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 --> 00:00:19.510 align:start position:0% [Music] 00:00:19.510 --> 00:00:19.520 align:start position:0% 00:00:19.520 --> 00:00:24.230 align:start position:0% that's<00:00:20.520> how<00:00:20.699> we<00:00:21.000> are<00:00:21.180> a<00:00:21.779> verifying<00:00:22.439> uh<00:00:23.400> a<00:00:24.000> stark 00:00:24.230 --> 00:00:24.240 align:start position:0% that's how we are a verifying uh a stark 00:00:24.240 --> 00:00:27.109 align:start position:0% that's how we are a verifying uh a stark with<00:00:24.840> a<00:00:24.960> snark<00:00:25.320> as<00:00:26.039> I<00:00:26.220> explained<00:00:26.460> it<00:00:26.699> before<00:00:26.880> in 00:00:27.109 --> 00:00:27.119 align:start position:0% with a snark as I explained it before in 00:00:27.119 --> 00:00:29.750 align:start position:0% with a snark as I explained it before in the<00:00:27.300> panel<00:00:27.599> the<00:00:28.439> last<00:00:28.560> piece<00:00:28.800> of<00:00:29.039> the<00:00:29.279> of<00:00:29.580> the 00:00:29.750 --> 00:00:29.760 align:start position:0% the panel the last piece of the of the 00:00:29.760 --> 00:00:32.510 align:start position:0% the panel the last piece of the of the of<00:00:30.000> the<00:00:30.180> proverb<00:00:30.660> is<00:00:31.260> mainly<00:00:31.619> converting<00:00:32.220> we 00:00:32.510 --> 00:00:32.520 align:start position:0% of the proverb is mainly converting we 00:00:32.520 --> 00:00:34.069 align:start position:0% of the proverb is mainly converting we have<00:00:32.700> a<00:00:32.820> stark<00:00:33.059> and<00:00:33.300> then<00:00:33.420> we<00:00:33.600> want<00:00:33.719> to<00:00:33.840> prove 00:00:34.069 --> 00:00:34.079 align:start position:0% have a stark and then we want to prove 00:00:34.079 --> 00:00:35.569 align:start position:0% have a stark and then we want to prove that<00:00:34.200> on<00:00:34.380> chain<00:00:34.620> and<00:00:34.920> what<00:00:35.040> we<00:00:35.160> do<00:00:35.280> is<00:00:35.399> we 00:00:35.569 --> 00:00:35.579 align:start position:0% that on chain and what we do is we 00:00:35.579 --> 00:00:36.889 align:start position:0% that on chain and what we do is we create<00:00:35.700> a<00:00:35.880> circuit<00:00:36.120> that<00:00:36.300> verifies<00:00:36.719> this 00:00:36.889 --> 00:00:36.899 align:start position:0% create a circuit that verifies this 00:00:36.899 --> 00:00:40.310 align:start position:0% create a circuit that verifies this start<00:00:37.260> and<00:00:38.160> then<00:00:38.760> we<00:00:39.000> we<00:00:39.180> prove<00:00:39.660> it<00:00:39.780> in<00:00:39.899> in<00:00:40.140> in 00:00:40.310 --> 00:00:40.320 align:start position:0% start and then we we prove it in in in 00:00:40.320 --> 00:00:42.830 align:start position:0% start and then we we prove it in in in the<00:00:40.860> snack<00:00:41.520> okay 00:00:42.830 --> 00:00:42.840 align:start position:0% the snack okay 00:00:42.840 --> 00:00:44.569 align:start position:0% the snack okay um 00:00:44.569 --> 00:00:44.579 align:start position:0% um 00:00:44.579 --> 00:00:48.229 align:start position:0% um well<00:00:45.120> this<00:00:45.480> is<00:00:45.600> uh<00:00:46.440> well<00:00:46.920> this<00:00:47.219> is<00:00:47.280> the<00:00:47.520> the<00:00:47.700> KVM 00:00:48.229 --> 00:00:48.239 align:start position:0% well this is uh well this is the the KVM 00:00:48.239 --> 00:00:49.790 align:start position:0% well this is uh well this is the the KVM that<00:00:48.539> we're<00:00:48.600> building<00:00:48.840> mainly<00:00:49.260> we<00:00:49.379> are<00:00:49.559> using 00:00:49.790 --> 00:00:49.800 align:start position:0% that we're building mainly we are using 00:00:49.800 --> 00:00:51.650 align:start position:0% that we're building mainly we are using pill<00:00:50.100> this<00:00:50.520> polynomial<00:00:51.059> identity<00:00:51.420> language 00:00:51.650 --> 00:00:51.660 align:start position:0% pill this polynomial identity language 00:00:51.660 --> 00:00:53.690 align:start position:0% pill this polynomial identity language to<00:00:52.020> build<00:00:52.140> out<00:00:52.320> the<00:00:52.559> full<00:00:52.680> system<00:00:52.860> and<00:00:53.460> at<00:00:53.579> the 00:00:53.690 --> 00:00:53.700 align:start position:0% to build out the full system and at the 00:00:53.700 --> 00:00:55.430 align:start position:0% to build out the full system and at the end<00:00:53.760> what<00:00:53.940> we<00:00:54.120> have<00:00:54.239> is<00:00:54.420> a<00:00:54.600> set<00:00:54.719> of<00:00:54.840> polynomials 00:00:55.430 --> 00:00:55.440 align:start position:0% end what we have is a set of polynomials 00:00:55.440 --> 00:00:56.869 align:start position:0% end what we have is a set of polynomials with<00:00:55.559> a<00:00:55.680> set<00:00:55.800> of<00:00:55.920> identities<00:00:56.340> that<00:00:56.579> needs<00:00:56.820> to 00:00:56.869 --> 00:00:56.879 align:start position:0% with a set of identities that needs to 00:00:56.879 --> 00:00:58.670 align:start position:0% with a set of identities that needs to fulfill<00:00:57.239> with<00:00:57.840> this<00:00:58.079> can<00:00:58.260> generate 00:00:58.670 --> 00:00:58.680 align:start position:0% fulfill with this can generate 00:00:58.680 --> 00:01:00.770 align:start position:0% fulfill with this can generate automatically<00:00:59.280> the<00:00:59.820> idea<00:01:00.180> of<00:01:00.300> this<00:01:00.480> is<00:01:00.600> that 00:01:00.770 --> 00:01:00.780 align:start position:0% automatically the idea of this is that 00:01:00.780 --> 00:01:02.209 align:start position:0% automatically the idea of this is that once<00:01:01.079> you<00:01:01.140> have<00:01:01.260> this<00:01:01.379> pill<00:01:01.559> you<00:01:01.800> can<00:01:01.920> generate 00:01:02.209 --> 00:01:02.219 align:start position:0% once you have this pill you can generate 00:01:02.219 --> 00:01:04.369 align:start position:0% once you have this pill you can generate automatically<00:01:02.760> a<00:01:02.940> stark<00:01:03.239> and<00:01:03.840> not<00:01:03.960> only<00:01:04.140> that 00:01:04.369 --> 00:01:04.379 align:start position:0% automatically a stark and not only that 00:01:04.379 --> 00:01:08.270 align:start position:0% automatically a stark and not only that that<00:01:05.159> uh<00:01:05.880> with<00:01:06.180> this<00:01:06.360> with<00:01:06.720> this<00:01:06.960> Stark<00:01:07.320> you 00:01:08.270 --> 00:01:08.280 align:start position:0% that uh with this with this Stark you 00:01:08.280 --> 00:01:09.890 align:start position:0% that uh with this with this Stark you can<00:01:08.400> also<00:01:08.640> automatically<00:01:09.180> generate<00:01:09.600> a<00:01:09.720> start 00:01:09.890 --> 00:01:09.900 align:start position:0% can also automatically generate a start 00:01:09.900 --> 00:01:12.530 align:start position:0% can also automatically generate a start that<00:01:10.140> verifies<00:01:10.500> that<00:01:10.740> that<00:01:11.220> that<00:01:11.580> other<00:01:12.060> Stark 00:01:12.530 --> 00:01:12.540 align:start position:0% that verifies that that that other Stark 00:01:12.540 --> 00:01:14.750 align:start position:0% that verifies that that that other Stark okay<00:01:12.840> so<00:01:13.140> we<00:01:13.260> have<00:01:13.380> our<00:01:13.560> recursion<00:01:14.040> Starks<00:01:14.580> and 00:01:14.750 --> 00:01:14.760 align:start position:0% okay so we have our recursion Starks and 00:01:14.760 --> 00:01:16.490 align:start position:0% okay so we have our recursion Starks and you<00:01:14.820> can<00:01:14.939> we<00:01:15.060> can<00:01:15.180> do<00:01:15.360> that<00:01:15.479> many<00:01:15.780> times<00:01:16.020> and<00:01:16.320> we 00:01:16.490 --> 00:01:16.500 align:start position:0% you can we can do that many times and we 00:01:16.500 --> 00:01:19.130 align:start position:0% you can we can do that many times and we can<00:01:16.619> even<00:01:16.799> aggregate<00:01:17.760> uh<00:01:18.659> we<00:01:18.900> can<00:01:18.960> even 00:01:19.130 --> 00:01:19.140 align:start position:0% can even aggregate uh we can even 00:01:19.140 --> 00:01:21.230 align:start position:0% can even aggregate uh we can even Aggregate<00:01:19.680> and<00:01:19.860> then<00:01:19.979> we<00:01:20.159> can<00:01:20.280> build<00:01:20.520> a<00:01:21.060> system 00:01:21.230 --> 00:01:21.240 align:start position:0% Aggregate and then we can build a system 00:01:21.240 --> 00:01:22.670 align:start position:0% Aggregate and then we can build a system that<00:01:21.540> looks<00:01:21.840> something<00:01:21.960> like<00:01:22.200> that<00:01:22.320> we<00:01:22.560> can 00:01:22.670 --> 00:01:22.680 align:start position:0% that looks something like that we can 00:01:22.680 --> 00:01:24.830 align:start position:0% that looks something like that we can have<00:01:22.860> many<00:01:23.100> proofs<00:01:23.640> of<00:01:23.939> many<00:01:24.119> blocks<00:01:24.540> and<00:01:24.659> then 00:01:24.830 --> 00:01:24.840 align:start position:0% have many proofs of many blocks and then 00:01:24.840 --> 00:01:27.350 align:start position:0% have many proofs of many blocks and then we<00:01:25.140> can<00:01:25.320> pack<00:01:25.920> them<00:01:26.220> together<00:01:26.400> in<00:01:26.820> a<00:01:26.939> kind<00:01:27.060> of<00:01:27.240> a 00:01:27.350 --> 00:01:27.360 align:start position:0% we can pack them together in a kind of a 00:01:27.360 --> 00:01:29.510 align:start position:0% we can pack them together in a kind of a tree<00:01:27.479> and<00:01:28.140> then<00:01:28.259> at<00:01:28.500> the<00:01:28.680> end<00:01:28.740> in<00:01:29.280> the<00:01:29.400> last 00:01:29.510 --> 00:01:29.520 align:start position:0% tree and then at the end in the last 00:01:29.520 --> 00:01:31.789 align:start position:0% tree and then at the end in the last step<00:01:29.820> before<00:01:30.299> before<00:01:30.840> sending<00:01:31.439> to<00:01:31.619> the 00:01:31.789 --> 00:01:31.799 align:start position:0% step before before sending to the 00:01:31.799 --> 00:01:35.090 align:start position:0% step before before sending to the ethereum<00:01:32.580> we<00:01:33.119> just<00:01:33.360> convert<00:01:34.259> this<00:01:34.380> Stark<00:01:34.799> to 00:01:35.090 --> 00:01:35.100 align:start position:0% ethereum we just convert this Stark to 00:01:35.100 --> 00:01:37.670 align:start position:0% ethereum we just convert this Stark to the<00:01:35.220> snark<00:01:35.579> and<00:01:36.119> this<00:01:36.240> is<00:01:36.420> this<00:01:37.020> is<00:01:37.200> done<00:01:37.380> quite 00:01:37.670 --> 00:01:37.680 align:start position:0% the snark and this is this is done quite 00:01:37.680 --> 00:01:39.469 align:start position:0% the snark and this is this is done quite automatically<00:01:38.159> so<00:01:38.400> you<00:01:38.579> need<00:01:38.700> to<00:01:38.759> care<00:01:39.000> just 00:01:39.469 --> 00:01:39.479 align:start position:0% automatically so you need to care just 00:01:39.479 --> 00:01:41.330 align:start position:0% automatically so you need to care just about<00:01:39.659> building<00:01:39.960> the<00:01:40.259> pill<00:01:40.380> and<00:01:40.860> the<00:01:40.979> rest<00:01:41.159> is 00:01:41.330 --> 00:01:41.340 align:start position:0% about building the pill and the rest is 00:01:41.340 --> 00:01:44.030 align:start position:0% about building the pill and the rest is quite<00:01:41.700> uh<00:01:42.240> straightforward 00:01:44.030 --> 00:01:44.040 align:start position:0% quite uh straightforward 00:01:44.040 --> 00:01:46.550 align:start position:0% quite uh straightforward okay<00:01:44.460> so<00:01:44.759> let's<00:01:44.939> see<00:01:45.180> how<00:01:45.420> how<00:01:45.900> we<00:01:46.140> do<00:01:46.380> that 00:01:46.550 --> 00:01:46.560 align:start position:0% okay so let's see how how we do that 00:01:46.560 --> 00:01:49.550 align:start position:0% okay so let's see how how we do that okay<00:01:46.740> so<00:01:47.460> what<00:01:48.299> we<00:01:48.420> want<00:01:48.600> to<00:01:48.720> do<00:01:48.840> is<00:01:49.079> we<00:01:49.320> want<00:01:49.439> to 00:01:49.550 --> 00:01:49.560 align:start position:0% okay so what we want to do is we want to 00:01:49.560 --> 00:01:51.350 align:start position:0% okay so what we want to do is we want to build<00:01:49.740> a<00:01:49.979> circuit<00:01:50.280> actually<00:01:50.579> we<00:01:51.119> want<00:01:51.240> to 00:01:51.350 --> 00:01:51.360 align:start position:0% build a circuit actually we want to 00:01:51.360 --> 00:01:54.950 align:start position:0% build a circuit actually we want to build<00:01:51.540> this<00:01:51.899> uh<00:01:52.140> circum<00:01:52.799> circuit<00:01:53.180> that<00:01:54.180> as<00:01:54.780> an 00:01:54.950 --> 00:01:54.960 align:start position:0% build this uh circum circuit that as an 00:01:54.960 --> 00:01:57.649 align:start position:0% build this uh circum circuit that as an input<00:01:55.200> you<00:01:55.619> have<00:01:55.799> a<00:01:55.979> star<00:01:56.159> proof 00:01:57.649 --> 00:01:57.659 align:start position:0% input you have a star proof 00:01:57.659 --> 00:01:59.630 align:start position:0% input you have a star proof okay<00:01:58.020> so<00:01:58.259> this<00:01:58.439> is<00:01:58.500> the<00:01:58.619> start<00:01:58.860> proof<00:01:59.159> so<00:01:59.280> in 00:01:59.630 --> 00:01:59.640 align:start position:0% okay so this is the start proof so in 00:01:59.640 --> 00:02:01.130 align:start position:0% okay so this is the start proof so in the<00:01:59.759> circuit<00:02:00.000> you<00:02:00.240> have<00:02:00.360> to<00:02:00.479> validate<00:02:00.899> this 00:02:01.130 --> 00:02:01.140 align:start position:0% the circuit you have to validate this 00:02:01.140 --> 00:02:04.550 align:start position:0% the circuit you have to validate this star<00:02:01.439> proof<00:02:01.799> so<00:02:02.280> we<00:02:02.460> need<00:02:02.640> to<00:02:02.880> dip<00:02:03.780> in<00:02:04.259> what's 00:02:04.550 --> 00:02:04.560 align:start position:0% star proof so we need to dip in what's 00:02:04.560 --> 00:02:07.130 align:start position:0% star proof so we need to dip in what's inside<00:02:04.860> the<00:02:05.100> star<00:02:05.280> proof<00:02:05.640> what<00:02:05.880> what's<00:02:06.180> what 00:02:07.130 --> 00:02:07.140 align:start position:0% inside the star proof what what's what 00:02:07.140 --> 00:02:09.290 align:start position:0% inside the star proof what what's what Circle<00:02:07.500> what<00:02:07.979> means<00:02:08.220> this<00:02:08.340> of<00:02:08.640> a<00:02:08.759> star<00:02:08.880> proof 00:02:09.290 --> 00:02:09.300 align:start position:0% Circle what means this of a star proof 00:02:09.300 --> 00:02:12.710 align:start position:0% Circle what means this of a star proof well<00:02:09.840> the<00:02:10.259> first<00:02:10.380> thing<00:02:10.560> that<00:02:11.340> one<00:02:12.060> things 00:02:12.710 --> 00:02:12.720 align:start position:0% well the first thing that one things 00:02:12.720 --> 00:02:14.089 align:start position:0% well the first thing that one things that<00:02:12.900> you<00:02:13.020> have<00:02:13.140> the<00:02:13.500> first<00:02:13.620> thing<00:02:13.739> that<00:02:13.980> you 00:02:14.089 --> 00:02:14.099 align:start position:0% that you have the first thing that you 00:02:14.099 --> 00:02:16.070 align:start position:0% that you have the first thing that you have<00:02:14.280> is<00:02:14.520> uh<00:02:15.120> you<00:02:15.420> have<00:02:15.599> the<00:02:15.720> transcript 00:02:16.070 --> 00:02:16.080 align:start position:0% have is uh you have the transcript 00:02:16.080 --> 00:02:18.949 align:start position:0% have is uh you have the transcript transcript<00:02:16.860> are<00:02:17.220> mainly<00:02:17.520> hashes<00:02:18.000> okay<00:02:18.660> so<00:02:18.900> you 00:02:18.949 --> 00:02:18.959 align:start position:0% transcript are mainly hashes okay so you 00:02:18.959 --> 00:02:20.869 align:start position:0% transcript are mainly hashes okay so you need<00:02:19.080> to<00:02:19.200> have<00:02:19.379> these<00:02:19.920> random<00:02:20.280> numbers<00:02:20.459> that 00:02:20.869 --> 00:02:20.879 align:start position:0% need to have these random numbers that 00:02:20.879 --> 00:02:22.610 align:start position:0% need to have these random numbers that goes<00:02:21.180> back<00:02:21.360> and<00:02:21.480> forth<00:02:21.780> this<00:02:22.319> is<00:02:22.440> something 00:02:22.610 --> 00:02:22.620 align:start position:0% goes back and forth this is something 00:02:22.620 --> 00:02:24.530 align:start position:0% goes back and forth this is something that<00:02:22.860> we<00:02:22.980> need<00:02:23.099> to<00:02:23.220> compute<00:02:23.580> inside<00:02:24.180> the 00:02:24.530 --> 00:02:24.540 align:start position:0% that we need to compute inside the 00:02:24.540 --> 00:02:26.570 align:start position:0% that we need to compute inside the inside<00:02:25.200> the<00:02:25.440> circuit<00:02:25.800> these<00:02:26.220> are<00:02:26.280> mainly 00:02:26.570 --> 00:02:26.580 align:start position:0% inside the circuit these are mainly 00:02:26.580 --> 00:02:29.150 align:start position:0% inside the circuit these are mainly hashes<00:02:27.000> okay<00:02:27.660> as<00:02:28.140> a<00:02:28.379> transcript<00:02:28.680> in<00:02:28.980> this<00:02:29.040> case 00:02:29.150 --> 00:02:29.160 align:start position:0% hashes okay as a transcript in this case 00:02:29.160 --> 00:02:32.750 align:start position:0% hashes okay as a transcript in this case we<00:02:29.400> are<00:02:29.580> using<00:02:29.879> uh<00:02:30.780> well<00:02:31.200> a<00:02:31.500> hash<00:02:31.800> function<00:02:32.040> in 00:02:32.750 --> 00:02:32.760 align:start position:0% we are using uh well a hash function in 00:02:32.760 --> 00:02:34.670 align:start position:0% we are using uh well a hash function in this<00:02:32.819> case<00:02:33.000> we<00:02:33.239> are<00:02:33.360> using<00:02:33.660> uh<00:02:34.020> for<00:02:34.260> the<00:02:34.440> Stark 00:02:34.670 --> 00:02:34.680 align:start position:0% this case we are using uh for the Stark 00:02:34.680 --> 00:02:36.350 align:start position:0% this case we are using uh for the Stark we<00:02:35.160> are<00:02:35.340> going<00:02:35.459> to<00:02:35.580> start<00:02:35.819> with<00:02:36.000> a<00:02:36.180> hash 00:02:36.350 --> 00:02:36.360 align:start position:0% we are going to start with a hash 00:02:36.360 --> 00:02:38.930 align:start position:0% we are going to start with a hash function<00:02:36.720> that's<00:02:37.080> a<00:02:38.040> fairly<00:02:38.459> hash<00:02:38.700> function 00:02:38.930 --> 00:02:38.940 align:start position:0% function that's a fairly hash function 00:02:38.940 --> 00:02:40.850 align:start position:0% function that's a fairly hash function in<00:02:39.120> this<00:02:39.239> case<00:02:39.360> a<00:02:39.599> Poseidon<00:02:40.020> with<00:02:40.260> a<00:02:40.379> BN<00:02:40.680> Corp 00:02:40.850 --> 00:02:40.860 align:start position:0% in this case a Poseidon with a BN Corp 00:02:40.860 --> 00:02:43.130 align:start position:0% in this case a Poseidon with a BN Corp we<00:02:41.280> are<00:02:41.459> just<00:02:41.519> using<00:02:41.760> this<00:02:41.879> hash<00:02:42.120> function<00:02:42.420> to 00:02:43.130 --> 00:02:43.140 align:start position:0% we are just using this hash function to 00:02:43.140 --> 00:02:46.630 align:start position:0% we are just using this hash function to compute<00:02:43.620> the<00:02:44.099> to<00:02:44.700> compute<00:02:45.120> the<00:02:45.420> the<00:02:46.379> the 00:02:46.630 --> 00:02:46.640 align:start position:0% compute the to compute the the the 00:02:46.640 --> 00:02:49.910 align:start position:0% compute the to compute the the the randomness<00:02:47.640> the<00:02:48.180> of<00:02:48.420> the<00:02:48.540> of<00:02:48.660> the<00:02:48.840> transcript 00:02:49.910 --> 00:02:49.920 align:start position:0% randomness the of the of the transcript 00:02:49.920 --> 00:02:53.150 align:start position:0% randomness the of the of the transcript okay<00:02:50.400> another<00:02:51.060> piece<00:02:51.480> is<00:02:51.780> well<00:02:52.440> if<00:02:52.739> you<00:02:52.800> have<00:02:53.040> a 00:02:53.150 --> 00:02:53.160 align:start position:0% okay another piece is well if you have a 00:02:53.160 --> 00:02:55.009 align:start position:0% okay another piece is well if you have a polynomial<00:02:53.519> evaluations<00:02:53.940> and<00:02:54.540> then<00:02:54.660> you<00:02:54.840> need 00:02:55.009 --> 00:02:55.019 align:start position:0% polynomial evaluations and then you need 00:02:55.019 --> 00:02:56.170 align:start position:0% polynomial evaluations and then you need to<00:02:55.140> check 00:02:56.170 --> 00:02:56.180 align:start position:0% to check 00:02:56.180 --> 00:02:58.850 align:start position:0% to check uh<00:02:57.180> you<00:02:57.660> need<00:02:57.780> to<00:02:57.900> check<00:02:58.140> that<00:02:58.680> this 00:02:58.850 --> 00:02:58.860 align:start position:0% uh you need to check that this 00:02:58.860 --> 00:03:01.729 align:start position:0% uh you need to check that this polynomials<00:02:59.459> evaluations<00:02:59.959> are<00:03:00.959> are<00:03:01.500> okay 00:03:01.729 --> 00:03:01.739 align:start position:0% polynomials evaluations are are okay 00:03:01.739 --> 00:03:03.470 align:start position:0% polynomials evaluations are are okay that<00:03:02.160> they<00:03:02.340> are<00:03:02.459> fitting<00:03:02.819> that<00:03:03.239> means<00:03:03.420> that 00:03:03.470 --> 00:03:03.480 align:start position:0% that they are fitting that means that 00:03:03.480 --> 00:03:05.630 align:start position:0% that they are fitting that means that you<00:03:03.660> need<00:03:03.720> to<00:03:03.840> do<00:03:03.959> a<00:03:04.080> lot<00:03:04.140> of<00:03:04.200> arithmetic<00:03:04.860> and 00:03:05.630 --> 00:03:05.640 align:start position:0% you need to do a lot of arithmetic and 00:03:05.640 --> 00:03:07.190 align:start position:0% you need to do a lot of arithmetic and in<00:03:05.940> the<00:03:06.060> case<00:03:06.180> of<00:03:06.360> us<00:03:06.540> we<00:03:06.780> are<00:03:06.900> using<00:03:07.080> the 00:03:07.190 --> 00:03:07.200 align:start position:0% in the case of us we are using the 00:03:07.200 --> 00:03:10.250 align:start position:0% in the case of us we are using the Goldilocks<00:03:07.800> brain<00:03:08.580> field<00:03:08.760> and<00:03:09.599> but<00:03:09.900> here<00:03:10.080> we 00:03:10.250 --> 00:03:10.260 align:start position:0% Goldilocks brain field and but here we 00:03:10.260 --> 00:03:12.050 align:start position:0% Goldilocks brain field and but here we are<00:03:10.379> in<00:03:10.440> the<00:03:10.560> BN<00:03:10.860> so<00:03:10.980> we<00:03:11.099> need<00:03:11.340> to<00:03:11.459> work<00:03:11.700> with 00:03:12.050 --> 00:03:12.060 align:start position:0% are in the BN so we need to work with 00:03:12.060 --> 00:03:14.750 align:start position:0% are in the BN so we need to work with this<00:03:12.300> cross<00:03:12.540> Prime<00:03:12.900> field<00:03:13.680> we<00:03:14.280> need<00:03:14.400> to<00:03:14.519> do 00:03:14.750 --> 00:03:14.760 align:start position:0% this cross Prime field we need to do 00:03:14.760 --> 00:03:16.850 align:start position:0% this cross Prime field we need to do this<00:03:15.060> cross<00:03:15.180> brain<00:03:15.540> field<00:03:15.720> operations<00:03:16.260> so<00:03:16.680> we 00:03:16.850 --> 00:03:16.860 align:start position:0% this cross brain field operations so we 00:03:16.860 --> 00:03:18.530 align:start position:0% this cross brain field operations so we need<00:03:16.980> to<00:03:17.040> do<00:03:17.159> cross<00:03:17.400> Prime<00:03:17.580> field<00:03:17.819> inside<00:03:18.180> the 00:03:18.530 --> 00:03:18.540 align:start position:0% need to do cross Prime field inside the 00:03:18.540 --> 00:03:22.670 align:start position:0% need to do cross Prime field inside the inside<00:03:19.140> the<00:03:19.620> the<00:03:20.459> the<00:03:20.659> inside<00:03:21.659> the<00:03:22.019> inside<00:03:22.379> the 00:03:22.670 --> 00:03:22.680 align:start position:0% inside the the the inside the inside the 00:03:22.680 --> 00:03:25.250 align:start position:0% inside the the the inside the inside the circuit 00:03:25.250 --> 00:03:25.260 align:start position:0% 00:03:25.260 --> 00:03:27.530 align:start position:0% um the<00:03:25.739> next<00:03:25.860> thing<00:03:26.099> that<00:03:26.400> we<00:03:26.760> have<00:03:27.000> to<00:03:27.180> do<00:03:27.360> is 00:03:27.530 --> 00:03:27.540 align:start position:0% um the next thing that we have to do is 00:03:27.540 --> 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align:start position:0% just validate these Miracle trees here the<00:03:34.800> trick<00:03:35.040> is<00:03:35.220> again<00:03:35.519> use<00:03:36.180> the<00:03:36.599> Poseidon<00:03:37.379> hash 00:03:37.670 --> 00:03:37.680 align:start position:0% the trick is again use the Poseidon hash 00:03:37.680 --> 00:03:40.250 align:start position:0% the trick is again use the Poseidon hash function<00:03:37.980> so<00:03:38.519> if<00:03:38.640> you<00:03:38.760> use<00:03:38.879> a<00:03:39.000> position<00:03:39.239> so<00:03:40.080> a 00:03:40.250 --> 00:03:40.260 align:start position:0% function so if you use a position so a 00:03:40.260 --> 00:03:42.710 align:start position:0% function so if you use a position so a snack<00:03:40.799> freely<00:03:41.159> hash<00:03:41.640> function<00:03:42.000> then<00:03:42.480> doing 00:03:42.710 --> 00:03:42.720 align:start position:0% snack freely hash function then doing 00:03:42.720 --> 00:03:44.990 align:start position:0% snack freely hash function then doing that<00:03:43.019> that<00:03:43.200> inside<00:03:43.620> this<00:03:43.920> inside<00:03:44.340> the<00:03:44.640> circuit 00:03:44.990 --> 00:03:45.000 align:start position:0% that that inside this inside the circuit 00:03:45.000 --> 00:03:48.890 align:start position:0% that that inside this inside the circuit is<00:03:45.599> relatively<00:03:46.319> cheap<00:03:46.560> so<00:03:47.220> we<00:03:47.340> do<00:03:47.519> that<00:03:47.760> uh<00:03:48.540> for 00:03:48.890 --> 00:03:48.900 align:start position:0% is relatively cheap so we do that uh for 00:03:48.900 --> 00:03:51.170 align:start position:0% is relatively cheap so we do that uh for the<00:03:49.140> for<00:03:49.620> the<00:03:49.739> openings<00:03:50.159> itself 00:03:51.170 --> 00:03:51.180 align:start position:0% the for the openings itself 00:03:51.180 --> 00:03:53.449 align:start position:0% the for the openings itself okay<00:03:51.659> once<00:03:52.200> you<00:03:52.260> have<00:03:52.379> the<00:03:52.620> openings<00:03:52.980> you<00:03:53.340> need 00:03:53.449 --> 00:03:53.459 align:start position:0% okay once you have the openings you need 00:03:53.459 --> 00:03:55.850 align:start position:0% okay once you have the openings you need to<00:03:53.640> evaluate<00:03:54.180> this<00:03:54.959> opening<00:03:55.379> polynomial 00:03:55.850 --> 00:03:55.860 align:start position:0% to evaluate this opening polynomial 00:03:55.860 --> 00:03:57.589 align:start position:0% to evaluate this opening polynomial which<00:03:56.340> is<00:03:56.459> a<00:03:56.580> derivative<00:03:56.940> polynomial<00:03:57.480> you 00:03:57.589 --> 00:03:57.599 align:start position:0% which is a derivative polynomial you 00:03:57.599 --> 00:03:59.750 align:start position:0% which is a derivative polynomial you need<00:03:57.780> to<00:03:57.900> evaluate<00:03:58.200> those<00:03:58.799> openings<00:03:59.220> at<00:03:59.519> that 00:03:59.750 --> 00:03:59.760 align:start position:0% need to evaluate those openings at that 00:03:59.760 --> 00:04:02.470 align:start position:0% need to evaluate those openings at that point<00:03:59.940> okay<00:04:00.360> so<00:04:00.720> you<00:04:00.840> need<00:04:01.019> here<00:04:01.260> more 00:04:02.470 --> 00:04:02.480 align:start position:0% point okay so you need here more 00:04:02.480 --> 00:04:04.490 align:start position:0% point okay so you need here more arithmetic<00:04:03.480> operations 00:04:04.490 --> 00:04:04.500 align:start position:0% arithmetic operations 00:04:04.500 --> 00:04:07.789 align:start position:0% arithmetic operations okay<00:04:05.120> and<00:04:06.120> finally<00:04:06.420> we<00:04:06.659> have<00:04:06.780> the<00:04:06.959> fry<00:04:07.260> okay 00:04:07.789 --> 00:04:07.799 align:start position:0% okay and finally we have the fry okay 00:04:07.799 --> 00:04:11.270 align:start position:0% okay and finally we have the fry okay fry<00:04:08.700> is<00:04:09.299> openings<00:04:09.959> again<00:04:10.200> so<00:04:10.799> lots<00:04:11.220> of 00:04:11.270 --> 00:04:11.280 align:start position:0% fry is openings again so lots of 00:04:11.280 --> 00:04:13.250 align:start position:0% fry is openings again so lots of openings<00:04:11.700> that's<00:04:12.299> one<00:04:12.540> thing<00:04:12.659> so<00:04:12.840> every<00:04:13.080> time 00:04:13.250 --> 00:04:13.260 align:start position:0% openings that's one thing so every time 00:04:13.260 --> 00:04:15.589 align:start position:0% openings that's one thing so every time that<00:04:13.439> you<00:04:13.620> go<00:04:13.739> to<00:04:13.860> us<00:04:14.159> back<00:04:14.700> in<00:04:14.879> the<00:04:15.060> step<00:04:15.180> you 00:04:15.589 --> 00:04:15.599 align:start position:0% that you go to us back in the step you 00:04:15.599 --> 00:04:17.930 align:start position:0% that you go to us back in the step you do<00:04:15.780> on<00:04:15.959> uh<00:04:16.199> you<00:04:16.380> do<00:04:16.500> openings<00:04:16.919> so<00:04:17.639> this<00:04:17.820> is 00:04:17.930 --> 00:04:17.940 align:start position:0% do on uh you do openings so this is 00:04:17.940 --> 00:04:21.830 align:start position:0% do on uh you do openings so this is again<00:04:18.199> Poseidon<00:04:19.199> uh<00:04:20.160> here<00:04:20.519> and<00:04:21.299> then<00:04:21.419> you<00:04:21.720> have 00:04:21.830 --> 00:04:21.840 align:start position:0% again Poseidon uh here and then you have 00:04:21.840 --> 00:04:24.590 align:start position:0% again Poseidon uh here and then you have to<00:04:21.959> do<00:04:22.079> polynomial<00:04:22.680> evaluations<00:04:23.160> but<00:04:24.060> this<00:04:24.479> is 00:04:24.590 --> 00:04:24.600 align:start position:0% to do polynomial evaluations but this is 00:04:24.600 --> 00:04:26.749 align:start position:0% to do polynomial evaluations but this is our<00:04:24.840> in<00:04:25.080> the<00:04:25.199> cross<00:04:25.440> Prime<00:04:25.740> this<00:04:26.460> is<00:04:26.520> in<00:04:26.639> the 00:04:26.749 --> 00:04:26.759 align:start position:0% our in the cross Prime this is in the 00:04:26.759 --> 00:04:29.450 align:start position:0% our in the cross Prime this is in the Goldilocks<00:04:27.360> Prime<00:04:27.900> field<00:04:28.139> okay<00:04:28.560> the<00:04:29.100> best<00:04:29.220> way 00:04:29.450 --> 00:04:29.460 align:start position:0% Goldilocks Prime field okay the best way 00:04:29.460 --> 00:04:32.870 align:start position:0% Goldilocks Prime field okay the best way to<00:04:29.699> do<00:04:29.940> a<00:04:30.440> polynomial<00:04:31.440> evaluation<00:04:31.919> is<00:04:32.460> mainly 00:04:32.870 --> 00:04:32.880 align:start position:0% to do a polynomial evaluation is mainly 00:04:32.880 --> 00:04:38.090 align:start position:0% to do a polynomial evaluation is mainly doing<00:04:33.540> an<00:04:33.960> fft<00:04:34.740> kind<00:04:35.699> of<00:04:35.880> a<00:04:36.360> kind<00:04:36.840> of<00:04:36.960> an<00:04:37.020> fft 00:04:38.090 --> 00:04:38.100 align:start position:0% doing an fft kind of a kind of an fft 00:04:38.100 --> 00:04:41.270 align:start position:0% doing an fft kind of a kind of an fft okay<00:04:38.580> so<00:04:39.479> and<00:04:40.020> finally<00:04:40.320> in<00:04:40.500> the<00:04:40.620> last<00:04:40.740> start<00:04:41.040> we 00:04:41.270 --> 00:04:41.280 align:start position:0% okay so and finally in the last start we 00:04:41.280 --> 00:04:42.890 align:start position:0% okay so and finally in the last start we also<00:04:41.520> need<00:04:41.639> to<00:04:41.759> do<00:04:41.940> uh 00:04:42.890 --> 00:04:42.900 align:start position:0% also need to do uh 00:04:42.900 --> 00:04:46.430 align:start position:0% also need to do uh um<00:04:42.960> an<00:04:43.940> fft<00:04:44.940> for<00:04:45.360> the<00:04:45.660> for<00:04:46.139> the<00:04:46.320> final 00:04:46.430 --> 00:04:46.440 align:start position:0% um an fft for the for the final 00:04:46.440 --> 00:04:48.170 align:start position:0% um an fft for the for the final polynomial<00:04:47.100> that<00:04:47.520> we<00:04:47.699> need<00:04:47.759> to<00:04:47.880> check<00:04:48.000> that 00:04:48.170 --> 00:04:48.180 align:start position:0% polynomial that we need to check that 00:04:48.180 --> 00:04:49.850 align:start position:0% polynomial that we need to check that the<00:04:48.300> final<00:04:48.419> polynomial<00:04:48.840> of<00:04:49.080> certain<00:04:49.440> degree 00:04:49.850 --> 00:04:49.860 align:start position:0% the final polynomial of certain degree 00:04:49.860 --> 00:04:51.770 align:start position:0% the final polynomial of certain degree mainly<00:04:50.400> you<00:04:50.520> do<00:04:50.639> an<00:04:50.699> fft<00:04:50.940> and<00:04:51.240> check<00:04:51.419> that<00:04:51.600> the 00:04:51.770 --> 00:04:51.780 align:start position:0% mainly you do an fft and check that the 00:04:51.780 --> 00:04:54.170 align:start position:0% mainly you do an fft and check that the half<00:04:51.960> of<00:04:52.139> the<00:04:52.320> or<00:04:52.620> that<00:04:52.860> part<00:04:53.040> of<00:04:53.220> the<00:04:53.400> bits<00:04:54.060> are 00:04:54.170 --> 00:04:54.180 align:start position:0% half of the or that part of the bits are 00:04:54.180 --> 00:04:55.189 align:start position:0% half of the or that part of the bits are zero 00:04:55.189 --> 00:04:55.199 align:start position:0% zero 00:04:55.199 --> 00:04:58.129 align:start position:0% zero okay<00:04:55.560> so<00:04:55.919> this<00:04:56.040> is<00:04:56.160> a<00:04:56.340> structure<00:04:56.759> of<00:04:57.360> the<00:04:57.600> of 00:04:58.129 --> 00:04:58.139 align:start position:0% okay so this is a structure of the of 00:04:58.139 --> 00:05:00.710 align:start position:0% okay so this is a structure of the of the<00:04:58.500> of<00:04:59.040> the<00:04:59.280> star 00:05:00.710 --> 00:05:00.720 align:start position:0% the of the star 00:05:00.720 --> 00:05:02.870 align:start position:0% the of the star so<00:05:01.020> here<00:05:01.500> the 00:05:02.870 --> 00:05:02.880 align:start position:0% so here the 00:05:02.880 --> 00:05:05.990 align:start position:0% so here the I'm<00:05:03.000> going<00:05:03.240> to<00:05:03.360> jump<00:05:03.479> this<00:05:03.780> so<00:05:04.380> here<00:05:04.560> the 00:05:05.990 --> 00:05:06.000 align:start position:0% I'm going to jump this so here the 00:05:06.000 --> 00:05:07.430 align:start position:0% I'm going to jump this so here the the 00:05:07.430 --> 00:05:07.440 align:start position:0% the 00:05:07.440 --> 00:05:10.249 align:start position:0% the well<00:05:07.979> the<00:05:08.160> the<00:05:08.340> the<00:05:08.340> trick<00:05:09.180> here<00:05:09.360> is<00:05:09.600> how<00:05:10.080> much 00:05:10.249 --> 00:05:10.259 align:start position:0% well the the the trick here is how much 00:05:10.259 --> 00:05:12.530 align:start position:0% well the the the trick here is how much so<00:05:10.560> how<00:05:10.740> we<00:05:10.979> do<00:05:11.160> this<00:05:11.759> cross<00:05:11.940> Prime<00:05:12.240> field 00:05:12.530 --> 00:05:12.540 align:start position:0% so how we do this cross Prime field 00:05:12.540 --> 00:05:14.930 align:start position:0% so how we do this cross Prime field operation<00:05:13.139> this<00:05:13.560> is<00:05:13.680> probably<00:05:13.860> the<00:05:14.160> most<00:05:14.340> uh 00:05:14.930 --> 00:05:14.940 align:start position:0% operation this is probably the most uh 00:05:14.940 --> 00:05:17.150 align:start position:0% operation this is probably the most uh simple<00:05:15.180> thing<00:05:15.540> and<00:05:15.840> the<00:05:16.020> idea<00:05:16.259> is<00:05:16.440> where<00:05:16.680> we 00:05:17.150 --> 00:05:17.160 align:start position:0% simple thing and the idea is where we 00:05:17.160 --> 00:05:20.150 align:start position:0% simple thing and the idea is where we are<00:05:17.280> just<00:05:17.400> doing<00:05:17.820> in<00:05:18.600> a<00:05:18.840> naive<00:05:19.320> so<00:05:19.740> in<00:05:19.979> a<00:05:20.040> very 00:05:20.150 --> 00:05:20.160 align:start position:0% are just doing in a naive so in a very 00:05:20.160 --> 00:05:23.450 align:start position:0% are just doing in a naive so in a very naive<00:05:20.460> way<00:05:20.639> okay<00:05:21.180> so<00:05:21.780> we<00:05:22.080> just<00:05:22.380> uh<00:05:22.860> if<00:05:23.400> we're 00:05:23.450 --> 00:05:23.460 align:start position:0% naive way okay so we just uh if we're 00:05:23.460 --> 00:05:25.430 align:start position:0% naive way okay so we just uh if we're doing<00:05:23.639> an<00:05:23.820> operation<00:05:24.120> like<00:05:24.840> that<00:05:24.960> like<00:05:25.320> a 00:05:25.430 --> 00:05:25.440 align:start position:0% doing an operation like that like a 00:05:25.440 --> 00:05:28.490 align:start position:0% doing an operation like that like a multiplication<00:05:26.000> uh<00:05:27.000> in<00:05:27.240> this<00:05:27.360> case<00:05:27.539> is<00:05:27.840> uh 00:05:28.490 --> 00:05:28.500 align:start position:0% multiplication uh in this case is uh 00:05:28.500 --> 00:05:31.189 align:start position:0% multiplication uh in this case is uh well<00:05:29.100> we<00:05:29.400> just<00:05:29.580> do<00:05:29.759> a<00:05:29.940> couple<00:05:30.060> of<00:05:30.300> uh<00:05:30.900> rain 00:05:31.189 --> 00:05:31.199 align:start position:0% well we just do a couple of uh rain 00:05:31.199 --> 00:05:34.370 align:start position:0% well we just do a couple of uh rain checks<00:05:31.680> okay<00:05:32.100> that<00:05:32.699> means<00:05:33.000> that<00:05:33.240> uh<00:05:33.720> more<00:05:34.259> or 00:05:34.370 --> 00:05:34.380 align:start position:0% checks okay that means that uh more or 00:05:34.380 --> 00:05:38.330 align:start position:0% checks okay that means that uh more or less<00:05:34.500> uh<00:05:35.880> Prime<00:05:36.479> cross<00:05:37.139> so<00:05:37.500> a<00:05:37.800> multiplication 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one thing that's specific 00:05:47.880 --> 00:05:49.909 align:start position:0% this is a one one thing that's specific on<00:05:48.120> the<00:05:48.240> fry<00:05:48.479> the<00:05:49.020> Goldilocks<00:05:49.560> is<00:05:49.680> a<00:05:49.800> very 00:05:49.909 --> 00:05:49.919 align:start position:0% on the fry the Goldilocks is a very 00:05:49.919 --> 00:05:52.969 align:start position:0% on the fry the Goldilocks is a very small<00:05:50.039> Prime<00:05:50.280> field<00:05:50.580> so<00:05:51.479> uh<00:05:52.259> once<00:05:52.740> you<00:05:52.800> work 00:05:52.969 --> 00:05:52.979 align:start position:0% small Prime field so uh once you work 00:05:52.979 --> 00:05:54.890 align:start position:0% small Prime field so uh once you work with<00:05:53.160> a<00:05:53.280> random<00:05:53.580> number<00:05:53.759> you<00:05:54.479> cannot<00:05:54.720> work 00:05:54.890 --> 00:05:54.900 align:start position:0% with a random number you cannot work 00:05:54.900 --> 00:05:56.930 align:start position:0% with a random number you cannot work with<00:05:55.139> the<00:05:55.320> base<00:05:55.440> field<00:05:55.740> because<00:05:56.160> it's<00:05:56.460> very 00:05:56.930 --> 00:05:56.940 align:start position:0% with the base field because it's very 00:05:56.940 --> 00:05:59.029 align:start position:0% with the base field because it's very small<00:05:57.120> so<00:05:57.600> you<00:05:57.720> need<00:05:57.840> to<00:05:57.960> work<00:05:58.199> with<00:05:58.500> extension 00:05:59.029 --> 00:05:59.039 align:start position:0% small so you need to work with extension 00:05:59.039 --> 00:06:00.710 align:start position:0% small so you need to work with extension Fields<00:05:59.400> so<00:05:59.520> you<00:05:59.759> work<00:05:59.940> with<00:06:00.120> extension<00:06:00.539> in 00:06:00.710 --> 00:06:00.720 align:start position:0% Fields so you work with extension in 00:06:00.720 --> 00:06:02.270 align:start position:0% Fields so you work with extension in this<00:06:00.960> in<00:06:01.080> our<00:06:01.259> case<00:06:01.380> we're<00:06:01.560> working<00:06:01.860> with<00:06:02.100> an 00:06:02.270 --> 00:06:02.280 align:start position:0% this in our case we're working with an 00:06:02.280 --> 00:06:04.790 align:start position:0% this in our case we're working with an extension<00:06:02.759> three<00:06:02.940> of<00:06:03.600> the<00:06:03.780> Goldilocks<00:06:04.440> okay 00:06:04.790 --> 00:06:04.800 align:start position:0% extension three of the Goldilocks okay 00:06:04.800 --> 00:06:05.930 align:start position:0% extension three of the Goldilocks okay so<00:06:05.160> that<00:06:05.280> means<00:06:05.460> that<00:06:05.580> doing<00:06:05.699> a 00:06:05.930 --> 00:06:05.940 align:start position:0% so that means that doing a 00:06:05.940 --> 00:06:08.029 align:start position:0% so that means that doing a multiplication<00:06:06.479> in<00:06:07.320> the<00:06:07.500> extension<00:06:07.860> field 00:06:08.029 --> 00:06:08.039 align:start position:0% multiplication in the extension field 00:06:08.039 --> 00:06:11.210 align:start position:0% multiplication in the extension field three<00:06:08.400> this<00:06:09.120> is<00:06:09.240> uh<00:06:09.780> something<00:06:10.020> that's<00:06:10.380> 400 00:06:11.210 --> 00:06:11.220 align:start position:0% three this is uh something that's 400 00:06:11.220 --> 00:06:13.870 align:start position:0% three this is uh something that's 400 400<00:06:12.000> 438 00:06:13.870 --> 00:06:13.880 align:start position:0% 400 438 00:06:13.880 --> 00:06:16.430 align:start position:0% 400 438 constraints<00:06:14.880> which<00:06:15.479> is<00:06:15.660> a<00:06:15.840> lot<00:06:16.020> you<00:06:16.320> know 00:06:16.430 --> 00:06:16.440 align:start position:0% constraints which is a lot you know 00:06:16.440 --> 00:06:17.890 align:start position:0% constraints which is a lot you know compared<00:06:16.800> to<00:06:16.860> one 00:06:17.890 --> 00:06:17.900 align:start position:0% compared to one 00:06:17.900 --> 00:06:23.090 align:start position:0% compared to one but<00:06:19.280> it's<00:06:20.280> not<00:06:21.000> that<00:06:21.180> much<00:06:21.360> okay<00:06:21.840> so<00:06:22.500> here<00:06:22.919> the 00:06:23.090 --> 00:06:23.100 align:start position:0% but it's not that much okay so here the 00:06:23.100 --> 00:06:24.590 align:start position:0% but it's not that much okay so here the thing<00:06:23.220> is<00:06:23.400> okay<00:06:23.639> let's<00:06:23.940> let's<00:06:24.120> do<00:06:24.419> some 00:06:24.590 --> 00:06:24.600 align:start position:0% thing is okay let's let's do some 00:06:24.600 --> 00:06:26.930 align:start position:0% thing is okay let's let's do some numbers<00:06:24.780> of<00:06:25.259> some<00:06:25.440> examples<00:06:25.919> of<00:06:26.160> some<00:06:26.340> Starks 00:06:26.930 --> 00:06:26.940 align:start position:0% numbers of some examples of some Starks 00:06:26.940 --> 00:06:30.170 align:start position:0% numbers of some examples of some Starks uh<00:06:27.720> how<00:06:27.960> it<00:06:28.199> would<00:06:28.440> look<00:06:28.740> like<00:06:28.919> okay<00:06:29.400> well<00:06:29.880> this 00:06:30.170 --> 00:06:30.180 align:start position:0% uh how it would look like okay well this 00:06:30.180 --> 00:06:31.309 align:start position:0% uh how it would look like okay well this is<00:06:30.300> the 00:06:31.309 --> 00:06:31.319 align:start position:0% is the 00:06:31.319 --> 00:06:34.730 align:start position:0% is the the<00:06:32.039> the<00:06:32.880> for<00:06:33.240> the<00:06:33.419> hash<00:06:33.539> functions<00:06:34.139> we<00:06:34.560> are 00:06:34.730 --> 00:06:34.740 align:start position:0% the the for the hash functions we are 00:06:34.740 --> 00:06:37.610 align:start position:0% the the for the hash functions we are using<00:06:34.979> a<00:06:35.100> 16<00:06:35.280> inputs<00:06:35.880> so<00:06:36.060> we<00:06:36.240> can<00:06:36.360> do<00:06:36.539> uh<00:06:36.900> trees 00:06:37.610 --> 00:06:37.620 align:start position:0% using a 16 inputs so we can do uh trees 00:06:37.620 --> 00:06:40.670 align:start position:0% using a 16 inputs so we can do uh trees that<00:06:38.400> goes<00:06:38.699> at<00:06:38.819> four<00:06:39.180> at<00:06:39.419> four<00:06:39.660> and<00:06:40.139> then<00:06:40.380> a 00:06:40.670 --> 00:06:40.680 align:start position:0% that goes at four at four and then a 00:06:40.680 --> 00:06:43.610 align:start position:0% that goes at four at four and then a constraint<00:06:41.220> is<00:06:41.460> just<00:06:41.840> 612<00:06:42.840> constraints<00:06:43.380> just 00:06:43.610 --> 00:06:43.620 align:start position:0% constraint is just 612 constraints just 00:06:43.620 --> 00:06:44.930 align:start position:0% constraint is just 612 constraints just doing<00:06:43.740> a<00:06:43.919> single<00:06:44.160> hash<00:06:44.340> which<00:06:44.639> is<00:06:44.759> quite 00:06:44.930 --> 00:06:44.940 align:start position:0% doing a single hash which is quite 00:06:44.940 --> 00:06:48.950 align:start position:0% doing a single hash which is quite optimal<00:06:45.479> uh<00:06:46.020> if<00:06:46.139> we<00:06:46.259> do<00:06:46.380> it<00:06:46.560> in<00:06:46.620> that<00:06:46.800> way<00:06:46.979> okay 00:06:48.950 --> 00:06:48.960 align:start position:0% optimal uh if we do it in that way okay 00:06:48.960 --> 00:06:51.710 align:start position:0% optimal uh if we do it in that way okay so<00:06:49.500> let's<00:06:49.680> put<00:06:50.340> some<00:06:50.520> example<00:06:50.880> this<00:06:51.180> is<00:06:51.300> these 00:06:51.710 --> 00:06:51.720 align:start position:0% so let's put some example this is these 00:06:51.720 --> 00:06:54.110 align:start position:0% so let's put some example this is these numbers<00:06:51.840> are<00:06:52.259> not<00:06:52.860> exactly<00:06:53.280> but<00:06:53.520> are<00:06:53.699> similar 00:06:54.110 --> 00:06:54.120 align:start position:0% numbers are not exactly but are similar 00:06:54.120 --> 00:06:55.550 align:start position:0% numbers are not exactly but are similar to<00:06:54.240> the<00:06:54.419> ones<00:06:54.600> that<00:06:54.720> we<00:06:54.840> are<00:06:54.960> using<00:06:55.199> for<00:06:55.440> the 00:06:55.550 --> 00:06:55.560 align:start position:0% to the ones that we are using for the 00:06:55.560 --> 00:06:57.950 align:start position:0% to the ones that we are using for the ckvm<00:06:56.220> circuit<00:06:56.639> in<00:06:57.120> this<00:06:57.180> case<00:06:57.360> we<00:06:57.600> are<00:06:57.780> talking 00:06:57.950 --> 00:06:57.960 align:start position:0% ckvm circuit in this case we are talking 00:06:57.960 --> 00:07:00.170 align:start position:0% ckvm circuit in this case we are talking about<00:06:58.259> let's<00:06:58.620> talk<00:06:58.860> about<00:06:59.039> uh<00:06:59.520> 1000 00:07:00.170 --> 00:07:00.180 align:start position:0% about let's talk about uh 1000 00:07:00.180 --> 00:07:05.450 align:start position:0% about let's talk about uh 1000 polynomials<00:07:01.139> okay<00:07:02.120> uh<00:07:03.120> we<00:07:03.660> have<00:07:03.840> a<00:07:04.259> let's<00:07:05.160> do<00:07:05.340> a 00:07:05.450 --> 00:07:05.460 align:start position:0% polynomials okay uh we have a let's do a 00:07:05.460 --> 00:07:07.790 align:start position:0% polynomials okay uh we have a let's do a blower<00:07:05.940> factor<00:07:06.360> of<00:07:06.479> two<00:07:06.660> that<00:07:07.259> means<00:07:07.500> that<00:07:07.620> we 00:07:07.790 --> 00:07:07.800 align:start position:0% blower factor of two that means that we 00:07:07.800 --> 00:07:10.909 align:start position:0% blower factor of two that means that we need<00:07:07.919> to<00:07:07.979> do<00:07:08.100> a<00:07:08.280> lot<00:07:08.340> of<00:07:08.460> queries<00:07:08.880> in<00:07:09.780> the<00:07:10.080> in 00:07:10.909 --> 00:07:10.919 align:start position:0% need to do a lot of queries in the in 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align:start position:0% important this raw factor of two because if<00:07:18.300> you<00:07:18.419> go<00:07:18.539> for<00:07:18.840> example<00:07:19.020> lower<00:07:19.440> factor<00:07:19.740> of 00:07:19.909 --> 00:07:19.919 align:start position:0% if you go for example lower factor of 00:07:19.919 --> 00:07:21.950 align:start position:0% if you go for example lower factor of four<00:07:20.099> that<00:07:20.520> means<00:07:20.819> that<00:07:21.060> we<00:07:21.360> are<00:07:21.479> doubling<00:07:21.780> the 00:07:21.950 --> 00:07:21.960 align:start position:0% four that means that we are doubling the 00:07:21.960 --> 00:07:25.070 align:start position:0% four that means that we are doubling the proving<00:07:22.259> the<00:07:22.440> proving<00:07:22.740> time<00:07:23.340> okay<00:07:23.819> so<00:07:24.180> we<00:07:24.960> need 00:07:25.070 --> 00:07:25.080 align:start position:0% proving the proving time okay so we need 00:07:25.080 --> 00:07:26.870 align:start position:0% proving the proving time okay so we need to<00:07:25.139> go<00:07:25.319> to<00:07:25.440> the<00:07:25.620> minimal<00:07:25.979> especially<00:07:26.580> when<00:07:26.699> we 00:07:26.870 --> 00:07:26.880 align:start position:0% to go to the minimal especially when we 00:07:26.880 --> 00:07:29.330 align:start position:0% to go to the minimal especially when we have<00:07:27.060> so<00:07:27.240> many<00:07:27.419> polynomials<00:07:28.199> here<00:07:28.860> so<00:07:29.099> that's 00:07:29.330 --> 00:07:29.340 align:start position:0% have so many polynomials here so that's 00:07:29.340 --> 00:07:31.670 align:start position:0% have so many polynomials here so that's why<00:07:29.580> we<00:07:29.819> use<00:07:29.940> a<00:07:30.120> row<00:07:30.419> of<00:07:30.539> factor<00:07:30.780> of<00:07:30.840> two<00:07:31.020> okay 00:07:31.670 --> 00:07:31.680 align:start position:0% why we use a row of factor of two okay 00:07:31.680 --> 00:07:34.010 align:start position:0% why we use a row of factor of two okay so<00:07:32.280> let's<00:07:32.699> talk<00:07:32.880> with<00:07:33.180> uh<00:07:33.360> sides<00:07:33.780> of<00:07:33.900> a 00:07:34.010 --> 00:07:34.020 align:start position:0% so let's talk with uh sides of a 00:07:34.020 --> 00:07:35.990 align:start position:0% so let's talk with uh sides of a polynomials<00:07:34.500> of<00:07:34.560> 2<00:07:34.680> to<00:07:34.860> 24<00:07:35.160> after<00:07:35.520> the<00:07:35.759> lower 00:07:35.990 --> 00:07:36.000 align:start position:0% polynomials of 2 to 24 after the lower 00:07:36.000 --> 00:07:40.129 align:start position:0% polynomials of 2 to 24 after the lower factors<00:07:36.360> so<00:07:36.539> 2<00:07:36.780> to<00:07:36.960> 23<00:07:37.259> to<00:07:37.440> 224<00:07:38.160> okay<00:07:39.060> and<00:07:39.900> of 00:07:40.129 --> 00:07:40.139 align:start position:0% factors so 2 to 23 to 224 okay and of 00:07:40.139 --> 00:07:41.749 align:start position:0% factors so 2 to 23 to 224 okay and of course<00:07:40.199> we<00:07:40.380> have<00:07:40.560> constraints<00:07:41.039> let's<00:07:41.400> assume 00:07:41.749 --> 00:07:41.759 align:start position:0% course we have constraints let's assume 00:07:41.759 --> 00:07:42.950 align:start position:0% course we have constraints let's assume that<00:07:41.819> the<00:07:41.940> number<00:07:42.060> of<00:07:42.180> constraints<00:07:42.599> is<00:07:42.780> more 00:07:42.950 --> 00:07:42.960 align:start position:0% that the number of constraints is more 00:07:42.960 --> 00:07:44.510 align:start position:0% that the number of constraints is more or<00:07:43.080> less<00:07:43.199> the<00:07:43.440> same<00:07:43.560> number<00:07:43.680> of<00:07:43.860> polynomials 00:07:44.510 --> 00:07:44.520 align:start position:0% or less the same number of polynomials 00:07:44.520 --> 00:07:46.790 align:start position:0% or less the same number of polynomials this<00:07:44.759> is<00:07:44.880> just<00:07:45.180> uh 00:07:46.790 --> 00:07:46.800 align:start position:0% this is just uh 00:07:46.800 --> 00:07:49.730 align:start position:0% this is just uh just<00:07:47.280> uh<00:07:47.520> subjection<00:07:48.300> and<00:07:48.840> then<00:07:49.199> we<00:07:49.440> have<00:07:49.560> in 00:07:49.730 --> 00:07:49.740 align:start position:0% just uh subjection and then we have in 00:07:49.740 --> 00:07:50.809 align:start position:0% just uh subjection and then we have in each<00:07:49.919> constraint<00:07:50.220> we<00:07:50.400> have<00:07:50.520> like<00:07:50.699> two 00:07:50.809 --> 00:07:50.819 align:start position:0% each constraint we have like two 00:07:50.819 --> 00:07:52.490 align:start position:0% each constraint we have like two multiplications<00:07:51.300> for<00:07:51.599> each<00:07:51.720> constraint<00:07:52.139> okay 00:07:52.490 --> 00:07:52.500 align:start position:0% multiplications for each constraint okay 00:07:52.500 --> 00:07:54.110 align:start position:0% multiplications for each constraint okay these<00:07:53.039> numbers<00:07:53.160> of<00:07:53.460> course<00:07:53.580> depend<00:07:53.880> on<00:07:54.000> the 00:07:54.110 --> 00:07:54.120 align:start position:0% these numbers of course depend on the 00:07:54.120 --> 00:07:55.490 align:start position:0% these numbers of course depend on the circuit<00:07:54.360> and<00:07:54.599> depend<00:07:54.780> what<00:07:54.960> you're<00:07:55.080> doing<00:07:55.319> and 00:07:55.490 --> 00:07:55.500 align:start position:0% circuit and depend what you're doing and 00:07:55.500 --> 00:07:57.469 align:start position:0% circuit and depend what you're doing and so<00:07:55.620> on<00:07:55.740> but<00:07:55.919> this<00:07:56.099> is<00:07:56.280> just<00:07:56.460> would<00:07:57.000> say<00:07:57.180> it 00:07:57.469 --> 00:07:57.479 align:start position:0% so on but this is just would say it 00:07:57.479 --> 00:08:00.170 align:start position:0% so on but this is just would say it would<00:07:57.660> be<00:07:57.780> a<00:07:57.960> good<00:07:58.020> example<00:07:58.380> of<00:07:58.680> a<00:07:59.180> zkbm 00:08:00.170 --> 00:08:00.180 align:start position:0% would be a good example of a zkbm 00:08:00.180 --> 00:08:03.249 align:start position:0% would be a good example of a zkbm circuit-like<00:08:00.960> okay<00:08:01.440> it's<00:08:01.860> a<00:08:02.039> big<00:08:02.160> circuit 00:08:03.249 --> 00:08:03.259 align:start position:0% circuit-like okay it's a big circuit 00:08:03.259 --> 00:08:07.010 align:start position:0% circuit-like okay it's a big circuit okay<00:08:04.259> so<00:08:04.979> for<00:08:05.280> this<00:08:05.400> is<00:08:05.699> okay<00:08:06.180> here<00:08:06.539> let's<00:08:06.780> see 00:08:07.010 --> 00:08:07.020 align:start position:0% okay so for this is okay here let's see 00:08:07.020 --> 00:08:10.550 align:start position:0% okay so for this is okay here let's see how<00:08:07.620> much<00:08:07.740> boot<00:08:08.340> it<00:08:08.400> costs<00:08:08.759> this<00:08:09.360> uh<00:08:10.259> in<00:08:10.440> in 00:08:10.550 --> 00:08:10.560 align:start position:0% how much boot it costs this uh in in 00:08:10.560 --> 00:08:13.309 align:start position:0% how much boot it costs this uh in in number<00:08:11.220> of<00:08:11.340> constraints<00:08:11.880> here<00:08:12.599> of<00:08:12.840> course<00:08:12.960> the 00:08:13.309 --> 00:08:13.319 align:start position:0% number of constraints here of course the 00:08:13.319 --> 00:08:15.770 align:start position:0% number of constraints here of course the transcript<00:08:13.800> is<00:08:14.039> not<00:08:14.280> that<00:08:14.520> much<00:08:14.699> the<00:08:15.360> checking 00:08:15.770 --> 00:08:15.780 align:start position:0% transcript is not that much the checking 00:08:15.780 --> 00:08:18.170 align:start position:0% transcript is not that much the checking the<00:08:15.900> polynomial<00:08:16.380> constraints<00:08:16.979> uh<00:08:17.639> uh<00:08:18.000> at<00:08:18.000> the 00:08:18.170 --> 00:08:18.180 align:start position:0% the polynomial constraints uh uh at the 00:08:18.180 --> 00:08:21.650 align:start position:0% the polynomial constraints uh uh at the random<00:08:18.419> Point<00:08:18.660> well<00:08:19.199> it's<00:08:19.800> start<00:08:20.460> to<00:08:20.639> being<00:08:20.879> an 00:08:21.650 --> 00:08:21.660 align:start position:0% random Point well it's start to being an 00:08:21.660 --> 00:08:24.110 align:start position:0% random Point well it's start to being an important<00:08:22.139> number<00:08:22.319> but<00:08:22.560> not<00:08:22.740> that<00:08:22.979> much<00:08:23.160> uh 00:08:24.110 --> 00:08:24.120 align:start position:0% important number but not that much uh 00:08:24.120 --> 00:08:25.850 align:start position:0% important number but not that much uh the<00:08:24.360> number<00:08:24.479> of<00:08:24.660> queries<00:08:25.139> we<00:08:25.440> have<00:08:25.560> so<00:08:25.740> many 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position:0% linear hash of the evaluations and then 00:08:31.020 --> 00:08:33.050 align:start position:0% linear hash of the evaluations and then do<00:08:31.199> the<00:08:31.319> miracle<00:08:31.620> lights<00:08:31.800> but<00:08:32.279> this<00:08:32.459> is<00:08:32.640> this 00:08:33.050 --> 00:08:33.060 align:start position:0% do the miracle lights but this is this 00:08:33.060 --> 00:08:35.029 align:start position:0% do the miracle lights but this is this is<00:08:33.180> just<00:08:33.419> for<00:08:33.719> the<00:08:33.899> the<00:08:34.140> queries<00:08:34.620> the<00:08:34.860> first 00:08:35.029 --> 00:08:35.039 align:start position:0% is just for the the queries the first 00:08:35.039 --> 00:08:37.250 align:start position:0% is just for the the queries the first query<00:08:35.279> is<00:08:35.459> not<00:08:35.580> in<00:08:35.700> the<00:08:35.880> fry<00:08:36.120> yet<00:08:36.300> but<00:08:36.899> for<00:08:37.080> the 00:08:37.250 --> 00:08:37.260 align:start position:0% query is not in the fry yet but for the 00:08:37.260 --> 00:08:38.810 align:start position:0% query is not in the fry yet but for the first<00:08:37.380> queries<00:08:37.800> of<00:08:37.979> all<00:08:38.099> the<00:08:38.219> polynomials 00:08:38.810 --> 00:08:38.820 align:start position:0% first queries of all the polynomials 00:08:38.820 --> 00:08:41.449 align:start position:0% first queries of all the polynomials this<00:08:39.479> is<00:08:39.659> our<00:08:39.839> DOT<00:08:40.260> and<00:08:40.740> here<00:08:40.979> is<00:08:41.099> the<00:08:41.339> big 00:08:41.449 --> 00:08:41.459 align:start position:0% this is our DOT and here is the big 00:08:41.459 --> 00:08:43.130 align:start position:0% this is our DOT and here is the big probably<00:08:41.760> the<00:08:42.060> biggest<00:08:42.180> part<00:08:42.479> okay<00:08:42.839> the 00:08:43.130 --> 00:08:43.140 align:start position:0% probably the biggest part okay the 00:08:43.140 --> 00:08:45.110 align:start position:0% probably the biggest part okay the biggest<00:08:43.260> part<00:08:43.620> is<00:08:44.099> when<00:08:44.279> we<00:08:44.459> need<00:08:44.580> to<00:08:44.700> compute 00:08:45.110 --> 00:08:45.120 align:start position:0% biggest part is when we need to compute 00:08:45.120 --> 00:08:48.130 align:start position:0% biggest part is when we need to compute this<00:08:45.560> opening<00:08:46.560> point<00:08:46.740> polynomial 00:08:48.130 --> 00:08:48.140 align:start position:0% this opening point polynomial 00:08:48.140 --> 00:08:50.870 align:start position:0% this opening point polynomial there<00:08:49.140> are<00:08:49.260> so<00:08:49.380> many<00:08:49.500> polynomials<00:08:50.220> we<00:08:50.640> need<00:08:50.760> to 00:08:50.870 --> 00:08:50.880 align:start position:0% there are so many polynomials we need to 00:08:50.880 --> 00:08:53.150 align:start position:0% there are so many polynomials we need to do<00:08:50.940> so<00:08:51.120> many<00:08:51.240> multiplications<00:08:51.959> out<00:08:52.860> of<00:08:52.980> the 00:08:53.150 --> 00:08:53.160 align:start position:0% do so many multiplications out of the 00:08:53.160 --> 00:08:56.030 align:start position:0% do so many multiplications out of the field<00:08:53.339> that<00:08:54.000> this<00:08:54.120> is<00:08:54.300> a<00:08:54.420> number<00:08:54.660> that<00:08:54.959> grows<00:08:55.380> a 00:08:56.030 --> 00:08:56.040 align:start position:0% field that this is a number that grows a 00:08:56.040 --> 00:08:58.550 align:start position:0% field that this is a number that grows a lot<00:08:56.160> okay<00:08:56.459> and<00:08:56.880> here<00:08:57.060> is<00:08:57.240> the<00:08:57.480> the<00:08:57.720> big<00:08:57.959> part<00:08:58.200> of 00:08:58.550 --> 00:08:58.560 align:start position:0% lot okay and here is the the big part of 00:08:58.560 --> 00:09:01.610 align:start position:0% lot okay and here is the the big part of the<00:08:58.680> proof<00:08:58.980> is<00:08:59.100> this<00:08:59.459> 112<00:09:00.360> Millions 00:09:01.610 --> 00:09:01.620 align:start position:0% the proof is this 112 Millions 00:09:01.620 --> 00:09:03.769 align:start position:0% the proof is this 112 Millions what<00:09:02.040> else<00:09:02.160> we<00:09:02.399> have<00:09:02.519> we<00:09:02.880> have<00:09:03.060> the<00:09:03.240> well<00:09:03.540> this 00:09:03.769 --> 00:09:03.779 align:start position:0% what else we have we have the well this 00:09:03.779 --> 00:09:05.690 align:start position:0% what else we have we have the well this is<00:09:03.899> the<00:09:03.959> queries<00:09:04.320> of<00:09:04.440> the<00:09:04.560> fry<00:09:04.860> here<00:09:05.339> are<00:09:05.580> the 00:09:05.690 --> 00:09:05.700 align:start position:0% is the queries of the fry here are the 00:09:05.700 --> 00:09:08.990 align:start position:0% is the queries of the fry here are the ffts<00:09:06.660> the<00:09:07.019> the<00:09:07.620> the<00:09:07.740> polynomial<00:09:08.580> ovulations 00:09:08.990 --> 00:09:09.000 align:start position:0% ffts the the the polynomial ovulations 00:09:09.000 --> 00:09:11.150 align:start position:0% ffts the the the polynomial ovulations the<00:09:09.300> entities<00:09:09.540> to<00:09:10.200> going<00:09:10.380> deep<00:09:10.620> in<00:09:10.740> the<00:09:10.920> fry 00:09:11.150 --> 00:09:11.160 align:start position:0% the entities to going deep in the fry 00:09:11.160 --> 00:09:13.370 align:start position:0% the entities to going deep in the fry and<00:09:11.580> the<00:09:11.820> final<00:09:11.940> and<00:09:12.480> the<00:09:12.660> final<00:09:12.779> and<00:09:13.080> the 00:09:13.370 --> 00:09:13.380 align:start position:0% and the final and the final and the 00:09:13.380 --> 00:09:16.070 align:start position:0% and the final and the final and the final<00:09:13.560> polynomial<00:09:14.360> evaluation<00:09:15.360> so<00:09:15.839> this 00:09:16.070 --> 00:09:16.080 align:start position:0% final polynomial evaluation so this 00:09:16.080 --> 00:09:19.610 align:start position:0% final polynomial evaluation so this gives<00:09:16.440> us<00:09:16.620> something<00:09:17.339> that's<00:09:17.700> huge<00:09:18.120> is<00:09:18.660> 127 00:09:19.610 --> 00:09:19.620 align:start position:0% gives us something that's huge is 127 00:09:19.620 --> 00:09:24.050 align:start position:0% gives us something that's huge is 127 million<00:09:20.399> constraints<00:09:20.880> but<00:09:21.920> it's<00:09:22.920> it's<00:09:23.580> doable 00:09:24.050 --> 00:09:24.060 align:start position:0% million constraints but it's it's doable 00:09:24.060 --> 00:09:25.970 align:start position:0% million constraints but it's it's doable this<00:09:24.540> is<00:09:24.660> a<00:09:24.899> circuit<00:09:25.320> that's<00:09:25.500> for<00:09:25.680> example<00:09:25.800> the 00:09:25.970 --> 00:09:25.980 align:start position:0% this is a circuit that's for example the 00:09:25.980 --> 00:09:28.490 align:start position:0% this is a circuit that's for example the Hermes<00:09:26.399> one<00:09:26.640> circuit<00:09:27.240> had<00:09:27.899> this<00:09:28.140> number<00:09:28.320> of 00:09:28.490 --> 00:09:28.500 align:start position:0% Hermes one circuit had this number of 00:09:28.500 --> 00:09:31.610 align:start position:0% Hermes one circuit had this number of constraints<00:09:29.100> more<00:09:29.760> or<00:09:29.880> less<00:09:30.000> so<00:09:30.779> and<00:09:31.140> you<00:09:31.500> can 00:09:31.610 --> 00:09:31.620 align:start position:0% constraints more or less so and you can 00:09:31.620 --> 00:09:34.970 align:start position:0% constraints more or less so and you can do<00:09:32.279> that<00:09:32.519> in<00:09:32.820> about<00:09:33.060> 100<00:09:33.360> seconds<00:09:33.839> in<00:09:34.380> a<00:09:34.620> big 00:09:34.970 --> 00:09:34.980 align:start position:0% do that in about 100 seconds in a big 00:09:34.980 --> 00:09:37.370 align:start position:0% do that in about 100 seconds in a big CPU<00:09:35.459> okay<00:09:35.820> so<00:09:36.060> in<00:09:36.240> Rapid<00:09:36.360> snark<00:09:36.899> so<00:09:37.260> that's 00:09:37.370 --> 00:09:37.380 align:start position:0% CPU okay so in Rapid snark so that's 00:09:37.380 --> 00:09:39.769 align:start position:0% CPU okay so in Rapid snark so that's something<00:09:37.560> that's<00:09:38.040> doable<00:09:39.000> but<00:09:39.480> you<00:09:39.720> know 00:09:39.769 --> 00:09:39.779 align:start position:0% something that's doable but you know 00:09:39.779 --> 00:09:42.290 align:start position:0% something that's doable but you know it's<00:09:40.019> going<00:09:40.260> to<00:09:40.380> be<00:09:40.440> a<00:09:40.560> big<00:09:40.680> circuit<00:09:41.100> okay 00:09:42.290 --> 00:09:42.300 align:start position:0% it's going to be a big circuit okay 00:09:42.300 --> 00:09:45.949 align:start position:0% it's going to be a big circuit okay the<00:09:42.839> thing<00:09:43.019> is<00:09:43.200> that<00:09:43.880> with<00:09:44.880> uh 00:09:45.949 --> 00:09:45.959 align:start position:0% the thing is that with uh 00:09:45.959 --> 00:09:48.829 align:start position:0% the thing is that with uh uh<00:09:46.800> what<00:09:47.580> we<00:09:47.760> can<00:09:47.880> do<00:09:48.000> the<00:09:48.180> technique<00:09:48.480> that<00:09:48.720> we 00:09:48.829 --> 00:09:48.839 align:start position:0% uh what we can do the technique that we 00:09:48.839 --> 00:09:50.509 align:start position:0% uh what we can do the technique that we are<00:09:48.959> using<00:09:49.140> is<00:09:49.320> that<00:09:49.500> instead<00:09:49.920> of<00:09:50.040> having<00:09:50.279> a 00:09:50.509 --> 00:09:50.519 align:start position:0% are using is that instead of having a 00:09:50.519 --> 00:09:52.910 align:start position:0% are using is that instead of having a snark<00:09:50.820> so<00:09:51.180> we<00:09:51.300> have<00:09:51.480> a<00:09:51.660> we<00:09:52.560> have<00:09:52.620> this<00:09:52.740> big 00:09:52.910 --> 00:09:52.920 align:start position:0% snark so we have a we have this big 00:09:52.920 --> 00:09:55.009 align:start position:0% snark so we have a we have this big circuit<00:09:53.220> so<00:09:53.459> instead<00:09:53.820> of<00:09:54.000> this<00:09:54.300> proving 00:09:55.009 --> 00:09:55.019 align:start position:0% circuit so instead of this proving 00:09:55.019 --> 00:09:57.170 align:start position:0% circuit so instead of this proving directly<00:09:55.380> with<00:09:55.680> a<00:09:55.860> snark<00:09:56.160> what<00:09:56.760> you<00:09:56.880> can<00:09:57.000> do<00:09:57.120> is 00:09:57.170 --> 00:09:57.180 align:start position:0% directly with a snark what you can do is 00:09:57.180 --> 00:09:59.090 align:start position:0% directly with a snark what you can do is you<00:09:57.420> can<00:09:57.540> do<00:09:57.720> different<00:09:57.899> level<00:09:58.140> of<00:09:58.440> different 00:09:59.090 --> 00:09:59.100 align:start position:0% you can do different level of different 00:09:59.100 --> 00:10:01.550 align:start position:0% you can do different level of different levels<00:09:59.519> of<00:09:59.640> recursion<00:10:00.120> so<00:10:00.540> you<00:10:00.660> can<00:10:00.839> build<00:10:01.019> a 00:10:01.550 --> 00:10:01.560 align:start position:0% levels of recursion so you can build a 00:10:01.560 --> 00:10:03.889 align:start position:0% levels of recursion so you can build a Stark<00:10:01.800> that<00:10:02.100> verifies<00:10:02.519> another<00:10:02.700> Stark<00:10:03.180> so<00:10:03.660> you 00:10:03.889 --> 00:10:03.899 align:start position:0% Stark that verifies another Stark so you 00:10:03.899 --> 00:10:05.930 align:start position:0% Stark that verifies another Stark so you get<00:10:04.080> a<00:10:04.200> proof<00:10:04.500> that's<00:10:04.680> much<00:10:04.980> smaller<00:10:05.399> maybe 00:10:05.930 --> 00:10:05.940 align:start position:0% get a proof that's much smaller maybe 00:10:05.940 --> 00:10:08.210 align:start position:0% get a proof that's much smaller maybe you<00:10:06.180> you<00:10:06.420> can<00:10:06.600> do<00:10:06.779> repeat<00:10:07.019> that<00:10:07.320> again<00:10:07.560> you<00:10:08.040> do 00:10:08.210 --> 00:10:08.220 align:start position:0% you you can do repeat that again you do 00:10:08.220 --> 00:10:10.730 align:start position:0% you you can do repeat that again you do another<00:10:08.459> Stark<00:10:09.060> that<00:10:09.480> verifies<00:10:09.839> the<00:10:10.080> Stark<00:10:10.320> so 00:10:10.730 --> 00:10:10.740 align:start position:0% another Stark that verifies the Stark so 00:10:10.740 --> 00:10:12.949 align:start position:0% another Stark that verifies the Stark so you<00:10:10.860> get<00:10:11.100> even<00:10:11.279> a<00:10:11.580> smaller<00:10:11.880> proof<00:10:12.240> and<00:10:12.660> at<00:10:12.839> the 00:10:12.949 --> 00:10:12.959 align:start position:0% you get even a smaller proof and at the 00:10:12.959 --> 00:10:15.710 align:start position:0% you get even a smaller proof and at the end<00:10:13.080> you<00:10:13.500> can<00:10:13.620> have<00:10:13.980> a 00:10:15.710 --> 00:10:15.720 align:start position:0% end you can have a 00:10:15.720 --> 00:10:18.050 align:start position:0% end you can have a a<00:10:16.140> final<00:10:16.320> proof<00:10:16.800> that<00:10:17.220> can<00:10:17.399> be<00:10:17.580> much<00:10:17.820> much<00:10:18.060> much 00:10:18.050 --> 00:10:18.060 align:start position:0% a final proof that can be much much much 00:10:18.060 --> 00:10:20.269 align:start position:0% a final proof that can be much much much smaller 00:10:20.269 --> 00:10:20.279 align:start position:0% smaller 00:10:20.279 --> 00:10:23.630 align:start position:0% smaller okay<00:10:20.760> and<00:10:21.600> this<00:10:22.140> is<00:10:22.260> this<00:10:22.680> is<00:10:22.800> actually<00:10:23.040> more 00:10:23.630 --> 00:10:23.640 align:start position:0% okay and this is this is actually more 00:10:23.640 --> 00:10:25.730 align:start position:0% okay and this is this is actually more or<00:10:23.760> less<00:10:23.880> what<00:10:24.120> we<00:10:24.240> are<00:10:24.420> doing<00:10:24.600> here<00:10:25.019> is<00:10:25.200> here<00:10:25.620> I 00:10:25.730 --> 00:10:25.740 align:start position:0% or less what we are doing here is here I 00:10:25.740 --> 00:10:27.290 align:start position:0% or less what we are doing here is here I put<00:10:25.860> you<00:10:26.040> the<00:10:26.220> real<00:10:26.459> numbers<00:10:26.700> of<00:10:27.000> the<00:10:27.120> current 00:10:27.290 --> 00:10:27.300 align:start position:0% put you the real numbers of the current 00:10:27.300 --> 00:10:29.269 align:start position:0% put you the real numbers of the current structure<00:10:27.899> this<00:10:28.440> is<00:10:28.560> a<00:10:28.740> structure<00:10:29.040> of<00:10:29.160> the 00:10:29.269 --> 00:10:29.279 align:start position:0% structure this is a structure of the 00:10:29.279 --> 00:10:31.009 align:start position:0% structure this is a structure of the proverb<00:10:29.640> that<00:10:29.760> we<00:10:29.880> are<00:10:30.000> running<00:10:30.120> right<00:10:30.420> now<00:10:30.600> in 00:10:31.009 --> 00:10:31.019 align:start position:0% proverb that we are running right now in 00:10:31.019 --> 00:10:33.290 align:start position:0% proverb that we are running right now in the<00:10:31.200> public<00:10:31.320> test<00:10:31.560> net<00:10:31.800> okay<00:10:32.279> so<00:10:32.820> this<00:10:33.000> is<00:10:33.120> a 00:10:33.290 --> 00:10:33.300 align:start position:0% the public test net okay so this is a 00:10:33.300 --> 00:10:36.590 align:start position:0% the public test net okay so this is a three<00:10:33.540> steps<00:10:34.019> okay<00:10:34.740> the<00:10:35.339> first<00:10:35.459> step<00:10:35.820> is<00:10:36.180> uh 00:10:36.590 --> 00:10:36.600 align:start position:0% three steps okay the first step is uh 00:10:36.600 --> 00:10:38.690 align:start position:0% three steps okay the first step is uh with<00:10:36.959> this<00:10:37.140> number<00:10:37.320> of<00:10:37.440> polynomials<00:10:38.100> but<00:10:38.339> you 00:10:38.690 --> 00:10:38.700 align:start position:0% with this number of polynomials but you 00:10:38.700 --> 00:10:40.370 align:start position:0% with this number of polynomials but you need<00:10:38.880> to<00:10:38.940> count<00:10:39.180> that<00:10:39.420> this<00:10:39.540> it's<00:10:39.720> about<00:10:39.899> 1000 00:10:40.370 --> 00:10:40.380 align:start position:0% need to count that this it's about 1000 00:10:40.380 --> 00:10:42.350 align:start position:0% need to count that this it's about 1000 polynomials<00:10:40.980> but<00:10:41.100> then<00:10:41.220> we<00:10:41.339> have<00:10:41.519> 43<00:10:42.060> block 00:10:42.350 --> 00:10:42.360 align:start position:0% polynomials but then we have 43 block 00:10:42.360 --> 00:10:44.569 align:start position:0% polynomials but then we have 43 block apps<00:10:42.779> one<00:10:43.200> permutation<00:10:43.740> check<00:10:43.920> but<00:10:44.220> we<00:10:44.399> have 00:10:44.569 --> 00:10:44.579 align:start position:0% apps one permutation check but we have 00:10:44.579 --> 00:10:46.310 align:start position:0% apps one permutation check but we have different<00:10:44.820> different<00:10:45.420> properties<00:10:45.899> so<00:10:46.140> this 00:10:46.310 --> 00:10:46.320 align:start position:0% different different properties so this 00:10:46.320 --> 00:10:48.650 align:start position:0% different different properties so this is<00:10:46.500> a<00:10:46.740> big<00:10:47.640> circuit<00:10:48.000> we<00:10:48.240> are<00:10:48.360> working<00:10:48.480> with 00:10:48.650 --> 00:10:48.660 align:start position:0% is a big circuit we are working with 00:10:48.660 --> 00:10:51.050 align:start position:0% is a big circuit we are working with 2223<00:10:49.380> we'll<00:10:49.680> have<00:10:49.800> a<00:10:49.920> factor<00:10:50.160> of<00:10:50.279> two<00:10:50.399> here<00:10:50.940> you 00:10:51.050 --> 00:10:51.060 align:start position:0% 2223 we'll have a factor of two here you 00:10:51.060 --> 00:10:52.910 align:start position:0% 2223 we'll have a factor of two here you see<00:10:51.180> the<00:10:51.360> structure<00:10:51.779> the<00:10:52.380> way<00:10:52.620> that<00:10:52.800> the 00:10:52.910 --> 00:10:52.920 align:start position:0% see the structure the way that the 00:10:52.920 --> 00:10:55.370 align:start position:0% see the structure the way that the structure<00:10:53.459> we<00:10:53.700> are<00:10:53.880> of<00:10:54.240> the<00:10:54.420> fry<00:10:54.720> so<00:10:54.959> we<00:10:55.260> are 00:10:55.370 --> 00:10:55.380 align:start position:0% structure we are of the fry so we are 00:10:55.380 --> 00:10:57.650 align:start position:0% structure we are of the fry so we are building<00:10:55.500> the<00:10:55.740> fry<00:10:55.980> okay<00:10:56.519> so<00:10:57.000> this<00:10:57.240> goes<00:10:57.540> to 00:10:57.650 --> 00:10:57.660 align:start position:0% building the fry okay so this goes to 00:10:57.660 --> 00:10:59.630 align:start position:0% building the fry okay so this goes to another<00:10:57.899> point<00:10:58.260> so<00:10:58.620> it<00:10:58.860> goes<00:10:59.339> to<00:10:59.459> another 00:10:59.630 --> 00:10:59.640 align:start position:0% another point so it goes to another 00:10:59.640 --> 00:11:01.490 align:start position:0% another point so it goes to another proof<00:11:00.120> second<00:11:00.540> proof<00:11:00.899> is<00:11:01.019> a<00:11:01.140> proof<00:11:01.380> that's 00:11:01.490 --> 00:11:01.500 align:start position:0% proof second proof is a proof that's 00:11:01.500 --> 00:11:04.670 align:start position:0% proof second proof is a proof that's much<00:11:01.800> smaller<00:11:02.279> it's<00:11:02.820> just<00:11:03.120> uh<00:11:03.480> 20<00:11:03.839> polynomials 00:11:04.670 --> 00:11:04.680 align:start position:0% much smaller it's just uh 20 polynomials 00:11:04.680 --> 00:11:08.750 align:start position:0% much smaller it's just uh 20 polynomials with<00:11:05.160> uh<00:11:05.779> sorry<00:11:06.779> 12<00:11:07.500> polynomials<00:11:08.220> 20<00:11:08.459> of<00:11:08.700> them 00:11:08.750 --> 00:11:08.760 align:start position:0% with uh sorry 12 polynomials 20 of them 00:11:08.760 --> 00:11:11.389 align:start position:0% with uh sorry 12 polynomials 20 of them are<00:11:08.940> constant<00:11:09.380> uh<00:11:10.380> 10<00:11:10.620> in<00:11:10.800> terminatory 00:11:11.389 --> 00:11:11.399 align:start position:0% are constant uh 10 in terminatory 00:11:11.399 --> 00:11:13.430 align:start position:0% are constant uh 10 in terminatory polynomials<00:11:12.000> no<00:11:12.300> block<00:11:12.540> ups<00:11:12.959> just<00:11:13.200> one 00:11:13.430 --> 00:11:13.440 align:start position:0% polynomials no block ups just one 00:11:13.440 --> 00:11:16.370 align:start position:0% polynomials no block ups just one connection<00:11:13.620> check<00:11:14.100> and<00:11:15.060> uh 00:11:16.370 --> 00:11:16.380 align:start position:0% connection check and uh 00:11:16.380 --> 00:11:19.910 align:start position:0% connection check and uh yep<00:11:17.040> and<00:11:17.519> 23<00:11:18.000> 23<00:11:18.540> identities<00:11:19.140> and<00:11:19.500> then<00:11:19.620> we<00:11:19.800> do 00:11:19.910 --> 00:11:19.920 align:start position:0% yep and 23 23 identities and then we do 00:11:19.920 --> 00:11:22.670 align:start position:0% yep and 23 23 identities and then we do go<00:11:20.160> to<00:11:20.279> the<00:11:20.519> third<00:11:20.700> one<00:11:20.880> this<00:11:21.600> is<00:11:21.720> also<00:11:22.079> you<00:11:22.500> see 00:11:22.670 --> 00:11:22.680 align:start position:0% go to the third one this is also you see 00:11:22.680 --> 00:11:24.889 align:start position:0% go to the third one this is also you see here<00:11:22.860> it<00:11:23.040> is<00:11:23.160> the<00:11:23.339> GL<00:11:23.519> GL<00:11:23.940> means<00:11:24.360> Road<00:11:24.480> Delux 00:11:24.889 --> 00:11:24.899 align:start position:0% here it is the GL GL means Road Delux 00:11:24.899 --> 00:11:27.650 align:start position:0% here it is the GL GL means Road Delux this<00:11:25.140> is<00:11:25.260> a<00:11:25.500> a<00:11:25.740> a<00:11:26.160> stark<00:11:26.880> does<00:11:27.120> ability<00:11:27.360> with 00:11:27.650 --> 00:11:27.660 align:start position:0% this is a a a stark does ability with 00:11:27.660 --> 00:11:29.389 align:start position:0% this is a a a stark does ability with Goldilocks<00:11:28.260> but<00:11:28.500> the<00:11:28.680> last<00:11:28.800> one<00:11:28.920> is<00:11:29.100> built 00:11:29.389 --> 00:11:29.399 align:start position:0% Goldilocks but the last one is built 00:11:29.399 --> 00:11:32.509 align:start position:0% Goldilocks but the last one is built with<00:11:29.459> BN<00:11:29.880> 128<00:11:30.660> okay<00:11:31.140> and<00:11:31.500> the<00:11:31.680> last<00:11:31.800> one<00:11:32.040> is 00:11:32.509 --> 00:11:32.519 align:start position:0% with BN 128 okay and the last one is 00:11:32.519 --> 00:11:34.610 align:start position:0% with BN 128 okay and the last one is just<00:11:32.700> a<00:11:32.820> smaller<00:11:33.180> it's<00:11:33.300> just<00:11:33.540> 20.<00:11:34.079> it<00:11:34.320> has<00:11:34.440> only 00:11:34.610 --> 00:11:34.620 align:start position:0% just a smaller it's just 20. it has only 00:11:34.620 --> 00:11:37.069 align:start position:0% just a smaller it's just 20. it has only 12<00:11:34.860> polynomials<00:11:35.640> but<00:11:36.180> the<00:11:36.360> and<00:11:36.600> the<00:11:36.720> size<00:11:36.839> of 00:11:37.069 --> 00:11:37.079 align:start position:0% 12 polynomials but the and the size of 00:11:37.079 --> 00:11:39.850 align:start position:0% 12 polynomials but the and the size of the<00:11:37.200> polynomial<00:11:37.620> is<00:11:37.920> 2<00:11:38.220> to<00:11:38.459> the<00:11:38.640> this<00:11:39.000> is<00:11:39.360> just 00:11:39.850 --> 00:11:39.860 align:start position:0% the polynomial is 2 to the this is just 00:11:39.860 --> 00:11:46.430 align:start position:0% the polynomial is 2 to the this is just 24<00:11:41.000> uh<00:11:42.500> so<00:11:43.500> 2<00:11:43.680> to<00:11:43.860> 24.<00:11:44.399> It's<00:11:45.360> 22<00:11:45.779> and<00:11:46.140> the<00:11:46.260> double 00:11:46.430 --> 00:11:46.440 align:start position:0% 24 uh so 2 to 24. It's 22 and the double 00:11:46.440 --> 00:11:49.430 align:start position:0% 24 uh so 2 to 24. It's 22 and the double factor<00:11:46.920> of<00:11:47.040> 4<00:11:47.220> in<00:11:47.700> this<00:11:47.820> case<00:11:47.940> we<00:11:48.600> could<00:11:48.779> do<00:11:49.260> it 00:11:49.430 --> 00:11:49.440 align:start position:0% factor of 4 in this case we could do it 00:11:49.440 --> 00:11:52.190 align:start position:0% factor of 4 in this case we could do it smaller<00:11:50.040> okay<00:11:50.339> but<00:11:50.640> at<00:11:50.820> the<00:11:51.000> end<00:11:51.060> here<00:11:51.779> is<00:11:51.959> a 00:11:52.190 --> 00:11:52.200 align:start position:0% smaller okay but at the end here is a 00:11:52.200 --> 00:11:53.990 align:start position:0% smaller okay but at the end here is a compromise<00:11:52.740> sometimes<00:11:53.279> you<00:11:53.399> you<00:11:53.579> get<00:11:53.880> it 00:11:53.990 --> 00:11:54.000 align:start position:0% compromise sometimes you you get it 00:11:54.000 --> 00:11:56.030 align:start position:0% compromise sometimes you you get it smaller<00:11:54.420> but<00:11:54.600> then<00:11:54.839> the<00:11:55.200> proving<00:11:55.560> time<00:11:55.800> of 00:11:56.030 --> 00:11:56.040 align:start position:0% smaller but then the proving time of 00:11:56.040 --> 00:11:58.490 align:start position:0% smaller but then the proving time of this<00:11:56.339> smaller<00:11:57.060> is<00:11:57.480> bigger<00:11:57.779> so<00:11:57.959> at<00:11:58.140> the<00:11:58.260> end<00:11:58.380> is 00:11:58.490 --> 00:11:58.500 align:start position:0% this smaller is bigger so at the end is 00:11:58.500 --> 00:12:00.889 align:start position:0% this smaller is bigger so at the end is better<00:11:58.740> maybe<00:11:59.100> to<00:11:59.579> have<00:11:59.760> a<00:12:00.000> bigger<00:12:00.300> last 00:12:00.889 --> 00:12:00.899 align:start position:0% better maybe to have a bigger last 00:12:00.899 --> 00:12:03.050 align:start position:0% better maybe to have a bigger last circuit<00:12:01.380> that 00:12:03.050 --> 00:12:03.060 align:start position:0% circuit that 00:12:03.060 --> 00:12:07.250 align:start position:0% circuit that it's<00:12:03.540> a<00:12:03.720> bigger<00:12:03.959> last<00:12:04.079> circuit<00:12:04.579> than<00:12:05.600> uh<00:12:06.600> that 00:12:07.250 --> 00:12:07.260 align:start position:0% it's a bigger last circuit than uh that 00:12:07.260 --> 00:12:08.930 align:start position:0% it's a bigger last circuit than uh that just<00:12:07.380> squeezing<00:12:07.920> to<00:12:08.100> the<00:12:08.220> end<00:12:08.399> through<00:12:08.760> the 00:12:08.930 --> 00:12:08.940 align:start position:0% just squeezing to the end through the 00:12:08.940 --> 00:12:12.350 align:start position:0% just squeezing to the end through the smaller<00:12:09.360> and<00:12:09.779> keeping<00:12:10.200> uh<00:12:10.800> uh<00:12:11.339> and<00:12:12.000> keeping 00:12:12.350 --> 00:12:12.360 align:start position:0% smaller and keeping uh uh and keeping 00:12:12.360 --> 00:12:14.150 align:start position:0% smaller and keeping uh uh and keeping bigger<00:12:12.600> so<00:12:12.779> this<00:12:12.899> is<00:12:13.079> our<00:12:13.260> balances<00:12:13.920> and 00:12:14.150 --> 00:12:14.160 align:start position:0% bigger so this is our balances and 00:12:14.160 --> 00:12:17.090 align:start position:0% bigger so this is our balances and checking<00:12:14.579> what's<00:12:14.880> the<00:12:15.120> best<00:12:15.240> structure<00:12:15.800> uh<00:12:16.800> uh 00:12:17.090 --> 00:12:17.100 align:start position:0% checking what's the best structure uh uh 00:12:17.100 --> 00:12:20.990 align:start position:0% checking what's the best structure uh uh on<00:12:17.579> that<00:12:17.700> okay<00:12:18.240> so<00:12:18.720> if<00:12:18.899> we<00:12:19.079> go<00:12:19.320> to<00:12:19.980> more<00:12:20.220> uh 00:12:20.990 --> 00:12:21.000 align:start position:0% on that okay so if we go to more uh 00:12:21.000 --> 00:12:23.630 align:start position:0% on that okay so if we go to more uh something<00:12:21.360> that<00:12:21.779> we<00:12:22.380> can<00:12:22.500> go<00:12:22.680> far<00:12:22.980> so<00:12:23.339> that<00:12:23.519> we 00:12:23.630 --> 00:12:23.640 align:start position:0% something that we can go far so that we 00:12:23.640 --> 00:12:26.630 align:start position:0% something that we can go far so that we can<00:12:23.760> squeeze<00:12:24.240> more<00:12:24.420> uh<00:12:25.260> the<00:12:25.440> last<00:12:25.560> circuit<00:12:25.980> you 00:12:26.630 --> 00:12:26.640 align:start position:0% can squeeze more uh the last circuit you 00:12:26.640 --> 00:12:30.069 align:start position:0% can squeeze more uh the last circuit you can<00:12:26.820> do<00:12:27.660> well<00:12:27.899> five<00:12:28.260> can<00:12:28.560> well<00:12:29.519> let<00:12:29.760> me<00:12:29.880> just 00:12:30.069 --> 00:12:30.079 align:start position:0% can do well five can well let me just 00:12:30.079 --> 00:12:33.050 align:start position:0% can do well five can well let me just with<00:12:31.079> something<00:12:31.320> that's<00:12:31.740> 60<00:12:32.220> polynomials 00:12:33.050 --> 00:12:33.060 align:start position:0% with something that's 60 polynomials 00:12:33.060 --> 00:12:37.370 align:start position:0% with something that's 60 polynomials with<00:12:33.480> a<00:12:33.600> blower<00:12:33.899> factor<00:12:34.440> of<00:12:35.100> uh<00:12:35.579> 16<00:12:36.060> uh<00:12:36.839> so<00:12:37.140> two 00:12:37.370 --> 00:12:37.380 align:start position:0% with a blower factor of uh 16 uh so two 00:12:37.380 --> 00:12:41.210 align:start position:0% with a blower factor of uh 16 uh so two to<00:12:37.560> the<00:12:37.740> four<00:12:37.920> and<00:12:38.820> uh 00:12:41.210 --> 00:12:41.220 align:start position:0% 00:12:41.220 --> 00:12:42.430 align:start position:0% um 00:12:42.430 --> 00:12:42.440 align:start position:0% um 00:12:42.440 --> 00:12:45.110 align:start position:0% um this<00:12:43.440> you<00:12:43.620> with<00:12:44.100> this<00:12:44.279> you<00:12:44.459> just<00:12:44.639> require<00:12:44.760> 16 00:12:45.110 --> 00:12:45.120 align:start position:0% this you with this you just require 16 00:12:45.120 --> 00:12:47.569 align:start position:0% this you with this you just require 16 queries<00:12:45.660> which<00:12:45.959> is<00:12:46.079> to<00:12:46.440> having<00:12:46.680> the<00:12:46.860> same<00:12:46.980> 120 00:12:47.569 --> 00:12:47.579 align:start position:0% queries which is to having the same 120 00:12:47.579 --> 00:12:50.090 align:start position:0% queries which is to having the same 120 128<00:12:48.420> bits<00:12:48.839> uh 00:12:50.090 --> 00:12:50.100 align:start position:0% 128 bits uh 00:12:50.100 --> 00:12:53.629 align:start position:0% 128 bits uh um<00:12:50.160> security<00:12:51.139> uh<00:12:52.139> you<00:12:52.500> can<00:12:52.620> go<00:12:52.860> uh<00:12:53.100> polynomial 00:12:53.629 --> 00:12:53.639 align:start position:0% um security uh you can go uh polynomial 00:12:53.639 --> 00:12:56.150 align:start position:0% um security uh you can go uh polynomial after<00:12:53.820> overload<00:12:54.420> factor<00:12:54.720> of<00:12:54.839> 2<00:12:55.380> to<00:12:55.440> 24<00:12:55.800> so 00:12:56.150 --> 00:12:56.160 align:start position:0% after overload factor of 2 to 24 so 00:12:56.160 --> 00:12:57.530 align:start position:0% after overload factor of 2 to 24 so we'll<00:12:56.339> be<00:12:56.459> a<00:12:56.519> polynomial<00:12:56.940> of<00:12:57.000> two<00:12:57.180> to<00:12:57.300> a<00:12:57.420> 20 00:12:57.530 --> 00:12:57.540 align:start position:0% we'll be a polynomial of two to a 20 00:12:57.540 --> 00:13:00.769 align:start position:0% we'll be a polynomial of two to a 20 that<00:12:58.079> goes<00:12:58.320> to<00:12:58.380> 2<00:12:58.560> to<00:12:58.740> 24<00:12:59.120> and<00:13:00.120> yeah<00:13:00.420> this<00:13:00.660> is 00:13:00.769 --> 00:13:00.779 align:start position:0% that goes to 2 to 24 and yeah this is 00:13:00.779 --> 00:13:02.569 align:start position:0% that goes to 2 to 24 and yeah this is our<00:13:00.899> number<00:13:01.079> of<00:13:01.260> constraints<00:13:01.800> and<00:13:02.220> if<00:13:02.279> we<00:13:02.399> do 00:13:02.569 --> 00:13:02.579 align:start position:0% our number of constraints and if we do 00:13:02.579 --> 00:13:03.769 align:start position:0% our number of constraints and if we do the<00:13:02.760> numbers 00:13:03.769 --> 00:13:03.779 align:start position:0% the numbers 00:13:03.779 --> 00:13:05.870 align:start position:0% the numbers with<00:13:04.320> this<00:13:04.560> see<00:13:05.100> that<00:13:05.279> the<00:13:05.459> numbers<00:13:05.579> are 00:13:05.870 --> 00:13:05.880 align:start position:0% with this see that the numbers are 00:13:05.880 --> 00:13:08.690 align:start position:0% with this see that the numbers are getting<00:13:06.060> much<00:13:06.300> much<00:13:06.480> smaller<00:13:07.380> at<00:13:07.920> the<00:13:08.100> end<00:13:08.160> we 00:13:08.690 --> 00:13:08.700 align:start position:0% getting much much smaller at the end we 00:13:08.700 --> 00:13:10.670 align:start position:0% getting much much smaller at the end we can<00:13:08.880> if<00:13:09.240> we<00:13:09.420> add<00:13:09.600> them<00:13:09.779> all<00:13:10.019> together<00:13:10.200> we<00:13:10.560> can 00:13:10.670 --> 00:13:10.680 align:start position:0% can if we add them all together we can 00:13:10.680 --> 00:13:12.590 align:start position:0% can if we add them all together we can have<00:13:10.920> something<00:13:11.160> that's<00:13:11.579> below<00:13:12.000> 2<00:13:12.240> million 00:13:12.590 --> 00:13:12.600 align:start position:0% have something that's below 2 million 00:13:12.600 --> 00:13:14.629 align:start position:0% have something that's below 2 million constraints<00:13:13.139> and<00:13:13.860> this<00:13:14.040> is<00:13:14.160> something<00:13:14.339> that 00:13:14.629 --> 00:13:14.639 align:start position:0% constraints and this is something that 00:13:14.639 --> 00:13:16.129 align:start position:0% constraints and this is something that can<00:13:14.820> be<00:13:15.000> built<00:13:15.300> in<00:13:15.420> less<00:13:15.600> than<00:13:15.779> two<00:13:15.959> seconds 00:13:16.129 --> 00:13:16.139 align:start position:0% can be built in less than two seconds 00:13:16.139 --> 00:13:18.650 align:start position:0% can be built in less than two seconds it's<00:13:16.560> really<00:13:16.860> uh<00:13:17.579> it's<00:13:17.820> quite<00:13:18.000> insignificant 00:13:18.650 --> 00:13:18.660 align:start position:0% it's really uh it's quite insignificant 00:13:18.660 --> 00:13:22.550 align:start position:0% it's really uh it's quite insignificant uh<00:13:19.560> compared<00:13:20.100> to<00:13:20.220> the<00:13:21.180> to<00:13:21.480> the<00:13:21.660> proving<00:13:22.079> to<00:13:22.380> the 00:13:22.550 --> 00:13:22.560 align:start position:0% uh compared to the to the proving to the 00:13:22.560 --> 00:13:25.970 align:start position:0% uh compared to the to the proving to the proving<00:13:22.980> to<00:13:23.459> the<00:13:23.579> proving<00:13:23.940> time<00:13:24.480> so 00:13:25.970 --> 00:13:25.980 align:start position:0% proving to the proving time so 00:13:25.980 --> 00:13:26.569 align:start position:0% proving to the proving time so um 00:13:26.569 --> 00:13:26.579 align:start position:0% um 00:13:26.579 --> 00:13:29.930 align:start position:0% um this<00:13:27.120> is<00:13:27.240> very<00:13:27.420> much<00:13:27.660> the<00:13:28.260> the<00:13:28.800> conclusion<00:13:29.639> I 00:13:29.930 --> 00:13:29.940 align:start position:0% this is very much the the conclusion I 00:13:29.940 --> 00:13:32.090 align:start position:0% this is very much the the conclusion I just<00:13:30.060> put<00:13:30.240> this<00:13:30.420> a<00:13:30.600> slide<00:13:30.779> from<00:13:30.959> the<00:13:31.019> ckbm<00:13:31.680> but 00:13:32.090 --> 00:13:32.100 align:start position:0% just put this a slide from the ckbm but 00:13:32.100 --> 00:13:34.790 align:start position:0% just put this a slide from the ckbm but this<00:13:32.339> is<00:13:32.519> uh<00:13:32.880> the<00:13:33.060> full<00:13:33.240> just<00:13:33.779> to<00:13:33.959> to<00:13:34.320> to<00:13:34.500> to 00:13:34.790 --> 00:13:34.800 align:start position:0% this is uh the full just to to to to 00:13:34.800 --> 00:13:36.470 align:start position:0% this is uh the full just to to to to explain<00:13:35.100> you<00:13:35.459> what<00:13:35.700> are<00:13:35.820> the<00:13:35.940> current<00:13:36.120> times 00:13:36.470 --> 00:13:36.480 align:start position:0% explain you what are the current times 00:13:36.480 --> 00:13:40.129 align:start position:0% explain you what are the current times of<00:13:37.260> the<00:13:37.440> of<00:13:37.680> the<00:13:37.920> full<00:13:38.160> ckvm<00:13:38.940> improver<00:13:39.300> okay<00:13:39.839> so 00:13:40.129 --> 00:13:40.139 align:start position:0% of the of the full ckvm improver okay so 00:13:40.139 --> 00:13:44.210 align:start position:0% of the of the full ckvm improver okay so currently<00:13:40.560> in<00:13:41.279> an<00:13:41.660> uh<00:13:42.660> in<00:13:43.440> uh 00:13:44.210 --> 00:13:44.220 align:start position:0% currently in an uh in uh 00:13:44.220 --> 00:13:47.949 align:start position:0% currently in an uh in uh big<00:13:44.820> machine<00:13:45.060> you<00:13:45.600> know<00:13:45.660> this<00:13:45.899> is<00:13:46.019> a<00:13:46.200> 192<00:13:47.040> cores 00:13:47.949 --> 00:13:47.959 align:start position:0% big machine you know this is a 192 cores 00:13:47.959 --> 00:13:51.290 align:start position:0% big machine you know this is a 192 cores uh<00:13:48.959> machine<00:13:49.260> uh<00:13:50.040> it's<00:13:50.279> uh<00:13:50.459> ten<00:13:50.700> dollars<00:13:51.000> per 00:13:51.290 --> 00:13:51.300 align:start position:0% uh machine uh it's uh ten dollars per 00:13:51.300 --> 00:13:56.030 align:start position:0% uh machine uh it's uh ten dollars per hour<00:13:51.620> machine<00:13:52.620> uh<00:13:53.339> more<00:13:53.579> or<00:13:53.639> less<00:13:53.700> in<00:13:53.880> AWS<00:13:54.420> okay 00:13:56.030 --> 00:13:56.040 align:start position:0% hour machine uh more or less in AWS okay 00:13:56.040 --> 00:14:00.410 align:start position:0% hour machine uh more or less in AWS okay um<00:13:56.600> the<00:13:57.600> this<00:13:58.260> proof<00:13:58.740> it<00:13:58.860> takes<00:13:59.160> nine<00:13:59.579> minutes 00:14:00.410 --> 00:14:00.420 align:start position:0% um the this proof it takes nine minutes 00:14:00.420 --> 00:14:03.829 align:start position:0% um the this proof it takes nine minutes okay<00:14:01.279> uh<00:14:02.279> we<00:14:02.579> can<00:14:02.700> well<00:14:02.940> you<00:14:03.180> can<00:14:03.300> process<00:14:03.600> four 00:14:03.829 --> 00:14:03.839 align:start position:0% okay uh we can well you can process four 00:14:03.839 --> 00:14:06.530 align:start position:0% okay uh we can well you can process four million<00:14:04.139> gas<00:14:04.380> in<00:14:04.980> this<00:14:05.220> proof<00:14:05.639> so<00:14:05.940> this<00:14:06.300> would 00:14:06.530 --> 00:14:06.540 align:start position:0% million gas in this proof so this would 00:14:06.540 --> 00:14:08.569 align:start position:0% million gas in this proof so this would be<00:14:06.720> equivalent<00:14:07.620> more<00:14:07.980> or<00:14:08.100> less<00:14:08.160> a<00:14:08.279> cost<00:14:08.399> per 00:14:08.569 --> 00:14:08.579 align:start position:0% be equivalent more or less a cost per 00:14:08.579 --> 00:14:10.670 align:start position:0% be equivalent more or less a cost per transaction<00:14:08.940> will<00:14:09.240> be<00:14:09.420> less<00:14:09.660> than<00:14:09.899> a<00:14:10.079> cent<00:14:10.380> so 00:14:10.670 --> 00:14:10.680 align:start position:0% transaction will be less than a cent so 00:14:10.680 --> 00:14:13.610 align:start position:0% transaction will be less than a cent so zero<00:14:11.399> seven<00:14:11.519> cents<00:14:11.820> per<00:14:12.360> dollar<00:14:12.600> but<00:14:13.260> you<00:14:13.440> see 00:14:13.610 --> 00:14:13.620 align:start position:0% zero seven cents per dollar but you see 00:14:13.620 --> 00:14:16.970 align:start position:0% zero seven cents per dollar but you see that<00:14:13.920> this<00:14:14.820> is<00:14:15.060> actually<00:14:15.540> uh<00:14:16.320> it's<00:14:16.620> a<00:14:16.740> proof 00:14:16.970 --> 00:14:16.980 align:start position:0% that this is actually uh it's a proof 00:14:16.980 --> 00:14:18.590 align:start position:0% that this is actually uh it's a proof that's<00:14:17.100> actually<00:14:17.339> running<00:14:17.639> the<00:14:18.240> public 00:14:18.590 --> 00:14:18.600 align:start position:0% that's actually running the public 00:14:18.600 --> 00:14:20.930 align:start position:0% that's actually running the public that's<00:14:18.899> not<00:14:19.139> is<00:14:19.320> running<00:14:19.620> so<00:14:20.040> and<00:14:20.459> you<00:14:20.639> can<00:14:20.760> see 00:14:20.930 --> 00:14:20.940 align:start position:0% that's not is running so and you can see 00:14:20.940 --> 00:14:23.150 align:start position:0% that's not is running so and you can see the<00:14:21.180> code<00:14:21.300> and<00:14:21.600> see<00:14:21.839> how<00:14:22.019> the<00:14:22.200> approver<00:14:22.560> works 00:14:23.150 --> 00:14:23.160 align:start position:0% the code and see how the approver works 00:14:23.160 --> 00:14:26.389 align:start position:0% the code and see how the approver works and<00:14:23.339> when<00:14:23.639> you<00:14:23.880> can<00:14:24.000> build<00:14:24.720> your<00:14:24.959> proof<00:14:25.380> uh<00:14:26.100> in 00:14:26.389 --> 00:14:26.399 align:start position:0% and when you can build your proof uh in 00:14:26.399 --> 00:14:30.050 align:start position:0% and when you can build your proof uh in there<00:14:26.639> okay<00:14:27.240> this<00:14:28.079> is<00:14:28.260> just<00:14:28.560> a<00:14:29.100> CPU<00:14:29.519> approver 00:14:30.050 --> 00:14:30.060 align:start position:0% there okay this is just a CPU approver 00:14:30.060 --> 00:14:33.769 align:start position:0% there okay this is just a CPU approver and<00:14:30.720> here<00:14:30.959> there<00:14:31.200> is<00:14:31.440> lots<00:14:32.399> of<00:14:32.459> margins<00:14:33.060> to<00:14:33.540> to 00:14:33.769 --> 00:14:33.779 align:start position:0% and here there is lots of margins to to 00:14:33.779 --> 00:14:37.310 align:start position:0% and here there is lots of margins to to improve<00:14:34.500> here<00:14:34.860> from<00:14:35.160> GPU<00:14:35.880> we<00:14:36.839> expect<00:14:36.959> maybe 00:14:37.310 --> 00:14:37.320 align:start position:0% improve here from GPU we expect maybe 00:14:37.320 --> 00:14:41.030 align:start position:0% improve here from GPU we expect maybe one<00:14:37.560> order<00:14:37.740> of<00:14:37.980> magnitude<00:14:38.459> faster<00:14:39.199> and<00:14:40.199> fpgas 00:14:41.030 --> 00:14:41.040 align:start position:0% one order of magnitude faster and fpgas 00:14:41.040 --> 00:14:44.810 align:start position:0% one order of magnitude faster and fpgas the<00:14:41.579> new<00:14:42.000> CPUs<00:14:42.540> are<00:14:42.959> doing<00:14:43.680> are<00:14:44.100> performing 00:14:44.810 --> 00:14:44.820 align:start position:0% the new CPUs are doing are performing 00:14:44.820 --> 00:14:46.850 align:start position:0% the new CPUs are doing are performing much<00:14:45.000> better<00:14:45.240> yeah<00:14:46.199> there<00:14:46.440> are<00:14:46.560> a<00:14:46.620> lot<00:14:46.740> of 00:14:46.850 --> 00:14:46.860 align:start position:0% much better yeah there are a lot of 00:14:46.860 --> 00:14:48.350 align:start position:0% much better yeah there are a lot of things<00:14:47.040> that<00:14:47.279> that<00:14:47.459> are<00:14:47.639> happening<00:14:47.940> but<00:14:48.120> this 00:14:48.350 --> 00:14:48.360 align:start position:0% things that that are happening but this 00:14:48.360 --> 00:14:50.750 align:start position:0% things that that are happening but this is<00:14:48.480> just<00:14:48.720> a<00:14:48.959> a<00:14:49.740> have<00:14:50.040> you<00:14:50.160> want<00:14:50.339> some<00:14:50.519> numbers 00:14:50.750 --> 00:14:50.760 align:start position:0% is just a a have you want some numbers 00:14:50.760 --> 00:14:53.350 align:start position:0% is just a a have you want some numbers some<00:14:51.180> idea<00:14:51.660> of<00:14:52.320> where<00:14:52.440> the<00:14:52.620> approving<00:14:53.100> times 00:14:53.350 --> 00:14:53.360 align:start position:0% some idea of where the approving times 00:14:53.360 --> 00:14:57.290 align:start position:0% some idea of where the approving times uh<00:14:54.360> are<00:14:55.040> on<00:14:56.040> the<00:14:56.399> direct<00:14:56.519> question<00:14:56.820> another 00:14:57.290 --> 00:14:57.300 align:start position:0% uh are on the direct question another 00:14:57.300 --> 00:14:59.389 align:start position:0% uh are on the direct question another thing<00:14:57.660> that's<00:14:57.899> not<00:14:58.079> here<00:14:58.320> but<00:14:58.620> somebody 00:14:59.389 --> 00:14:59.399 align:start position:0% thing that's not here but somebody 00:14:59.399 --> 00:15:02.110 align:start position:0% thing that's not here but somebody already<00:14:59.760> put<00:15:00.000> it<00:15:00.120> in<00:15:00.360> for<00:15:00.899> and<00:15:01.440> is<00:15:01.740> that 00:15:02.110 --> 00:15:02.120 align:start position:0% already put it in for and is that 00:15:02.120 --> 00:15:05.829 align:start position:0% already put it in for and is that verifying<00:15:03.120> a<00:15:03.300> growth<00:15:03.660> 16<00:15:03.839> in<00:15:04.740> evm<00:15:05.220> this<00:15:05.519> is 00:15:05.829 --> 00:15:05.839 align:start position:0% verifying a growth 16 in evm this is 00:15:05.839 --> 00:15:10.250 align:start position:0% verifying a growth 16 in evm this is 200k<00:15:07.339> around<00:15:08.339> 200k<00:15:09.000> gas<00:15:09.240> which<00:15:09.899> is<00:15:10.079> probably 00:15:10.250 --> 00:15:10.260 align:start position:0% 200k around 200k gas which is probably 00:15:10.260 --> 00:15:12.470 align:start position:0% 200k around 200k gas which is probably the<00:15:10.500> cheapest<00:15:10.980> way<00:15:11.279> the<00:15:11.699> cheapest<00:15:12.000> thing<00:15:12.180> that 00:15:12.470 --> 00:15:12.480 align:start position:0% the cheapest way the cheapest thing that 00:15:12.480 --> 00:15:14.810 align:start position:0% the cheapest way the cheapest thing that you<00:15:12.720> can<00:15:12.839> that<00:15:13.440> you<00:15:13.620> can<00:15:13.680> do<00:15:13.800> plonk<00:15:14.220> is<00:15:14.339> 300K 00:15:14.810 --> 00:15:14.820 align:start position:0% you can that you can do plonk is 300K 00:15:14.820 --> 00:15:16.910 align:start position:0% you can that you can do plonk is 300K which<00:15:15.120> is<00:15:15.240> not<00:15:15.420> that<00:15:15.600> much<00:15:15.779> you<00:15:16.560> save<00:15:16.740> the 00:15:16.910 --> 00:15:16.920 align:start position:0% which is not that much you save the 00:15:16.920 --> 00:15:19.129 align:start position:0% which is not that much you save the truth<00:15:17.220> so<00:15:17.880> probably<00:15:18.060> it's<00:15:18.240> going<00:15:18.420> to<00:15:18.540> be<00:15:18.540> the 00:15:19.129 --> 00:15:19.139 align:start position:0% truth so probably it's going to be the 00:15:19.139 --> 00:15:22.490 align:start position:0% truth so probably it's going to be the options<00:15:19.680> that<00:15:20.100> we<00:15:20.279> will<00:15:20.459> put<00:15:21.060> it<00:15:21.240> in<00:15:21.360> mainnet 00:15:22.490 --> 00:15:22.500 align:start position:0% options that we will put it in mainnet 00:15:22.500 --> 00:15:24.290 align:start position:0% options that we will put it in mainnet and<00:15:22.920> yeah<00:15:23.040> that's<00:15:23.279> mainly<00:15:23.579> my<00:15:23.760> presentation<00:15:24.120> I 00:15:24.290 --> 00:15:24.300 align:start position:0% and yeah that's mainly my presentation I 00:15:24.300 --> 00:15:25.850 align:start position:0% and yeah that's mainly my presentation I don't<00:15:24.420> know<00:15:24.480> if<00:15:24.600> there<00:15:24.720> are<00:15:24.839> questions 00:15:25.850 --> 00:15:25.860 align:start position:0% don't know if there are questions 00:15:25.860 --> 00:15:26.370 align:start position:0% don't know if there are questions thank<00:15:26.279> you 00:15:26.370 --> 00:15:26.380 align:start position:0% thank you 00:15:26.380 --> 00:15:32.210 align:start position:0% thank you [Applause]