a 00:18:22.799 --> 00:18:24.350 align:start position:0% verifiable computation so this is a scary<00:18:22.919> word<00:18:23.220> but<00:18:23.520> it's<00:18:23.700> basically<00:18:23.940> the<00:18:24.120> idea 00:18:24.350 --> 00:18:24.360 align:start position:0% scary word but it's basically the idea 00:18:24.360 --> 00:18:26.090 align:start position:0% scary word but it's basically the idea that<00:18:24.539> if<00:18:24.720> you<00:18:24.840> have<00:18:24.960> a<00:18:25.080> computation 00:18:26.090 --> 00:18:26.100 align:start position:0% that if you have a computation 00:18:26.100 --> 00:18:29.510 align:start position:0% that if you have a computation which<00:18:26.580> you<00:18:26.760> can<00:18:26.880> split<00:18:27.299> in<00:18:27.600> steps<00:18:28.080> which<00:18:28.799> are 00:18:29.510 --> 00:18:29.520 align:start position:0% which you can split in steps which are 00:18:29.520 --> 00:18:31.850 align:start position:0% which you can split in steps which are basically<00:18:29.880> the<00:18:30.120> same<00:18:30.299> function 00:18:31.850 --> 00:18:31.860 align:start position:0% basically the same function 00:18:31.860 --> 00:18:34.130 align:start position:0% basically the same function being<00:18:32.340> run<00:18:32.640> over<00:18:33.059> and<00:18:33.240> over<00:18:33.480> again<00:18:33.660> on<00:18:34.020> the 00:18:34.130 --> 00:18:34.140 align:start position:0% being run over and over again on the 00:18:34.140 --> 00:18:36.230 align:start position:0% being run over and over again on the same<00:18:34.320> on<00:18:34.679> on<00:18:34.799> the<00:18:35.039> state<00:18:35.220> and<00:18:35.520> updating<00:18:36.000> the 00:18:36.230 --> 00:18:36.240 align:start position:0% same on on the state and updating the 00:18:36.240 --> 00:18:37.690 align:start position:0% same on on the state and updating the state 00:18:37.690 --> 00:18:37.700 align:start position:0% state 00:18:37.700 --> 00:18:40.549 align:start position:0% state then<00:18:38.700> you<00:18:39.179> can<00:18:39.299> actually<00:18:39.539> use<00:18:40.020> recursive 00:18:40.549 --> 00:18:40.559 align:start position:0% then you can actually use recursive 00:18:40.559 --> 00:18:42.650 align:start position:0% then you can actually use recursive snarks<00:18:41.160> to<00:18:41.700> prove<00:18:42.000> this<00:18:42.120> computation 00:18:42.650 --> 00:18:42.660 align:start position:0% snarks to prove this computation 00:18:42.660 --> 00:18:45.289 align:start position:0% snarks to prove this computation incrementally<00:18:43.559> so<00:18:44.340> as<00:18:44.520> opposed<00:18:44.820> to<00:18:44.820> Socrates 00:18:45.289 --> 00:18:45.299 align:start position:0% incrementally so as opposed to Socrates 00:18:45.299 --> 00:18:47.270 align:start position:0% incrementally so as opposed to Socrates currently<00:18:45.780> to<00:18:46.080> others<00:18:46.620> proof<00:18:46.799> systems<00:18:47.100> where 00:18:47.270 --> 00:18:47.280 align:start position:0% currently to others proof systems where 00:18:47.280 --> 00:18:48.710 align:start position:0% currently to others proof systems where we<00:18:47.400> can<00:18:47.520> think<00:18:47.640> of<00:18:47.760> them<00:18:47.940> as<00:18:48.179> more<00:18:48.419> like<00:18:48.539> an 00:18:48.710 --> 00:18:48.720 align:start position:0% we can think of them as more like an 00:18:48.720 --> 00:18:51.110 align:start position:0% we can think of them as more like an Asic<00:18:49.080> so<00:18:49.679> your<00:18:49.799> circuit<00:18:50.220> is<00:18:50.400> like<00:18:50.580> this<00:18:50.700> Asic 00:18:51.110 --> 00:18:51.120 align:start position:0% Asic so your circuit is like this Asic 00:18:51.120 --> 00:18:53.210 align:start position:0% Asic so your circuit is like this Asic that's<00:18:51.360> really<00:18:51.600> set<00:18:52.140> in<00:18:52.380> a<00:18:52.500> stone<00:18:52.620> and<00:18:52.980> you<00:18:53.100> can 00:18:53.210 --> 00:18:53.220 align:start position:0% that's really set in a stone and you can 00:18:53.220 --> 00:18:54.650 align:start position:0% that's really set in a stone and you can do<00:18:53.460> only<00:18:53.640> one<00:18:53.880> computation<00:18:54.299> and<00:18:54.539> everything 00:18:54.650 --> 00:18:54.660 align:start position:0% do only one computation and everything 00:18:54.660 --> 00:18:57.409 align:start position:0% do only one computation and everything is<00:18:55.020> bounded<00:18:55.440> and<00:18:55.740> static<00:18:56.160> in<00:18:56.940> this<00:18:57.059> case<00:18:57.179> you 00:18:57.409 --> 00:18:57.419 align:start position:0% is bounded and static in this case you 00:18:57.419 --> 00:19:00.169 align:start position:0% is bounded and static in this case you can<00:18:57.539> have<00:18:57.720> a<00:18:58.020> computation<00:18:58.440> where<00:18:58.740> you<00:18:58.919> run<00:18:59.179> one 00:19:00.169 --> 00:19:00.179 align:start position:0% can have a computation where you run one 00:19:00.179 --> 00:19:01.549 align:start position:0% can have a computation where you run one round<00:19:00.360> of<00:19:00.600> the<00:19:00.780> computation<00:19:01.140> and<00:19:01.440> then 00:19:01.549 --> 00:19:01.559 align:start position:0% round of the computation and then 00:19:01.559 --> 00:19:04.070 align:start position:0% round of the computation and then another<00:19:01.740> one<00:19:02.039> later<00:19:02.220> and<00:19:02.460> you<00:19:02.640> can<00:19:03.020> prove<00:19:04.020> the 00:19:04.070 --> 00:19:04.080 align:start position:0% another one later and you can prove the 00:19:04.080 --> 00:19:06.169 align:start position:0% another one later and you can prove the execute<00:19:04.440> the<00:19:04.860> execution<00:19:05.280> of<00:19:06.000> that 00:19:06.169 --> 00:19:06.179 align:start position:0% execute the execution of that 00:19:06.179 --> 00:19:09.289 align:start position:0% execute the execution of that competition<00:19:06.660> at<00:19:07.440> each<00:19:07.620> step 00:19:09.289 --> 00:19:09.299 align:start position:0% competition at each step 00:19:09.299 --> 00:19:11.529 align:start position:0% competition at each step so<00:19:09.720> some<00:19:09.960> use<00:19:10.140> cases<00:19:10.440> for<00:19:10.740> that<00:19:10.919> are 00:19:11.529 --> 00:19:11.539 align:start position:0% so some use cases for that are 00:19:11.539 --> 00:19:13.669 align:start position:0% so some use cases for that are succinctly<00:19:12.539> verifiable<00:19:13.140> blockchain<00:19:13.500> so 00:19:13.669 --> 00:19:13.679 align:start position:0% succinctly verifiable blockchain so 00:19:13.679 --> 00:19:15.289 align:start position:0% succinctly verifiable blockchain so maybe<00:19:13.860> some<00:19:14.039> of<00:19:14.160> you<00:19:14.220> have<00:19:14.340> heard<00:19:14.520> of<00:19:14.700> the<00:19:15.059> Mina 00:19:15.289 --> 00:19:15.299 align:start position:0% maybe some of you have heard of the Mina 00:19:15.299 --> 00:19:17.990 align:start position:0% maybe some of you have heard of the Mina blockchain<00:19:15.840> where<00:19:16.440> basically<00:19:16.919> you<00:19:17.580> use<00:19:17.760> this 00:19:17.990 --> 00:19:18.000 align:start position:0% blockchain where basically you use this 00:19:18.000 --> 00:19:21.950 align:start position:0% blockchain where basically you use this to<00:19:18.299> have<00:19:18.480> a<00:19:19.200> a<00:19:19.740> blockchain<00:19:20.340> where<00:19:20.780> each<00:19:21.780> time 00:19:21.950 --> 00:19:21.960 align:start position:0% to have a a blockchain where each time 00:19:21.960 --> 00:19:24.350 align:start position:0% to have a a blockchain where each time you<00:19:22.140> get<00:19:22.260> a<00:19:22.380> new<00:19:22.500> block<00:19:22.679> you 00:19:24.350 --> 00:19:24.360 align:start position:0% you get a new block you 00:19:24.360 --> 00:19:26.510 align:start position:0% you get a new block you you<00:19:24.419> verify<00:19:25.260> the<00:19:25.500> previous<00:19:25.679> block<00:19:25.980> as<00:19:26.220> well<00:19:26.400> as 00:19:26.510 --> 00:19:26.520 align:start position:0% you verify the previous block as well as 00:19:26.520 --> 00:19:27.890 align:start position:0% you verify the previous block as well as the<00:19:26.640> transaction<00:19:26.940> of<00:19:27.179> this<00:19:27.299> block<00:19:27.480> and<00:19:27.720> it 00:19:27.890 --> 00:19:27.900 align:start position:0% the transaction of this block and it 00:19:27.900 --> 00:19:29.390 align:start position:0% the transaction of this block and it creates<00:19:28.320> a<00:19:28.440> snark<00:19:28.679> and<00:19:28.919> then<00:19:29.039> you<00:19:29.160> have<00:19:29.280> this 00:19:29.390 --> 00:19:29.400 align:start position:0% creates a snark and then you have this 00:19:29.400 --> 00:19:32.390 align:start position:0% creates a snark and then you have this kind<00:19:29.580> of<00:19:29.640> recursive<00:19:30.179> verification 00:19:32.390 --> 00:19:32.400 align:start position:0% kind of recursive verification 00:19:32.400 --> 00:19:35.630 align:start position:0% kind of recursive verification another<00:19:32.940> use<00:19:33.900> case<00:19:34.080> is<00:19:34.320> vdfs<00:19:35.220> because<00:19:35.340> some<00:19:35.520> of 00:19:35.630 --> 00:19:35.640 align:start position:0% another use case is vdfs because some of 00:19:35.640 --> 00:19:37.730 align:start position:0% another use case is vdfs because some of the<00:19:35.760> vdfs<00:19:36.240> actually<00:19:36.360> have<00:19:36.539> the<00:19:36.720> structure<00:19:37.140> of 00:19:37.730 --> 00:19:37.740 align:start position:0% the vdfs actually have the structure of 00:19:37.740 --> 00:19:41.210 align:start position:0% the vdfs actually have the structure of having<00:19:38.039> some<00:19:38.940> state<00:19:39.179> which<00:19:40.080> is<00:19:40.380> then<00:19:40.559> to<00:19:40.980> which 00:19:41.210 --> 00:19:41.220 align:start position:0% having some state which is then to which 00:19:41.220 --> 00:19:42.169 align:start position:0% having some state which is then to which you 00:19:42.169 --> 00:19:42.179 align:start position:0% you 00:19:42.179 --> 00:19:45.289 align:start position:0% you um<00:19:42.720> apply<00:19:43.380> a<00:19:43.500> function<00:19:43.740> recursively<00:19:44.340> and<00:19:45.059> then 00:19:45.289 --> 00:19:45.299 align:start position:0% um apply a function recursively and then 00:19:45.299 --> 00:19:47.690 align:start position:0% um apply a function recursively and then being<00:19:46.200> able<00:19:46.440> to<00:19:46.620> have<00:19:46.860> a<00:19:47.100> snark<00:19:47.400> of<00:19:47.580> this 00:19:47.690 --> 00:19:47.700 align:start position:0% being able to have a snark of this 00:19:47.700 --> 00:19:49.130 align:start position:0% being able to have a snark of this computation<00:19:48.120> can<00:19:48.360> be<00:19:48.480> really<00:19:48.600> really<00:19:48.780> useful 00:19:49.130 --> 00:19:49.140 align:start position:0% computation can be really really useful 00:19:49.140 --> 00:19:51.110 align:start position:0% computation can be really really useful so<00:19:49.740> what<00:19:49.919> we're<00:19:50.039> working<00:19:50.220> on<00:19:50.400> now<00:19:50.640> now<00:19:50.880> we're 00:19:51.110 --> 00:19:51.120 align:start position:0% so what we're working on now now we're 00:19:51.120 --> 00:19:52.370 align:start position:0% so what we're working on now now we're actually<00:19:51.240> pretty<00:19:51.480> close<00:19:51.720> to<00:19:51.900> having<00:19:52.080> this 00:19:52.370 --> 00:19:52.380 align:start position:0% actually pretty close to having this 00:19:52.380 --> 00:19:56.150 align:start position:0% actually pretty close to having this ready<00:19:52.559> in<00:19:52.799> production<00:19:53.100> uh<00:19:54.000> is<00:19:54.240> integrating<00:19:54.900> a 00:19:56.150 --> 00:19:56.160 align:start position:0% ready in production uh is integrating a 00:19:56.160 --> 00:19:59.870 align:start position:0% ready in production uh is integrating a um<00:19:56.640> proof<00:19:57.059> system<00:19:57.179> called<00:19:57.539> Nova<00:19:58.580> which<00:19:59.580> does 00:19:59.870 --> 00:19:59.880 align:start position:0% um proof system called Nova which does 00:19:59.880 --> 00:20:02.810 align:start position:0% um proof system called Nova which does exactly<00:20:00.299> this<00:20:00.559> and<00:20:01.559> the<00:20:02.039> way<00:20:02.220> that<00:20:02.400> I'm<00:20:02.700> not 00:20:02.810 --> 00:20:02.820 align:start position:0% exactly this and the way that I'm not 00:20:02.820 --> 00:20:04.250 align:start position:0% exactly this and the way that I'm not going<00:20:02.940> to<00:20:03.000> go<00:20:03.059> too<00:20:03.240> much<00:20:03.360> in<00:20:03.539> detail<00:20:03.780> here<00:20:04.020> but 00:20:04.250 --> 00:20:04.260 align:start position:0% going to go too much in detail here but 00:20:04.260 --> 00:20:06.529 align:start position:0% going to go too much in detail here but the<00:20:04.559> way<00:20:04.679> that<00:20:04.860> the<00:20:05.340> API<00:20:06.059> would<00:20:06.240> work<00:20:06.419> for 00:20:06.529 --> 00:20:06.539 align:start position:0% the way that the API would work for 00:20:06.539 --> 00:20:08.570 align:start position:0% the way that the API would work for developers<00:20:06.960> today<00:20:07.200> is<00:20:07.559> that<00:20:07.740> you<00:20:07.919> write<00:20:08.100> a 00:20:08.570 --> 00:20:08.580 align:start position:0% developers today is that you write a 00:20:08.580 --> 00:20:10.990 align:start position:0% developers today is that you write a function<00:20:08.940> and<00:20:09.660> the<00:20:09.900> only 00:20:10.990 --> 00:20:11.000 align:start position:0% function and the only 00:20:11.000 --> 00:20:13.549 align:start position:0% function and the only restriction<00:20:12.000> here<00:20:12.299> is<00:20:12.480> that<00:20:12.660> the<00:20:12.900> input<00:20:13.140> needs 00:20:13.549 --> 00:20:13.559 align:start position:0% restriction here is that the input needs 00:20:13.559 --> 00:20:15.350 align:start position:0% restriction here is that the input needs to<00:20:13.620> be<00:20:13.799> the<00:20:14.280> type<00:20:14.460> the<00:20:14.640> input<00:20:14.820> type<00:20:15.000> needs<00:20:15.299> to 00:20:15.350 --> 00:20:15.360 align:start position:0% to be the type the input type needs to 00:20:15.360 --> 00:20:17.090 align:start position:0% to be the type the input type needs to be<00:20:15.480> the<00:20:15.600> output<00:20:15.900> type<00:20:16.080> because<00:20:16.380> you<00:20:16.679> want<00:20:16.799> the 00:20:17.090 --> 00:20:17.100 align:start position:0% be the output type because you want the 00:20:17.100 --> 00:20:19.789 align:start position:0% be the output type because you want the recursive<00:20:17.580> aspect<00:20:18.360> to<00:20:18.600> to<00:20:18.840> work 00:20:19.789 --> 00:20:19.799 align:start position:0% recursive aspect to to work 00:20:19.799 --> 00:20:22.250 align:start position:0% recursive aspect to to work and<00:20:20.340> then<00:20:20.520> you<00:20:20.760> can<00:20:20.880> compile<00:20:21.539> this<00:20:21.960> function 00:20:22.250 --> 00:20:22.260 align:start position:0% and then you can compile this function 00:20:22.260 --> 00:20:24.230 align:start position:0% and then you can compile this function to<00:20:22.799> a<00:20:22.980> specific<00:20:23.220> curve<00:20:23.580> so<00:20:23.700> you<00:20:23.880> need<00:20:24.000> to<00:20:24.059> use 00:20:24.230 --> 00:20:24.240 align:start position:0% to a specific curve so you need to use 00:20:24.240 --> 00:20:26.690 align:start position:0% to a specific curve so you need to use this<00:20:24.600> balance<00:20:25.200> curve<00:20:25.559> because<00:20:26.100> under<00:20:26.460> the 00:20:26.690 --> 00:20:26.700 align:start position:0% this balance curve because under the 00:20:26.700 --> 00:20:30.049 align:start position:0% this balance curve because under the hood<00:20:26.820> Nova<00:20:27.720> uses<00:20:28.280> cycles<00:20:29.280> of<00:20:29.460> electric<00:20:29.580> curves 00:20:30.049 --> 00:20:30.059 align:start position:0% hood Nova uses cycles of electric curves 00:20:30.059 --> 00:20:31.789 align:start position:0% hood Nova uses cycles of electric curves so<00:20:30.179> this<00:20:30.360> doesn't<00:20:30.480> work<00:20:30.720> for<00:20:30.960> any<00:20:31.140> curve<00:20:31.500> but 00:20:31.789 --> 00:20:31.799 align:start position:0% so this doesn't work for any curve but 00:20:31.799 --> 00:20:34.850 align:start position:0% so this doesn't work for any curve but we<00:20:32.340> support<00:20:32.580> the<00:20:32.880> curves<00:20:33.179> that<00:20:33.419> enable<00:20:33.960> that 00:20:34.850 --> 00:20:34.860 align:start position:0% we support the curves that enable that 00:20:34.860 --> 00:20:37.610 align:start position:0% we support the curves that enable that and<00:20:35.280> then<00:20:35.400> you<00:20:35.640> can<00:20:35.820> basically<00:20:36.240> prove<00:20:36.960> a 00:20:37.610 --> 00:20:37.620 align:start position:0% and then you can basically prove a 00:20:37.620 --> 00:20:41.270 align:start position:0% and then you can basically prove a number<00:20:37.799> of<00:20:37.980> steps<00:20:38.520> starting<00:20:38.940> from<00:20:39.480> a<00:20:40.440> given<00:20:40.980> a 00:20:41.270 --> 00:20:41.280 align:start position:0% number of steps starting from a given a 00:20:41.280 --> 00:20:44.690 align:start position:0% number of steps starting from a given a given<00:20:41.580> State<00:20:41.900> and<00:20:42.900> even<00:20:43.260> after<00:20:43.679> running<00:20:44.400> this 00:20:44.690 --> 00:20:44.700 align:start position:0% given State and even after running this 00:20:44.700 --> 00:20:46.610 align:start position:0% given State and even after running this you<00:20:44.880> could<00:20:45.000> run<00:20:45.179> it<00:20:45.360> again<00:20:45.539> starting<00:20:46.020> from<00:20:46.380> the 00:20:46.610 --> 00:20:46.620 align:start position:0% you could run it again starting from the 00:20:46.620 --> 00:20:48.230 align:start position:0% you could run it again starting from the last<00:20:46.740> state<00:20:46.980> that<00:20:47.340> you<00:20:47.520> had 00:20:48.230 --> 00:20:48.240 align:start position:0% last state that you had 00:20:48.240 --> 00:20:51.230 align:start position:0% last state that you had this<00:20:48.840> hope<00:20:49.020> this<00:20:49.320> opens<00:20:49.740> a<00:20:50.400> lot<00:20:50.520> of<00:20:50.640> use<00:20:51.000> cases 00:20:51.230 --> 00:20:51.240 align:start position:0% this hope this opens a lot of use cases 00:20:51.240 --> 00:20:53.090 align:start position:0% this hope this opens a lot of use cases for<00:20:51.600> people<00:20:51.720> who<00:20:51.900> want<00:20:52.080> to<00:20:52.200> to<00:20:52.500> experiment 00:20:53.090 --> 00:20:53.100 align:start position:0% for people who want to to experiment 00:20:53.100 --> 00:20:54.250 align:start position:0% for people who want to to experiment with 00:20:54.250 --> 00:20:54.260 align:start position:0% with 00:20:54.260 --> 00:20:57.049 align:start position:0% with incrementable<00:20:55.460> incremental<00:20:56.460> verifiable 00:20:57.049 --> 00:20:57.059 align:start position:0% incrementable incremental verifiable 00:20:57.059 --> 00:20:59.750 align:start position:0% incrementable incremental verifiable computation<00:20:58.020> so<00:20:58.620> I<00:20:58.740> invite<00:20:59.039> you<00:20:59.100> to<00:20:59.340> to<00:20:59.520> test 00:20:59.750 --> 00:20:59.760 align:start position:0% computation so I invite you to to test 00:20:59.760 --> 00:21:01.490 align:start position:0% computation so I invite you to to test that<00:20:59.940> it's<00:21:00.240> it's<00:21:00.419> going<00:21:00.660> to<00:21:00.720> be<00:21:00.840> out<00:21:00.960> very<00:21:01.320> soon 00:21:01.490 --> 00:21:01.500 align:start position:0% that it's it's going to be out very soon 00:21:01.500 --> 00:21:03.409 align:start position:0% that it's it's going to be out very soon okay 00:21:03.409 --> 00:21:03.419 align:start position:0% okay 00:21:03.419 --> 00:21:04.850 align:start position:0% okay um<00:21:03.480> since<00:21:03.900> I<00:21:04.020> only<00:21:04.200> have<00:21:04.380> two<00:21:04.500> minutes<00:21:04.620> left 00:21:04.850 --> 00:21:04.860 align:start position:0% um since I only have two minutes left 00:21:04.860 --> 00:21:07.549 align:start position:0% um since I only have two minutes left I'll<00:21:05.100> just<00:21:05.220> go<00:21:05.460> very<00:21:05.700> quickly<00:21:06.320> through<00:21:07.320> some 00:21:07.549 --> 00:21:07.559 align:start position:0% I'll just go very quickly through some 00:21:07.559 --> 00:21:09.710 align:start position:0% I'll just go very quickly through some things<00:21:07.799> that<00:21:08.100> we<00:21:08.280> that<00:21:08.520> we<00:21:08.700> added<00:21:08.940> recently<00:21:09.240> so 00:21:09.710 --> 00:21:09.720 align:start position:0% things that we that we added recently so 00:21:09.720 --> 00:21:11.510 align:start position:0% things that we that we added recently so there's<00:21:09.900> the<00:21:10.080> powers<00:21:10.140> of<00:21:10.440> Tau<00:21:10.679> ceremony<00:21:11.160> so<00:21:11.400> if 00:21:11.510 --> 00:21:11.520 align:start position:0% there's the powers of Tau ceremony so if 00:21:11.520 --> 00:21:14.450 align:start position:0% there's the powers of Tau ceremony so if you<00:21:11.640> look<00:21:11.760> at<00:21:11.940> gross<00:21:12.360> 16<00:21:12.539> for<00:21:12.960> example<00:21:13.140> it's<00:21:13.679> it 00:21:14.450 --> 00:21:14.460 align:start position:0% you look at gross 16 for example it's it 00:21:14.460 --> 00:21:16.789 align:start position:0% you look at gross 16 for example it's it requires<00:21:14.820> a<00:21:14.940> trusted<00:21:15.240> setup<00:21:15.600> and<00:21:16.500> the<00:21:16.620> powers 00:21:16.789 --> 00:21:16.799 align:start position:0% requires a trusted setup and the powers 00:21:16.799 --> 00:21:19.610 align:start position:0% requires a trusted setup and the powers of<00:21:16.980> tower<00:21:17.220> ceremony<00:21:17.900> enables<00:21:18.900> you<00:21:18.960> to<00:21:19.140> do<00:21:19.380> that 00:21:19.610 --> 00:21:19.620 align:start position:0% of tower ceremony enables you to do that 00:21:19.620 --> 00:21:21.289 align:start position:0% of tower ceremony enables you to do that using<00:21:20.100> NPC 00:21:21.289 --> 00:21:21.299 align:start position:0% using NPC 00:21:21.299 --> 00:21:22.789 align:start position:0% using NPC so<00:21:21.720> you<00:21:21.840> can<00:21:21.960> do<00:21:22.080> that<00:21:22.200> directly<00:21:22.440> with<00:21:22.679> this 00:21:22.789 --> 00:21:22.799 align:start position:0% so you can do that directly with this 00:21:22.799 --> 00:21:25.370 align:start position:0% so you can do that directly with this oxtail<00:21:23.220> CLI<00:21:23.640> and<00:21:24.419> also<00:21:24.660> in<00:21:24.780> the<00:21:24.960> in<00:21:25.140> soccer 00:21:25.370 --> 00:21:25.380 align:start position:0% oxtail CLI and also in the in soccer 00:21:25.380 --> 00:21:26.690 align:start position:0% oxtail CLI and also in the in soccer says<00:21:25.740> JS<00:21:25.919> actually 00:21:26.690 --> 00:21:26.700 align:start position:0% says JS actually 00:21:26.700 --> 00:21:28.669 align:start position:0% says JS actually we<00:21:27.120> also<00:21:27.299> have<00:21:27.360> support<00:21:27.539> for<00:21:27.780> lock<00:21:27.960> statements 00:21:28.669 --> 00:21:28.679 align:start position:0% we also have support for lock statements 00:21:28.679 --> 00:21:30.830 align:start position:0% we also have support for lock statements uh<00:21:29.340> that<00:21:29.520> you<00:21:29.640> can<00:21:29.760> where<00:21:30.179> you<00:21:30.299> can<00:21:30.419> inspect 00:21:30.830 --> 00:21:30.840 align:start position:0% uh that you can where you can inspect 00:21:30.840 --> 00:21:33.710 align:start position:0% uh that you can where you can inspect certain<00:21:31.620> values<00:21:32.039> of<00:21:32.280> your<00:21:32.520> code<00:21:32.820> at<00:21:33.179> runtime 00:21:33.710 --> 00:21:33.720 align:start position:0% certain values of your code at runtime 00:21:33.720 --> 00:21:35.930 align:start position:0% certain values of your code at runtime we<00:21:34.320> have<00:21:34.440> support<00:21:34.620> for<00:21:35.100> the<00:21:35.340> more<00:21:35.580> input 00:21:35.930 --> 00:21:35.940 align:start position:0% we have support for the more input 00:21:35.940 --> 00:21:38.450 align:start position:0% we have support for the more input system<00:21:36.179> that<00:21:36.600> I<00:21:36.840> mentioned<00:21:37.620> earlier<00:21:37.980> which<00:21:38.280> is 00:21:38.450 --> 00:21:38.460 align:start position:0% system that I mentioned earlier which is 00:21:38.460 --> 00:21:41.029 align:start position:0% system that I mentioned earlier which is a<00:21:38.820> universal<00:21:39.780> setup<00:21:40.140> which<00:21:40.559> means<00:21:40.799> that<00:21:40.919> you 00:21:41.029 --> 00:21:41.039 align:start position:0% a universal setup which means that you 00:21:41.039 --> 00:21:42.590 align:start position:0% a universal setup which means that you can<00:21:41.159> do<00:21:41.280> one<00:21:41.460> setup<00:21:41.760> and<00:21:41.940> then<00:21:42.059> use<00:21:42.240> it<00:21:42.419> for 00:21:42.590 --> 00:21:42.600 align:start position:0% can do one setup and then use it for 00:21:42.600 --> 00:21:44.990 align:start position:0% can do one setup and then use it for different<00:21:42.780> circuits<00:21:43.320> we<00:21:44.280> also<00:21:44.520> change<00:21:44.700> a<00:21:44.940> lot 00:21:44.990 --> 00:21:45.000 align:start position:0% different circuits we also change a lot 00:21:45.000 --> 00:21:47.510 align:start position:0% different circuits we also change a lot of<00:21:45.120> the<00:21:45.299> syntax<00:21:46.039> following<00:21:47.039> some<00:21:47.159> feedback 00:21:47.510 --> 00:21:47.520 align:start position:0% of the syntax following some feedback 00:21:47.520 --> 00:21:50.210 align:start position:0% of the syntax following some feedback from<00:21:47.940> from<00:21:48.240> members<00:21:49.020> of<00:21:49.140> the<00:21:49.200> community<00:21:49.440> and 00:21:50.210 --> 00:21:50.220 align:start position:0% from from members of the community and 00:21:50.220 --> 00:21:52.730 align:start position:0% from from members of the community and finally<00:21:50.520> yeah<00:21:50.760> the<00:21:51.179> this<00:21:51.480> this<00:21:51.740> playground 00:21:52.730 --> 00:21:52.740 align:start position:0% finally yeah the this this playground 00:21:52.740 --> 00:21:54.770 align:start position:0% finally yeah the this this playground which<00:21:53.400> is<00:21:53.580> now<00:21:53.760> accessible 00:21:54.770 --> 00:21:54.780 align:start position:0% which is now accessible 00:21:54.780 --> 00:21:57.710 align:start position:0% which is now accessible which<00:21:55.380> I<00:21:55.620> invite<00:21:55.860> you<00:21:56.039> to<00:21:56.159> to<00:21:56.520> check<00:21:56.700> out<00:21:56.940> okay 00:21:57.710 --> 00:21:57.720 align:start position:0% which I invite you to to check out okay 00:21:57.720 --> 00:21:59.330 align:start position:0% which I invite you to to check out okay I<00:21:58.080> think<00:21:58.200> that's<00:21:58.380> that's<00:21:58.620> all<00:21:58.799> I<00:21:58.980> had<00:21:59.039> to<00:21:59.159> share 00:21:59.330 --> 00:21:59.340 align:start position:0% I think that's that's all I had to share 00:21:59.340 --> 00:22:01.789 align:start position:0% I think that's that's all I had to share uh<00:22:00.059> so<00:22:00.299> thanks<00:22:00.539> for<00:22:00.720> listening<00:22:01.380> if<00:22:01.679> there's 00:22:01.789 --> 00:22:01.799 align:start position:0% uh so thanks for listening if there's 00:22:01.799 --> 00:22:03.169 align:start position:0% uh so thanks for listening if there's any<00:22:01.919> questions<00:22:02.159> yeah<00:22:02.520> I'm<00:22:02.700> happy<00:22:02.880> to<00:22:03.059> take 00:22:03.169 --> 00:22:03.179 align:start position:0% any questions yeah I'm happy to take 00:22:03.179 --> 00:22:04.490 align:start position:0% any questions yeah I'm happy to take questions 00:22:04.490 --> 00:22:04.500 align:start position:0% questions 00:22:04.500 --> 00:22:07.490 align:start position:0% questions um<00:22:04.620> can<00:22:04.860> we<00:22:05.039> use<00:22:05.220> the<00:22:05.640> new<00:22:05.820> Nova<00:22:06.299> support<00:22:06.500> to 00:22:07.490 --> 00:22:07.500 align:start position:0% um can we use the new Nova support to 00:22:07.500 --> 00:22:08.510 align:start position:0% um can we use the new Nova support to write 00:22:08.510 --> 00:22:08.520 align:start position:0% write 00:22:08.520 --> 00:22:11.330 align:start position:0% write um<00:22:08.580> another<00:22:08.880> but<00:22:09.360> shorter<00:22:09.780> SDK<00:22:10.200> VM 00:22:11.330 --> 00:22:11.340 align:start position:0% um another but shorter SDK VM 00:22:11.340 --> 00:22:13.250 align:start position:0% um another but shorter SDK VM I<00:22:11.640> think<00:22:11.760> in<00:22:11.880> theory<00:22:12.240> yes<00:22:12.539> I'm<00:22:12.840> not<00:22:13.020> sure<00:22:13.080> it 00:22:13.250 --> 00:22:13.260 align:start position:0% I think in theory yes I'm not sure it 00:22:13.260 --> 00:22:14.690 align:start position:0% I think in theory yes I'm not sure it would<00:22:13.380> be<00:22:13.500> the<00:22:13.620> most<00:22:13.740> efficient 00:22:14.690 --> 00:22:14.700 align:start position:0% would be the most efficient 00:22:14.700 --> 00:22:16.789 align:start position:0% would be the most efficient but<00:22:15.480> they<00:22:15.600> were<00:22:15.780> already 00:22:16.789 --> 00:22:16.799 align:start position:0% but they were already 00:22:16.799 --> 00:22:18.890 align:start position:0% but they were already actually<00:22:17.280> a<00:22:17.520> long<00:22:17.640> time<00:22:17.820> ago 00:22:18.890 --> 00:22:18.900 align:start position:0% actually a long time ago 00:22:18.900 --> 00:22:20.750 align:start position:0% actually a long time ago VMS<00:22:19.500> that<00:22:19.679> were<00:22:19.799> built<00:22:19.980> on<00:22:20.100> top<00:22:20.220> of<00:22:20.340> recursive 00:22:20.750 --> 00:22:20.760 align:start position:0% VMS that were built on top of recursive 00:22:20.760 --> 00:22:24.110 align:start position:0% VMS that were built on top of recursive snarks<00:22:21.440> but<00:22:22.440> they<00:22:22.559> were<00:22:22.679> using<00:22:22.919> recursion 00:22:24.110 --> 00:22:24.120 align:start position:0% snarks but they were using recursion 00:22:24.120 --> 00:22:27.770 align:start position:0% snarks but they were using recursion at<00:22:24.720> each<00:22:24.960> cycle<00:22:25.320> of<00:22:25.679> the<00:22:25.799> CPU<00:22:26.280> which<00:22:27.000> was 00:22:27.770 --> 00:22:27.780 align:start position:0% at each cycle of the CPU which was 00:22:27.780 --> 00:22:29.870 align:start position:0% at each cycle of the CPU which was quite<00:22:28.320> inefficient<00:22:28.860> but<00:22:29.340> maybe<00:22:29.520> there's<00:22:29.760> a 00:22:29.870 --> 00:22:29.880 align:start position:0% quite inefficient but maybe there's a 00:22:29.880 --> 00:22:31.730 align:start position:0% quite inefficient but maybe there's a new<00:22:30.000> take<00:22:30.179> that<00:22:30.360> could<00:22:30.539> be 00:22:31.730 --> 00:22:31.740 align:start position:0% new take that could be 00:22:31.740 --> 00:22:34.310 align:start position:0% new take that could be that<00:22:32.159> you<00:22:32.340> can<00:22:32.460> have<00:22:32.580> on<00:22:32.820> on<00:22:33.000> that<00:22:33.299> so<00:22:34.020> that 00:22:34.310 --> 00:22:34.320 align:start position:0% that you can have on on that so that 00:22:34.320 --> 00:22:35.870 align:start position:0% that you can have on on that so that would<00:22:34.500> be 00:22:35.870 --> 00:22:35.880 align:start position:0% would be 00:22:35.880 --> 00:22:38.870 align:start position:0% would be one<00:22:36.720> cycle<00:22:37.020> for<00:22:37.200> each<00:22:37.320> op<00:22:37.559> code<00:22:37.740> right<00:22:38.100> that 00:22:38.870 --> 00:22:38.880 align:start position:0% one cycle for each op code right that 00:22:38.880 --> 00:22:40.909 align:start position:0% one cycle for each op code right that that's<00:22:39.059> that<00:22:39.299> was<00:22:39.539> the<00:22:39.659> case<00:22:39.780> and<00:22:40.140> those<00:22:40.380> uh 00:22:40.909 --> 00:22:40.919 align:start position:0% that's that was the case and those uh 00:22:40.919 --> 00:22:42.230 align:start position:0% that's that was the case and those uh project<00:22:41.159> 10<00:22:41.460> years<00:22:41.640> ago<00:22:41.820> it's<00:22:42.000> a<00:22:42.120> project 00:22:42.230 --> 00:22:42.240 align:start position:0% project 10 years ago it's a project 00:22:42.240 --> 00:22:43.549 align:start position:0% project 10 years ago it's a project called<00:22:42.419> tiny<00:22:42.780> Ram 00:22:43.549 --> 00:22:43.559 align:start position:0% called tiny Ram 00:22:43.559 --> 00:22:44.990 align:start position:0% called tiny Ram where<00:22:43.919> that's<00:22:44.100> what<00:22:44.400> they<00:22:44.520> did<00:22:44.700> they 00:22:44.990 --> 00:22:45.000 align:start position:0% where that's what they did they 00:22:45.000 --> 00:22:47.990 align:start position:0% where that's what they did they basically<00:22:45.360> took<00:22:45.600> the<00:22:45.780> state<00:22:46.020> of<00:22:46.500> the<00:22:46.740> CPU<00:22:47.340> and 00:22:47.990 --> 00:22:48.000 align:start position:0% basically took the state of the CPU and 00:22:48.000 --> 00:22:51.590 align:start position:0% basically took the state of the CPU and just<00:22:48.179> run<00:22:48.480> each<00:22:49.080> time<00:22:49.320> one<00:22:49.860> one<00:22:50.280> up<00:22:50.580> code<00:22:50.820> and 00:22:51.590 --> 00:22:51.600 align:start position:0% just run each time one one up code and 00:22:51.600 --> 00:22:53.990 align:start position:0% just run each time one one up code and then<00:22:51.720> have<00:22:51.900> a<00:22:52.080> recursive<00:22:52.440> snarks<00:22:52.919> a<00:22:53.340> recursive 00:22:53.990 --> 00:22:54.000 align:start position:0% then have a recursive snarks a recursive 00:22:54.000 --> 00:22:56.210 align:start position:0% then have a recursive snarks a recursive snark<00:22:54.299> each<00:22:54.480> time<00:22:54.659> but<00:22:55.320> maybe<00:22:55.860> there's<00:22:56.039> other 00:22:56.210 --> 00:22:56.220 align:start position:0% snark each time but maybe there's other 00:22:56.220 --> 00:22:59.630 align:start position:0% snark each time but maybe there's other approaches<00:22:57.059> to<00:22:57.320> leverage<00:22:58.320> this<00:22:58.559> proof<00:22:58.919> system 00:22:59.630 --> 00:22:59.640 align:start position:0% approaches to leverage this proof system 00:22:59.640 --> 00:23:02.870 align:start position:0% approaches to leverage this proof system so<00:23:00.299> instead<00:23:01.140> of<00:23:01.260> making<00:23:01.679> users<00:23:02.159> to<00:23:02.400> write<00:23:02.580> very 00:23:02.870 --> 00:23:02.880 align:start position:0% so instead of making users to write very 00:23:02.880 --> 00:23:05.810 align:start position:0% so instead of making users to write very optimized<00:23:03.480> code<00:23:03.720> have<00:23:04.559> you<00:23:04.740> put<00:23:05.159> effort<00:23:05.640> on 00:23:05.810 --> 00:23:05.820 align:start position:0% optimized code have you put effort on 00:23:05.820 --> 00:23:08.690 align:start position:0% optimized code have you put effort on kind<00:23:06.179> of<00:23:06.299> making<00:23:06.900> the<00:23:07.340> compiler<00:23:08.340> kind<00:23:08.580> of 00:23:08.690 --> 00:23:08.700 align:start position:0% kind of making the compiler kind of 00:23:08.700 --> 00:23:10.130 align:start position:0% kind of making the compiler kind of figure<00:23:08.820> out<00:23:09.000> what<00:23:09.240> the<00:23:09.419> user<00:23:09.659> wants<00:23:09.900> and<00:23:10.020> then 00:23:10.130 --> 00:23:10.140 align:start position:0% figure out what the user wants and then 00:23:10.140 --> 00:23:12.529 align:start position:0% figure out what the user wants and then optimize<00:23:10.559> the<00:23:10.740> circuit<00:23:11.039> based<00:23:11.400> on<00:23:11.460> that<00:23:11.640> so 00:23:12.529 --> 00:23:12.539 align:start position:0% optimize the circuit based on that so 00:23:12.539 --> 00:23:13.850 align:start position:0% optimize the circuit based on that so are<00:23:12.659> you<00:23:12.780> saying<00:23:13.020> that<00:23:13.140> okay<00:23:13.380> is<00:23:13.620> your 00:23:13.850 --> 00:23:13.860 align:start position:0% are you saying that okay is your 00:23:13.860 --> 00:23:15.110 align:start position:0% are you saying that okay is your question 00:23:15.110 --> 00:23:15.120 align:start position:0% question 00:23:15.120 --> 00:23:16.970 align:start position:0% question that<00:23:15.780> we<00:23:16.020> should<00:23:16.140> instead<00:23:16.440> of<00:23:16.559> having<00:23:16.679> low 00:23:16.970 --> 00:23:16.980 align:start position:0% that we should instead of having low 00:23:16.980 --> 00:23:19.549 align:start position:0% that we should instead of having low level<00:23:17.220> code<00:23:17.520> have<00:23:17.940> the<00:23:18.120> have<00:23:18.840> the<00:23:19.020> compiler 00:23:19.549 --> 00:23:19.559 align:start position:0% level code have the have the compiler 00:23:19.559 --> 00:23:21.230 align:start position:0% level code have the have the compiler detect<00:23:20.039> when<00:23:20.400> it<00:23:20.580> can<00:23:20.760> do<00:23:20.880> those 00:23:21.230 --> 00:23:21.240 align:start position:0% detect when it can do those 00:23:21.240 --> 00:23:24.409 align:start position:0% detect when it can do those optimizations<00:23:21.780> right<00:23:22.080> I'm<00:23:22.980> in<00:23:23.159> both<00:23:23.340> but<00:23:23.760> like 00:23:24.409 --> 00:23:24.419 align:start position:0% optimizations right I'm in both but like 00:23:24.419 --> 00:23:26.510 align:start position:0% optimizations right I'm in both but like you<00:23:24.780> will<00:23:24.960> only<00:23:25.140> talk<00:23:25.380> about<00:23:25.559> what<00:23:26.159> the<00:23:26.340> case 00:23:26.510 --> 00:23:26.520 align:start position:0% you will only talk about what the case 00:23:26.520 --> 00:23:28.190 align:start position:0% you will only talk about what the case right 00:23:28.190 --> 00:23:28.200 align:start position:0% right 00:23:28.200 --> 00:23:29.990 align:start position:0% right so<00:23:28.679> this<00:23:28.799> is<00:23:28.919> something<00:23:29.100> that<00:23:29.400> as<00:23:29.580> I<00:23:29.760> mentioned 00:23:29.990 --> 00:23:30.000 align:start position:0% so this is something that as I mentioned 00:23:30.000 --> 00:23:31.250 align:start position:0% so this is something that as I mentioned this<00:23:30.240> is<00:23:30.299> something<00:23:30.419> that<00:23:30.659> we<00:23:30.780> do<00:23:30.900> currently 00:23:31.250 --> 00:23:31.260 align:start position:0% this is something that we do currently 00:23:31.260 --> 00:23:33.110 align:start position:0% this is something that we do currently where<00:23:31.740> we<00:23:31.919> identify<00:23:32.460> some<00:23:32.700> of<00:23:32.820> those<00:23:32.940> use 00:23:33.110 --> 00:23:33.120 align:start position:0% where we identify some of those use 00:23:33.120 --> 00:23:35.510 align:start position:0% where we identify some of those use cases<00:23:33.419> I<00:23:33.840> mean<00:23:33.960> some<00:23:34.140> of<00:23:34.260> those<00:23:34.440> cases<00:23:34.860> and 00:23:35.510 --> 00:23:35.520 align:start position:0% cases I mean some of those cases and 00:23:35.520 --> 00:23:37.850 align:start position:0% cases I mean some of those cases and just<00:23:35.700> have<00:23:35.820> them<00:23:36.000> in<00:23:36.179> the<00:23:36.299> compiler 00:23:37.850 --> 00:23:37.860 align:start position:0% just have them in the compiler 00:23:37.860 --> 00:23:39.409 align:start position:0% just have them in the compiler um<00:23:37.919> but<00:23:38.159> it's<00:23:38.340> just<00:23:38.520> really<00:23:38.700> hard<00:23:38.940> to<00:23:39.240> cover 00:23:39.409 --> 00:23:39.419 align:start position:0% um but it's just really hard to cover 00:23:39.419 --> 00:23:41.029 align:start position:0% um but it's just really hard to cover them<00:23:39.600> to<00:23:39.900> cover<00:23:40.140> them<00:23:40.380> all<00:23:40.559> because<00:23:40.799> it's 00:23:41.029 --> 00:23:41.039 align:start position:0% them to cover them all because it's 00:23:41.039 --> 00:23:43.789 align:start position:0% them to cover them all because it's really<00:23:41.159> use<00:23:41.400> case<00:23:41.520> dependent<00:23:42.140> uh<00:23:43.140> here<00:23:43.440> this 00:23:43.789 --> 00:23:43.799 align:start position:0% really use case dependent uh here this 00:23:43.799 --> 00:23:46.070 align:start position:0% really use case dependent uh here this is<00:23:43.980> just<00:23:44.580> for<00:23:44.820> one<00:23:45.120> part<00:23:45.240> of<00:23:45.360> the<00:23:45.480> shot<00:23:45.600> 256 00:23:46.070 --> 00:23:46.080 align:start position:0% is just for one part of the shot 256 00:23:46.080 --> 00:23:47.750 align:start position:0% is just for one part of the shot 256 function<00:23:46.440> but<00:23:46.679> there's<00:23:46.919> so<00:23:47.400> many<00:23:47.520> different 00:23:47.750 --> 00:23:47.760 align:start position:0% function but there's so many different 00:23:47.760 --> 00:23:51.470 align:start position:0% function but there's so many different things<00:23:48.000> that<00:23:48.240> you<00:23:48.900> could<00:23:49.559> optimize 00:23:51.470 --> 00:23:51.480 align:start position:0% things that you could optimize 00:23:51.480 --> 00:23:52.970 align:start position:0% things that you could optimize um so<00:23:51.720> I<00:23:51.840> think<00:23:52.020> it's<00:23:52.140> actually<00:23:52.320> a<00:23:52.500> good<00:23:52.620> idea 00:23:52.970 --> 00:23:52.980 align:start position:0% um so I think it's actually a good idea 00:23:52.980 --> 00:23:55.549 align:start position:0% um so I think it's actually a good idea to<00:23:53.460> open<00:23:53.940> that<00:23:54.179> to<00:23:54.360> developers<00:23:54.840> but<00:23:55.140> in<00:23:55.260> a<00:23:55.440> way 00:23:55.549 --> 00:23:55.559 align:start position:0% to open that to developers but in a way 00:23:55.559 --> 00:23:57.950 align:start position:0% to open that to developers but in a way that<00:23:55.799> that's<00:23:56.100> quite<00:23:56.480> separated<00:23:57.480> from<00:23:57.780> the 00:23:57.950 --> 00:23:57.960 align:start position:0% that that's quite separated from the 00:23:57.960 --> 00:24:01.270 align:start position:0% that that's quite separated from the rest<00:23:58.020> of<00:23:58.200> the<00:23:58.320> high<00:23:58.440> level<00:23:58.620> code 00:24:01.270 --> 00:24:01.280 align:start position:0% 00:24:01.280 --> 00:24:04.710 align:start position:0% [Applause]