WEBVTT Kind: captions Language: en 00:00:01.070 --> 00:00:12.690 align:start position:0% [Applause] 00:00:12.690 --> 00:00:12.700 align:start position:0% 00:00:12.700 --> 00:00:16.540 align:start position:0% welcome<00:00:13.700> everyone<00:00:13.940> to<00:00:14.090> the<00:00:14.330> open<00:00:14.840> zkp<00:00:15.590> worship 00:00:16.540 --> 00:00:16.550 align:start position:0% welcome everyone to the open zkp worship 00:00:16.550 --> 00:00:20.109 align:start position:0% welcome everyone to the open zkp worship we're<00:00:16.670> always<00:00:16.790> showing<00:00:18.099> the<00:00:19.119> starting 00:00:20.109 --> 00:00:20.119 align:start position:0% we're always showing the starting 00:00:20.119 --> 00:00:22.950 align:start position:0% we're always showing the starting computation<00:00:20.720> that<00:00:21.349> we<00:00:21.590> recently<00:00:22.009> announced 00:00:22.950 --> 00:00:22.960 align:start position:0% computation that we recently announced 00:00:22.960 --> 00:00:25.569 align:start position:0% computation that we recently announced so<00:00:23.960> it's<00:00:24.290> building<00:00:24.529> in<00:00:24.740> rust<00:00:24.980> that<00:00:25.189> anyone 00:00:25.569 --> 00:00:25.579 align:start position:0% so it's building in rust that anyone 00:00:25.579 --> 00:00:28.600 align:start position:0% so it's building in rust that anyone wants<00:00:25.910> to<00:00:25.970> go<00:00:26.210> to<00:00:26.270> I<00:00:26.930> really<00:00:27.919> recommend<00:00:28.489> that 00:00:28.600 --> 00:00:28.610 align:start position:0% wants to go to I really recommend that 00:00:28.610 --> 00:00:30.909 align:start position:0% wants to go to I really recommend that you<00:00:28.880> get<00:00:29.060> through<00:00:29.360> these<00:00:29.599> commands<00:00:30.169> right<00:00:30.649> now 00:00:30.909 --> 00:00:30.919 align:start position:0% you get through these commands right now 00:00:30.919 --> 00:00:34.300 align:start position:0% you get through these commands right now because<00:00:31.700> it<00:00:31.970> will<00:00:32.090> download<00:00:32.470> the<00:00:33.470> relative<00:00:34.220> to 00:00:34.300 --> 00:00:34.310 align:start position:0% because it will download the relative to 00:00:34.310 --> 00:00:37.900 align:start position:0% because it will download the relative to the<00:00:34.399> line<00:00:34.520> principles<00:00:35.170> and<00:00:36.170> even<00:00:36.910> the 00:00:37.900 --> 00:00:37.910 align:start position:0% the line principles and even the 00:00:37.910 --> 00:00:40.660 align:start position:0% the line principles and even the conference<00:00:38.390> Wi-Fi<00:00:38.800> you<00:00:39.800> might<00:00:39.980> wanna<00:00:40.190> do<00:00:40.489> this 00:00:40.660 --> 00:00:40.670 align:start position:0% conference Wi-Fi you might wanna do this 00:00:40.670 --> 00:00:41.259 align:start position:0% conference Wi-Fi you might wanna do this now 00:00:41.259 --> 00:00:41.269 align:start position:0% now 00:00:41.269 --> 00:00:43.000 align:start position:0% now I'll<00:00:41.750> keep<00:00:41.929> this<00:00:42.109> tech<00:00:42.350> stuff<00:00:42.559> in<00:00:42.739> every 00:00:43.000 --> 00:00:43.010 align:start position:0% I'll keep this tech stuff in every 00:00:43.010 --> 00:00:44.830 align:start position:0% I'll keep this tech stuff in every single<00:00:43.160> slide<00:00:43.519> so<00:00:43.969> you<00:00:44.000> don't<00:00:44.449> have<00:00:44.660> to 00:00:44.830 --> 00:00:44.840 align:start position:0% single slide so you don't have to 00:00:44.840 --> 00:00:46.930 align:start position:0% single slide so you don't have to remember<00:00:45.199> ever<00:00:45.620> cut<00:00:45.800> it<00:00:45.920> down<00:00:46.100> last<00:00:46.489> numbers 00:00:46.930 --> 00:00:46.940 align:start position:0% remember ever cut it down last numbers 00:00:46.940 --> 00:00:51.830 align:start position:0% remember ever cut it down last numbers just<00:00:47.239> don't<00:00:47.719> wait<00:00:47.809> while<00:00:47.989> I'm<00:00:48.109> talking<00:00:49.719> so 00:00:51.830 --> 00:00:51.840 align:start position:0% just don't wait while I'm talking so 00:00:51.840 --> 00:00:52.950 align:start position:0% just don't wait while I'm talking so [Music] 00:00:52.950 --> 00:00:52.960 align:start position:0% [Music] 00:00:52.960 --> 00:00:58.419 align:start position:0% [Music] come<00:00:53.960> onto<00:00:54.109> the<00:00:54.320> upper<00:00:54.469> right<00:00:54.589> corner<00:00:57.429> also 00:00:58.419 --> 00:00:58.429 align:start position:0% come onto the upper right corner also 00:00:58.429 --> 00:01:00.700 align:start position:0% come onto the upper right corner also I'm<00:00:59.179> assuming<00:00:59.719> that<00:00:59.899> if<00:01:00.140> you're<00:01:00.260> coding<00:01:00.409> along 00:01:00.700 --> 00:01:00.710 align:start position:0% I'm assuming that if you're coding along 00:01:00.710 --> 00:01:03.910 align:start position:0% I'm assuming that if you're coding along you're<00:01:00.949> familiar<00:01:01.159> with<00:01:01.489> rust<00:01:01.969> if<00:01:02.659> not<00:01:02.960> you'll 00:01:03.910 --> 00:01:03.920 align:start position:0% you're familiar with rust if not you'll 00:01:03.920 --> 00:01:07.090 align:start position:0% you're familiar with rust if not you'll be<00:01:03.949> fine<00:01:04.280> just<00:01:04.309> listening<00:01:05.680> so<00:01:06.680> what<00:01:06.860> is<00:01:06.980> the 00:01:07.090 --> 00:01:07.100 align:start position:0% be fine just listening so what is the 00:01:07.100 --> 00:01:11.410 align:start position:0% be fine just listening so what is the zero<00:01:07.310> knowledge<00:01:07.870> protocol<00:01:09.550> essentially<00:01:10.550> you 00:01:11.410 --> 00:01:11.420 align:start position:0% zero knowledge protocol essentially you 00:01:11.420 --> 00:01:14.050 align:start position:0% zero knowledge protocol essentially you have<00:01:11.600> a<00:01:11.630> thing<00:01:12.020> that<00:01:12.260> is<00:01:12.409> a<00:01:12.440> claim<00:01:12.820> which<00:01:13.820> you 00:01:14.050 --> 00:01:14.060 align:start position:0% have a thing that is a claim which you 00:01:14.060 --> 00:01:16.539 align:start position:0% have a thing that is a claim which you can<00:01:14.270> prove<00:01:14.649> given<00:01:15.649> some<00:01:15.920> additional 00:01:16.539 --> 00:01:16.549 align:start position:0% can prove given some additional 00:01:16.549 --> 00:01:19.899 align:start position:0% can prove given some additional information<00:01:16.759> call<00:01:17.600> a<00:01:17.810> witness<00:01:18.649> or<00:01:18.829> a<00:01:19.280> private 00:01:19.899 --> 00:01:19.909 align:start position:0% information call a witness or a private 00:01:19.909 --> 00:01:23.710 align:start position:0% information call a witness or a private income<00:01:20.210> or<00:01:20.689> to<00:01:21.200> secret<00:01:21.619> and<00:01:22.610> that<00:01:23.119> results<00:01:23.600> in 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smaller than a witness and 00:01:31.759 --> 00:01:34.209 align:start position:0% proving so smaller than a witness and you<00:01:32.030> can<00:01:32.329> verify<00:01:32.630> this<00:01:32.930> thing<00:01:33.469> so<00:01:33.710> you<00:01:33.740> can<00:01:34.040> if 00:01:34.209 --> 00:01:34.219 align:start position:0% you can verify this thing so you can if 00:01:34.219 --> 00:01:36.219 align:start position:0% you can verify this thing so you can if you<00:01:34.310> have<00:01:34.340> a<00:01:34.490> claim<00:01:34.759> and<00:01:35.600> you<00:01:35.659> have<00:01:35.899> a<00:01:35.930> proof 00:01:36.219 --> 00:01:36.229 align:start position:0% you have a claim and you have a proof 00:01:36.229 --> 00:01:40.240 align:start position:0% you have a claim and you have a proof you<00:01:37.189> can<00:01:37.340> verify<00:01:37.610> it<00:01:38.140> you<00:01:39.140> can<00:01:39.350> make<00:01:39.500> sure<00:01:39.530> that 00:01:40.240 --> 00:01:40.250 align:start position:0% you can verify it you can make sure that 00:01:40.250 --> 00:01:45.310 align:start position:0% you can verify it you can make sure that indeed<00:01:40.969> any<00:01:41.750> witness<00:01:42.430> exists<00:01:43.750> that<00:01:44.750> satisfies 00:01:45.310 --> 00:01:45.320 align:start position:0% indeed any witness exists that satisfies 00:01:45.320 --> 00:01:49.450 align:start position:0% indeed any witness exists that satisfies this<00:01:45.500> claim<00:01:45.740> I'll<00:01:46.729> give<00:01:46.939> an<00:01:47.060> example<00:01:47.680> now<00:01:48.680> the 00:01:49.450 --> 00:01:49.460 align:start position:0% this claim I'll give an example now the 00:01:49.460 --> 00:01:51.580 align:start position:0% this claim I'll give an example now the particular<00:01:49.640> kind<00:01:50.329> of<00:01:50.630> chrome<00:01:50.990> that<00:01:51.380> we 00:01:51.580 --> 00:01:51.590 align:start position:0% particular kind of chrome that we 00:01:51.590 --> 00:01:55.029 align:start position:0% particular kind of chrome that we implement<00:01:52.159> here<00:01:52.490> is<00:01:52.850> a<00:01:53.180> start<00:01:54.049> this<00:01:54.829> is<00:01:55.009> a 00:01:55.029 --> 00:01:55.039 align:start position:0% implement here is a start this is a 00:01:55.039 --> 00:01:57.580 align:start position:0% implement here is a start this is a protocol<00:01:55.549> family<00:01:55.899> developed<00:01:56.899> by<00:01:57.079> elephants 00:01:57.580 --> 00:01:57.590 align:start position:0% protocol family developed by elephants 00:01:57.590 --> 00:02:00.279 align:start position:0% protocol family developed by elephants and<00:01:58.039> make<00:01:58.670> you<00:01:58.759> only<00:01:58.909> observe<00:01:59.359> near<00:01:59.780> Goldberg 00:02:00.279 --> 00:02:00.289 align:start position:0% and make you only observe near Goldberg 00:02:00.289 --> 00:02:01.870 align:start position:0% and make you only observe near Goldberg and<00:02:00.590> father 00:02:01.870 --> 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position:0% working on this for a long while and high-quality<00:02:09.649> protocol<00:02:10.460> variants<00:02:10.940> and 00:02:11.080 --> 00:02:11.090 align:start position:0% high-quality protocol variants and 00:02:11.090 --> 00:02:12.850 align:start position:0% high-quality protocol variants and implementations<00:02:11.840> of<00:02:12.050> this<00:02:12.440> particular 00:02:12.850 --> 00:02:12.860 align:start position:0% implementations of this particular 00:02:12.860 --> 00:02:15.280 align:start position:0% implementations of this particular protocol<00:02:13.400> family<00:02:13.550> are<00:02:14.000> made<00:02:14.330> by<00:02:14.600> start<00:02:15.080> work 00:02:15.280 --> 00:02:15.290 align:start position:0% protocol family are made by start work 00:02:15.290 --> 00:02:18.040 align:start position:0% protocol family are made by start work so<00:02:15.700> you<00:02:16.700> shout<00:02:17.030> out<00:02:17.240> to<00:02:17.420> them<00:02:17.570> for<00:02:17.600> all<00:02:17.930> the 00:02:18.040 --> 00:02:18.050 align:start position:0% so you shout out to them for all the 00:02:18.050 --> 00:02:19.620 align:start position:0% so you shout out to them for all the amazing<00:02:18.230> work<00:02:18.590> they've<00:02:18.800> done<00:02:18.830> in<00:02:19.130> this<00:02:19.250> field 00:02:19.620 --> 00:02:19.630 align:start position:0% amazing work they've done in this field 00:02:19.630 --> 00:02:22.870 align:start position:0% amazing work they've done in this field open<00:02:20.630> start<00:02:20.930> is<00:02:21.170> an<00:02:21.410> independent<00:02:22.070> and<00:02:22.280> partial 00:02:22.870 --> 00:02:22.880 align:start position:0% open start is an independent and partial 00:02:22.880 --> 00:02:25.540 align:start position:0% open start is an independent and partial implementation<00:02:23.260> of<00:02:24.260> the<00:02:24.500> specific<00:02:25.220> start 00:02:25.540 --> 00:02:25.550 align:start position:0% implementation of the specific start 00:02:25.550 --> 00:02:31.510 align:start position:0% implementation of the specific start variant<00:02:26.000> used<00:02:26.360> in<00:02:26.630> the<00:02:26.720> startx<00:02:27.200> them<00:02:29.530> so<00:02:30.530> why 00:02:31.510 --> 00:02:31.520 align:start position:0% variant used in the startx them so why 00:02:31.520 --> 00:02:33.580 align:start position:0% variant used in the startx them so why stars<00:02:31.880> stocks<00:02:32.540> have<00:02:32.750> some<00:02:32.930> very<00:02:33.260> interesting 00:02:33.580 --> 00:02:33.590 align:start position:0% stars stocks have some very interesting 00:02:33.590 --> 00:02:35.530 align:start position:0% stars stocks have some very interesting and<00:02:34.070> unique<00:02:34.190> qualities<00:02:34.820> they<00:02:35.120> have<00:02:35.300> no 00:02:35.530 --> 00:02:35.540 align:start position:0% and unique qualities they have no 00:02:35.540 --> 00:02:38.160 align:start position:0% and unique qualities they have no trusted<00:02:35.959> setup<00:02:36.290> they<00:02:36.890> require<00:02:37.640> only 00:02:38.160 --> 00:02:38.170 align:start position:0% trusted setup they require only 00:02:38.170 --> 00:02:41.590 align:start position:0% trusted setup they require only elementary<00:02:39.170> mark<00:02:40.300> because<00:02:41.300> of<00:02:41.330> their 00:02:41.590 --> 00:02:41.600 align:start position:0% elementary mark because of their 00:02:41.600 --> 00:02:44.170 align:start position:0% elementary mark because of their simplicity<00:02:41.840> they've<00:02:42.680> had<00:02:42.920> very<00:02:43.190> good<00:02:43.850> proof 00:02:44.170 --> 00:02:44.180 align:start position:0% simplicity they've had very good proof 00:02:44.180 --> 00:02:47.130 align:start position:0% simplicity they've had very good proof or<00:02:44.390> in<00:02:44.540> verifier<00:02:45.020> performance<00:02:45.709> they<00:02:46.459> have 00:02:47.130 --> 00:02:47.140 align:start position:0% or in verifier performance they have 00:02:47.140 --> 00:02:50.350 align:start position:0% or in verifier performance they have small<00:02:48.140> proves<00:02:48.440> not<00:02:49.070> fighting<00:02:49.489> not<00:02:49.640> as<00:02:49.970> tiny<00:02:50.239> as 00:02:50.350 --> 00:02:50.360 align:start position:0% small proves not fighting not as tiny as 00:02:50.360 --> 00:02:52.449 align:start position:0% small proves not fighting not as tiny as the<00:02:50.600> proof<00:02:50.810> you<00:02:50.989> can<00:02:51.170> get<00:02:51.350> using<00:02:51.650> bearing 00:02:52.449 --> 00:02:52.459 align:start position:0% the proof you can get using bearing 00:02:52.459 --> 00:02:55.900 align:start position:0% the proof you can get using bearing cryptography<00:02:53.090> constructions<00:02:54.640> but<00:02:55.640> this 00:02:55.900 --> 00:02:55.910 align:start position:0% cryptography constructions but this 00:02:55.910 --> 00:02:59.560 align:start position:0% cryptography constructions but this comes<00:02:56.090> with<00:02:56.300> a<00:02:56.709> Gabi<00:02:57.709> they<00:02:58.580> have<00:02:58.760> a<00:02:58.790> unique<00:02:59.150> but 00:02:59.560 --> 00:02:59.570 align:start position:0% comes with a Gabi they have a unique but 00:02:59.570 --> 00:03:01.630 align:start position:0% comes with a Gabi they have a unique but completely<00:03:00.080> different<00:03:00.380> constraint<00:03:01.190> system 00:03:01.630 --> 00:03:01.640 align:start position:0% completely different constraint system 00:03:01.640 --> 00:03:03.370 align:start position:0% completely different constraint system from<00:03:01.940> everything<00:03:02.420> you<00:03:02.570> are<00:03:02.600> used<00:03:02.870> to<00:03:02.959> and<00:03:03.140> this 00:03:03.370 --> 00:03:03.380 align:start position:0% from everything you are used to and this 00:03:03.380 --> 00:03:05.259 align:start position:0% from everything you are used to and this makes<00:03:03.620> them<00:03:03.800> so<00:03:03.980> interesting<00:03:04.010> so<00:03:04.610> study<00:03:05.030> and 00:03:05.259 --> 00:03:05.269 align:start position:0% makes them so interesting so study and 00:03:05.269 --> 00:03:10.180 align:start position:0% makes them so interesting so study and play<00:03:05.900> around<00:03:07.840> so<00:03:08.840> quick<00:03:09.320> over<00:03:09.620> to<00:03:09.739> you<00:03:09.830> of<00:03:10.010> how 00:03:10.180 --> 00:03:10.190 align:start position:0% play around so quick over to you of how 00:03:10.190 --> 00:03:12.650 align:start position:0% play around so quick over to you of how these<00:03:10.370> things 00:03:12.650 --> 00:03:12.660 align:start position:0% these things 00:03:12.660 --> 00:03:14.270 align:start position:0% these things and<00:03:12.930> to<00:03:13.020> prove<00:03:13.200> that<00:03:13.260> the<00:03:13.470> program<00:03:13.980> has 00:03:14.270 --> 00:03:14.280 align:start position:0% and to prove that the program has 00:03:14.280 --> 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thick<00:03:23.280> tape<00:03:23.960> now<00:03:24.960> this<00:03:25.740> trace 00:03:26.030 --> 00:03:26.040 align:start position:0% trace in a thick tape now this trace 00:03:26.040 --> 00:03:28.820 align:start position:0% trace in a thick tape now this trace also<00:03:26.610> contains<00:03:26.940> your<00:03:27.000> privately<00:03:27.600> so<00:03:28.290> this 00:03:28.820 --> 00:03:28.830 align:start position:0% also contains your privately so this 00:03:28.830 --> 00:03:31.820 align:start position:0% also contains your privately so this table<00:03:29.010> is<00:03:29.220> sort<00:03:29.400> of<00:03:29.430> secret<00:03:29.850> but<00:03:30.810> we<00:03:31.470> want<00:03:31.680> to 00:03:31.820 --> 00:03:31.830 align:start position:0% table is sort of secret but we want to 00:03:31.830 --> 00:03:34.910 align:start position:0% table is sort of secret but we want to have<00:03:32.760> a<00:03:32.790> prove<00:03:33.120> and<00:03:33.420> binds<00:03:33.810> you<00:03:34.260> to<00:03:34.740> this 00:03:34.910 --> 00:03:34.920 align:start position:0% have a prove and binds you to this 00:03:34.920 --> 00:03:37.340 align:start position:0% have a prove and binds you to this particular<00:03:35.250> trait<00:03:35.670> and<00:03:35.970> in<00:03:36.630> starts<00:03:36.990> we<00:03:37.170> do 00:03:37.340 --> 00:03:37.350 align:start position:0% particular trait and in starts we do 00:03:37.350 --> 00:03:41.570 align:start position:0% particular trait and in starts we do this<00:03:37.530> by<00:03:37.860> creating<00:03:37.920> several<00:03:39.170> equations<00:03:40.580> which 00:03:41.570 --> 00:03:41.580 align:start position:0% this by creating several equations which 00:03:41.580 --> 00:03:44.090 align:start position:0% this by creating several equations which you<00:03:41.970> will<00:03:42.390> evaluate<00:03:42.690> over<00:03:43.320> the<00:03:43.470> traced<00:03:43.710> able 00:03:44.090 --> 00:03:44.100 align:start position:0% you will evaluate over the traced able 00:03:44.100 --> 00:03:47.420 align:start position:0% you will evaluate over the traced able to<00:03:44.820> prove<00:03:45.060> that<00:03:45.120> the<00:03:45.540> disk<00:03:45.750> array<00:03:46.400> will<00:03:47.400> be 00:03:47.420 --> 00:03:47.430 align:start position:0% to prove that the disk array will be 00:03:47.430 --> 00:03:52.700 align:start position:0% to prove that the disk array will be even<00:03:47.760> explicitly<00:03:48.420> say<00:03:49.380> simulated<00:03:51.530> but<00:03:52.530> it 00:03:52.700 --> 00:03:52.710 align:start position:0% even explicitly say simulated but it 00:03:52.710 --> 00:03:54.410 align:start position:0% even explicitly say simulated but it will<00:03:52.800> not<00:03:52.950> only<00:03:53.040> need<00:03:53.220> to<00:03:53.340> do<00:03:53.460> that<00:03:53.730> hey<00:03:53.940> every 00:03:54.410 --> 00:03:54.420 align:start position:0% will not only need to do that hey every 00:03:54.420 --> 00:03:57.290 align:start position:0% will not only need to do that hey every next<00:03:54.720> row<00:03:55.170> effort<00:03:55.860> every<00:03:56.220> next<00:03:56.550> row<00:03:56.760> needs<00:03:57.090> to 00:03:57.290 --> 00:03:57.300 align:start position:0% next row effort every next row needs to 00:03:57.300 --> 00:03:59.060 align:start position:0% next row effort every next row needs to contain<00:03:57.570> to<00:03:57.810> someone<00:03:58.170> we've<00:03:58.380> used<00:03:58.620> two<00:03:58.800> rows 00:03:59.060 --> 00:03:59.070 align:start position:0% contain to someone we've used two rows 00:03:59.070 --> 00:04:02.330 align:start position:0% contain to someone we've used two rows more<00:03:59.550> and<00:04:00.000> so<00:04:00.180> on<00:04:00.530> or<00:04:01.530> you<00:04:01.650> can<00:04:01.800> say<00:04:01.980> that<00:04:02.190> it 00:04:02.330 --> 00:04:02.340 align:start position:0% more and so on or you can say that it 00:04:02.340 --> 00:04:03.580 align:start position:0% more and so on or you can say that it needs<00:04:02.490> to<00:04:02.580> be<00:04:02.670> equal<00:04:02.970> to<00:04:03.090> a<00:04:03.120> particular<00:04:03.240> value 00:04:03.580 --> 00:04:03.590 align:start position:0% needs to be equal to a particular value 00:04:03.590 --> 00:04:07.310 align:start position:0% needs to be equal to a particular value so<00:04:05.090> big<00:04:06.090> slightly<00:04:06.420> big<00:04:06.570> scariest<00:04:06.930> I<00:04:07.020> don't 00:04:07.310 --> 00:04:07.320 align:start position:0% so big slightly big scariest I don't 00:04:07.320 --> 00:04:09.770 align:start position:0% so big slightly big scariest I don't worry<00:04:07.440> they'll<00:04:07.650> go<00:04:07.740> to<00:04:07.770> a<00:04:07.920> bit<00:04:08.190> byte<00:04:08.780> what 00:04:09.770 --> 00:04:09.780 align:start position:0% worry they'll go to a bit byte what 00:04:09.780 --> 00:04:13.100 align:start position:0% worry they'll go to a bit byte what we're<00:04:09.870> gonna<00:04:09.960> do<00:04:10.230> is<00:04:10.500> fibonacci<00:04:11.280> so<00:04:12.210> quite<00:04:12.930> the 00:04:13.100 --> 00:04:13.110 align:start position:0% we're gonna do is fibonacci so quite the 00:04:13.110 --> 00:04:15.560 align:start position:0% we're gonna do is fibonacci so quite the nest<00:04:13.320> notation<00:04:13.980> people<00:04:14.400> not<00:04:14.550> she<00:04:14.820> is<00:04:14.970> you<00:04:15.330> have 00:04:15.560 --> 00:04:15.570 align:start position:0% nest notation people not she is you have 00:04:15.570 --> 00:04:18.590 align:start position:0% nest notation people not she is you have a<00:04:15.870> and<00:04:16.410> B<00:04:16.560> but<00:04:17.460> the<00:04:17.520> initialized<00:04:18.000> a<00:04:18.180> with<00:04:18.420> one 00:04:18.590 --> 00:04:18.600 align:start position:0% a and B but the initialized a with one 00:04:18.600 --> 00:04:21.470 align:start position:0% a and B but the initialized a with one we<00:04:19.320> initialized<00:04:19.890> B<00:04:20.190> with<00:04:20.549> on<00:04:20.880> this<00:04:21.120> case<00:04:21.270> not 00:04:21.470 --> 00:04:21.480 align:start position:0% we initialized B with on this case not 00:04:21.480 --> 00:04:25.370 align:start position:0% we initialized B with on this case not one<00:04:21.690> but<00:04:22.200> some<00:04:22.740> secret<00:04:23.070> value<00:04:23.340> right<00:04:24.260> this<00:04:25.260> is 00:04:25.370 --> 00:04:25.380 align:start position:0% one but some secret value right this is 00:04:25.380 --> 00:04:28.730 align:start position:0% one but some secret value right this is going<00:04:25.590> to<00:04:25.710> be<00:04:25.860> our<00:04:26.850> private<00:04:27.270> equity<00:04:27.330> and<00:04:27.960> then 00:04:28.730 --> 00:04:28.740 align:start position:0% going to be our private equity and then 00:04:28.740 --> 00:04:32.060 align:start position:0% going to be our private equity and then we<00:04:29.460> just<00:04:29.700> iterate<00:04:29.910> we<00:04:30.840> update<00:04:31.260> a<00:04:31.290> and<00:04:31.620> B<00:04:31.740> with 00:04:32.060 --> 00:04:32.070 align:start position:0% we just iterate we update a and B with 00:04:32.070 --> 00:04:35.270 align:start position:0% we just iterate we update a and B with the<00:04:32.970> previous<00:04:33.300> be<00:04:33.450> value<00:04:33.870> and<00:04:34.110> a<00:04:34.260> plus<00:04:34.470> B<00:04:34.650> so 00:04:35.270 --> 00:04:35.280 align:start position:0% the previous be value and a plus B so 00:04:35.280 --> 00:04:37.250 align:start position:0% the previous be value and a plus B so this<00:04:35.430> is<00:04:35.490> a<00:04:35.610> standard<00:04:36.300> Fibonacci<00:04:36.960> sequence 00:04:37.250 --> 00:04:37.260 align:start position:0% this is a standard Fibonacci sequence 00:04:37.260 --> 00:04:44.540 align:start position:0% this is a standard Fibonacci sequence and<00:04:37.950> then<00:04:38.430> we<00:04:38.730> return<00:04:39.360> a<00:04:40.130> for<00:04:41.130> some<00:04:41.730> index<00:04:43.550> so 00:04:44.540 --> 00:04:44.550 align:start position:0% and then we return a for some index so 00:04:44.550 --> 00:04:46.460 align:start position:0% and then we return a for some index so if<00:04:44.820> we<00:04:44.970> have<00:04:45.150> this<00:04:45.330> function<00:04:45.390> and<00:04:45.990> we<00:04:46.050> run<00:04:46.320> it 00:04:46.460 --> 00:04:46.470 align:start position:0% if we have this function and we run it 00:04:46.470 --> 00:04:50.120 align:start position:0% if we have this function and we run it we<00:04:46.650> can<00:04:46.740> do<00:04:47.040> through<00:04:47.970> Bonacci<00:04:48.210> the<00:04:49.170> 200<00:04:49.710> value 00:04:50.120 --> 00:04:50.130 align:start position:0% we can do through Bonacci the 200 value 00:04:50.130 --> 00:04:53.600 align:start position:0% we can do through Bonacci the 200 value starting<00:04:51.120> with<00:04:51.300> secret<00:04:51.660> value<00:04:52.380> 42<00:04:52.920> and<00:04:53.340> you'll 00:04:53.600 --> 00:04:53.610 align:start position:0% starting with secret value 42 and you'll 00:04:53.610 --> 00:04:54.980 align:start position:0% starting with secret value 42 and you'll end<00:04:53.760> up<00:04:53.880> with<00:04:53.940> a<00:04:54.090> large<00:04:54.360> number<00:04:54.660> in<00:04:54.870> this 00:04:54.980 --> 00:04:54.990 align:start position:0% end up with a large number in this 00:04:54.990 --> 00:04:58.670 align:start position:0% end up with a large number in this starts<00:04:55.350> with<00:04:55.380> one<00:04:55.860> one<00:04:55.890> nine<00:04:57.230> now<00:04:58.230> we<00:04:58.290> want<00:04:58.590> to 00:04:58.670 --> 00:04:58.680 align:start position:0% starts with one one nine now we want to 00:04:58.680 --> 00:05:02.660 align:start position:0% starts with one one nine now we want to create<00:04:58.920> a<00:04:59.190> zero<00:04:59.400> knowledge<00:05:00.320> claim<00:05:01.320> on<00:05:01.650> this<00:05:01.830> by 00:05:02.660 --> 00:05:02.670 align:start position:0% create a zero knowledge claim on this by 00:05:02.670 --> 00:05:04.070 align:start position:0% create a zero knowledge claim on this by the<00:05:02.700> way<00:05:02.790> I'm<00:05:03.000> saying<00:05:03.270> zero<00:05:03.540> knowledge<00:05:03.900> but 00:05:04.070 --> 00:05:04.080 align:start position:0% the way I'm saying zero knowledge but 00:05:04.080 --> 00:05:05.630 align:start position:0% the way I'm saying zero knowledge but actually<00:05:04.440> the<00:05:04.530> implementation<00:05:05.160> we<00:05:05.280> have<00:05:05.310> is<00:05:05.610> a 00:05:05.630 --> 00:05:05.640 align:start position:0% actually the implementation we have is a 00:05:05.640 --> 00:05:07.040 align:start position:0% actually the implementation we have is a broad<00:05:06.000> erasing 00:05:07.040 --> 00:05:07.050 align:start position:0% broad erasing 00:05:07.050 --> 00:05:11.779 align:start position:0% broad erasing and<00:05:07.800> I'll<00:05:07.949> see<00:05:08.129> rich<00:05:08.690> have<00:05:09.690> a<00:05:09.720> detail<00:05:10.669> so<00:05:11.669> we 00:05:11.779 --> 00:05:11.789 align:start position:0% and I'll see rich have a detail so we 00:05:11.789 --> 00:05:14.089 align:start position:0% and I'll see rich have a detail so we went<00:05:11.970> to<00:05:12.000> claim<00:05:12.330> that<00:05:12.629> we<00:05:12.960> know<00:05:13.229> some<00:05:13.620> number 00:05:14.089 --> 00:05:14.099 align:start position:0% went to claim that we know some number 00:05:14.099 --> 00:05:15.920 align:start position:0% went to claim that we know some number and<00:05:14.340> I'm<00:05:14.400> not<00:05:14.610> gonna<00:05:14.789> tell<00:05:15.000> you<00:05:15.150> that<00:05:15.180> it's<00:05:15.449> 42 00:05:15.920 --> 00:05:15.930 align:start position:0% and I'm not gonna tell you that it's 42 00:05:15.930 --> 00:05:18.170 align:start position:0% and I'm not gonna tell you that it's 42 is<00:05:16.470> such<00:05:16.770> that<00:05:17.009> if<00:05:17.340> we<00:05:17.550> compute<00:05:17.879> the<00:05:18.060> Fibonacci 00:05:18.170 --> 00:05:18.180 align:start position:0% is such that if we compute the Fibonacci 00:05:18.180 --> 00:05:20.629 align:start position:0% is such that if we compute the Fibonacci sequence<00:05:18.780> on<00:05:19.139> this<00:05:19.319> and<00:05:19.620> take<00:05:19.830> the<00:05:19.919> 200<00:05:20.340> value 00:05:20.629 --> 00:05:20.639 align:start position:0% sequence on this and take the 200 value 00:05:20.639 --> 00:05:23.089 align:start position:0% sequence on this and take the 200 value we<00:05:21.120> get<00:05:21.270> this<00:05:21.389> big<00:05:21.599> number<00:05:21.930> so<00:05:22.080> this<00:05:22.800> is<00:05:22.919> going 00:05:23.089 --> 00:05:23.099 align:start position:0% we get this big number so this is going 00:05:23.099 --> 00:05:24.830 align:start position:0% we get this big number so this is going to<00:05:23.220> be<00:05:23.340> our<00:05:23.580> public<00:05:24.270> claim 00:05:24.830 --> 00:05:24.840 align:start position:0% to be our public claim 00:05:24.840 --> 00:05:27.710 align:start position:0% to be our public claim all<00:05:25.650> right<00:05:25.830> so<00:05:26.789> let's<00:05:26.970> go<00:05:27.120> through<00:05:27.539> the<00:05:27.659> steps 00:05:27.710 --> 00:05:27.720 align:start position:0% all right so let's go through the steps 00:05:27.720 --> 00:05:29.719 align:start position:0% all right so let's go through the steps the<00:05:28.169> first<00:05:28.409> thing<00:05:28.590> we<00:05:28.680> need<00:05:28.800> to<00:05:28.830> do<00:05:29.069> is<00:05:29.370> create 00:05:29.719 --> 00:05:29.729 align:start position:0% the first thing we need to do is create 00:05:29.729 --> 00:05:35.390 align:start position:0% the first thing we need to do is create a<00:05:30.650> computational<00:05:31.650> trace<00:05:32.750> so<00:05:33.750> we<00:05:34.220> run<00:05:35.220> this 00:05:35.390 --> 00:05:35.400 align:start position:0% a computational trace so we run this 00:05:35.400 --> 00:05:38.809 align:start position:0% a computational trace so we run this people<00:05:35.759> not<00:05:35.909> cheat<00:05:36.120> program<00:05:36.539> and<00:05:37.550> we<00:05:38.550> write 00:05:38.809 --> 00:05:38.819 align:start position:0% people not cheat program and we write 00:05:38.819 --> 00:05:41.450 align:start position:0% people not cheat program and we write down<00:05:39.060> at<00:05:39.509> each<00:05:39.900> step<00:05:40.229> what<00:05:40.590> the<00:05:40.710> values<00:05:41.069> of<00:05:41.310> a 00:05:41.450 --> 00:05:41.460 align:start position:0% down at each step what the values of a 00:05:41.460 --> 00:05:45.020 align:start position:0% down at each step what the values of a and<00:05:41.490> B<00:05:41.909> are<00:05:42.240> so<00:05:43.139> in<00:05:43.259> the<00:05:43.379> first<00:05:43.560> row<00:05:43.740> a<00:05:44.250> is<00:05:44.550> 1<00:05:44.789> and 00:05:45.020 --> 00:05:45.030 align:start position:0% and B are so in the first row a is 1 and 00:05:45.030 --> 00:05:48.559 align:start position:0% and B are so in the first row a is 1 and B<00:05:45.120> is<00:05:45.960> our<00:05:46.229> secret<00:05:46.409> value<00:05:46.710> 42<00:05:47.610> because<00:05:48.360> we're 00:05:48.559 --> 00:05:48.569 align:start position:0% B is our secret value 42 because we're 00:05:48.569 --> 00:05:52.939 align:start position:0% B is our secret value 42 because we're calling<00:05:49.169> it<00:05:49.289> with<00:05:49.560> index<00:05:50.449> 207<00:05:51.449> 42<00:05:51.840> so<00:05:52.139> a<00:05:52.289> is<00:05:52.440> 1<00:05:52.469> B 00:05:52.939 --> 00:05:52.949 align:start position:0% calling it with index 207 42 so a is 1 B 00:05:52.949 --> 00:05:56.029 align:start position:0% calling it with index 207 42 so a is 1 B is<00:05:53.340> 42<00:05:53.879> and<00:05:54.120> then<00:05:54.599> we<00:05:54.719> go<00:05:54.840> into<00:05:54.990> those<00:05:55.169> 11<00:05:55.620> so 00:05:56.029 --> 00:05:56.039 align:start position:0% is 42 and then we go into those 11 so 00:05:56.039 --> 00:06:01.490 align:start position:0% is 42 and then we go into those 11 so for<00:05:56.310> I<00:05:56.580> in<00:05:57.000> 0<00:05:57.449> to<00:05:57.509> index<00:05:58.340> we<00:05:59.340> get<00:05:59.550> a<00:05:59.819> equals<00:06:00.419> B<00:06:00.659> so 00:06:01.490 --> 00:06:01.500 align:start position:0% for I in 0 to index we get a equals B so 00:06:01.500 --> 00:06:04.700 align:start position:0% for I in 0 to index we get a equals B so the<00:06:02.400> next<00:06:02.639> day<00:06:02.849> is<00:06:03.210> a<00:06:03.240> PBS<00:06:03.690> B<00:06:03.900> and<00:06:04.409> you<00:06:04.500> can<00:06:04.590> see 00:06:04.700 --> 00:06:04.710 align:start position:0% the next day is a PBS B and you can see 00:06:04.710 --> 00:06:07.430 align:start position:0% the next day is a PBS B and you can see that<00:06:04.889> this<00:06:05.180> happens<00:06:06.180> everywhere<00:06:06.449> and<00:06:06.810> the<00:06:07.289> new 00:06:07.430 --> 00:06:07.440 align:start position:0% that this happens everywhere and the new 00:06:07.440 --> 00:06:09.770 align:start position:0% that this happens everywhere and the new B<00:06:07.650> is<00:06:07.949> the<00:06:08.099> sum<00:06:08.280> of<00:06:08.340> the<00:06:08.580> previous<00:06:08.729> table<00:06:09.090> so 00:06:09.770 --> 00:06:09.780 align:start position:0% B is the sum of the previous table so 00:06:09.780 --> 00:06:13.550 align:start position:0% B is the sum of the previous table so this<00:06:10.409> value<00:06:10.710> here<00:06:10.919> is<00:06:11.279> 1<00:06:11.849> plus<00:06:12.120> 42<00:06:12.449> what<00:06:13.349> stream 00:06:13.550 --> 00:06:13.560 align:start position:0% this value here is 1 plus 42 what stream 00:06:13.560 --> 00:06:16.879 align:start position:0% this value here is 1 plus 42 what stream same<00:06:14.310> here<00:06:14.699> and<00:06:14.880> this<00:06:15.599> goes<00:06:15.779> on<00:06:15.990> until<00:06:16.289> we<00:06:16.680> made 00:06:16.879 --> 00:06:16.889 align:start position:0% same here and this goes on until we made 00:06:16.889 --> 00:06:19.730 align:start position:0% same here and this goes on until we made the<00:06:17.009> road<00:06:17.190> 200<00:06:17.940> and<00:06:18.389> then<00:06:18.779> we<00:06:18.900> get<00:06:19.020> our<00:06:19.440> eight 00:06:19.730 --> 00:06:19.740 align:start position:0% the road 200 and then we get our eight 00:06:19.740 --> 00:06:24.909 align:start position:0% the road 200 and then we get our eight number<00:06:20.360> that<00:06:21.360> we<00:06:21.449> want<00:06:21.630> to<00:06:22.219> demonstrate<00:06:23.750> now 00:06:24.909 --> 00:06:24.919 align:start position:0% number that we want to demonstrate now 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align:start position:0% that capture the entire nature of the problem<00:06:35.520> that<00:06:35.550> would<00:06:35.759> find<00:06:36.000> cream<00:06:36.360> and<00:06:37.370> these 00:06:38.360 --> 00:06:38.370 align:start position:0% problem that would find cream and these 00:06:38.370 --> 00:06:41.300 align:start position:0% problem that would find cream and these rules<00:06:38.699> are<00:06:39.259> written<00:06:40.259> down<00:06:40.560> here<00:06:40.800> there<00:06:41.039> they 00:06:41.300 --> 00:06:41.310 align:start position:0% rules are written down here there they 00:06:41.310 --> 00:06:45.290 align:start position:0% rules are written down here there they are<00:06:41.340> the<00:06:41.580> so-called<00:06:41.960> constraints<00:06:44.090> they<00:06:45.090> come 00:06:45.290 --> 00:06:45.300 align:start position:0% are the so-called constraints they come 00:06:45.300 --> 00:06:48.529 align:start position:0% are the so-called constraints they come in<00:06:45.560> two<00:06:46.560> basic<00:06:46.800> kinds<00:06:47.310> called<00:06:47.940> boundary 00:06:48.529 --> 00:06:48.539 align:start position:0% in two basic kinds called boundary 00:06:48.539 --> 00:06:54.499 align:start position:0% in two basic kinds called boundary constraints<00:06:49.229> and<00:06:51.860> repeating<00:06:52.860> constraints 00:06:54.499 --> 00:06:54.509 align:start position:0% constraints and repeating constraints 00:06:54.509 --> 00:06:57.840 align:start position:0% constraints and repeating constraints Adamo<00:06:55.509> constraints<00:06:56.169> are<00:06:56.259> the<00:06:56.320> first<00:06:56.639> we<00:06:57.639> need 00:06:57.840 --> 00:06:57.850 align:start position:0% Adamo constraints are the first we need 00:06:57.850 --> 00:07:02.580 align:start position:0% Adamo constraints are the first we need to<00:06:58.060> have<00:06:58.889> the<00:06:59.889> first<00:07:00.190> column<00:07:00.699> being<00:07:00.940> one<00:07:01.590> but 00:07:02.580 --> 00:07:02.590 align:start position:0% to have the first column being one but 00:07:02.590 --> 00:07:06.570 align:start position:0% to have the first column being one but only<00:07:02.970> for<00:07:03.970> row<00:07:04.150> zero<00:07:05.009> so<00:07:06.009> this<00:07:06.190> value<00:07:06.430> here 00:07:06.570 --> 00:07:06.580 align:start position:0% only for row zero so this value here 00:07:06.580 --> 00:07:09.749 align:start position:0% only for row zero so this value here needs<00:07:07.030> to<00:07:07.150> be<00:07:07.270> one<00:07:08.130> then<00:07:09.130> we<00:07:09.460> have<00:07:09.639> another 00:07:09.749 --> 00:07:09.759 align:start position:0% needs to be one then we have another 00:07:09.759 --> 00:07:11.850 align:start position:0% needs to be one then we have another boundary<00:07:10.300> constraint<00:07:10.840> similar<00:07:11.320> to<00:07:11.470> that<00:07:11.590> one 00:07:11.850 --> 00:07:11.860 align:start position:0% boundary constraint similar to that one 00:07:11.860 --> 00:07:16.110 align:start position:0% boundary constraint similar to that one that<00:07:12.400> says<00:07:12.729> that<00:07:13.289> the<00:07:14.490> first<00:07:15.490> column<00:07:15.820> needs<00:07:15.940> to 00:07:16.110 --> 00:07:16.120 align:start position:0% that says that the first column needs to 00:07:16.120 --> 00:07:19.499 align:start position:0% that says that the first column needs to be<00:07:16.240> our<00:07:16.449> big<00:07:16.660> outcome<00:07:17.110> but<00:07:18.070> only<00:07:18.310> on<00:07:18.699> road<00:07:18.970> 200 00:07:19.499 --> 00:07:19.509 align:start position:0% be our big outcome but only on road 200 00:07:19.509 --> 00:07:23.540 align:start position:0% be our big outcome but only on road 200 so<00:07:19.900> this<00:07:20.080> value<00:07:20.350> needs<00:07:21.310> to<00:07:21.490> be<00:07:21.639> our<00:07:22.060> big<00:07:22.470> and 00:07:23.540 --> 00:07:23.550 align:start position:0% so this value needs to be our big and 00:07:23.550 --> 00:07:26.969 align:start position:0% so this value needs to be our big and then<00:07:24.550> we<00:07:25.270> need<00:07:25.479> to<00:07:25.750> demonstrate<00:07:26.349> that<00:07:26.800> it 00:07:26.969 --> 00:07:26.979 align:start position:0% then we need to demonstrate that it 00:07:26.979 --> 00:07:29.610 align:start position:0% then we need to demonstrate that it actually<00:07:27.160> executed<00:07:27.940> is<00:07:28.060> the<00:07:28.240> dilute<00:07:28.570> here<00:07:28.930> so 00:07:29.610 --> 00:07:29.620 align:start position:0% actually executed is the dilute here so 00:07:29.620 --> 00:07:35.580 align:start position:0% actually executed is the dilute here so we<00:07:30.220> need<00:07:30.460> that<00:07:32.220> for<00:07:33.220> each<00:07:33.610> row<00:07:34.240> the<00:07:35.020> first 00:07:35.580 --> 00:07:35.590 align:start position:0% we need that for each row the first 00:07:35.590 --> 00:07:39.960 align:start position:0% we need that for each row the first column<00:07:36.030> is<00:07:37.030> equal<00:07:37.599> to<00:07:38.229> the<00:07:38.560> previous<00:07:38.770> row<00:07:39.280> the 00:07:39.960 --> 00:07:39.970 align:start position:0% column is equal to the previous row the 00:07:39.970 --> 00:07:42.029 align:start position:0% column is equal to the previous row the second<00:07:40.690> element<00:07:40.930> is<00:07:41.320> should<00:07:41.530> have<00:07:41.620> been<00:07:41.770> 1 00:07:42.029 --> 00:07:42.039 align:start position:0% second element is should have been 1 00:07:42.039 --> 00:07:47.400 align:start position:0% second element is should have been 1 here<00:07:42.280> so<00:07:42.310> here<00:07:42.669> of<00:07:42.789> that<00:07:44.550> and<00:07:45.690> this<00:07:46.690> holds<00:07:47.110> for 00:07:47.400 --> 00:07:47.410 align:start position:0% here so here of that and this holds for 00:07:47.410 --> 00:07:50.520 align:start position:0% here so here of that and this holds for each<00:07:47.729> row<00:07:48.729> in<00:07:48.910> this<00:07:49.060> table<00:07:49.270> so<00:07:50.229> this<00:07:50.380> is<00:07:50.500> a 00:07:50.520 --> 00:07:50.530 align:start position:0% each row in this table so this is a 00:07:50.530 --> 00:07:53.310 align:start position:0% each row in this table so this is a repeating<00:07:51.039> constraint<00:07:51.750> similarly<00:07:52.750> the 00:07:53.310 --> 00:07:53.320 align:start position:0% repeating constraint similarly the 00:07:53.320 --> 00:07:57.240 align:start position:0% repeating constraint similarly the second<00:07:53.800> column<00:07:54.150> or<00:07:55.150> the<00:07:55.539> next<00:07:55.810> row<00:07:56.020> is<00:07:56.620> the<00:07:56.949> sum 00:07:57.240 --> 00:07:57.250 align:start position:0% second column or the next row is the sum 00:07:57.250 --> 00:07:59.960 align:start position:0% second column or the next row is the sum of<00:07:57.490> the<00:07:58.000> two<00:07:58.150> columns<00:07:58.630> in<00:07:58.810> the<00:07:58.990> previous<00:07:59.380> row 00:07:59.960 --> 00:07:59.970 align:start position:0% of the two columns in the previous row 00:07:59.970 --> 00:08:02.399 align:start position:0% of the two columns in the previous row so<00:08:00.970> this<00:08:01.150> value<00:08:01.360> for<00:08:01.990> some<00:08:02.139> of<00:08:02.289> these 00:08:02.399 --> 00:08:02.409 align:start position:0% so this value for some of these 00:08:02.409 --> 00:08:05.939 align:start position:0% so this value for some of these difficulties<00:08:03.030> now<00:08:04.030> these<00:08:04.720> are<00:08:04.930> four<00:08:05.229> simple 00:08:05.939 --> 00:08:05.949 align:start position:0% difficulties now these are four simple 00:08:05.949 --> 00:08:10.589 align:start position:0% difficulties now these are four simple rules<00:08:06.810> but<00:08:07.919> if<00:08:08.919> you<00:08:09.070> think<00:08:09.340> about<00:08:09.430> it<00:08:09.789> this 00:08:10.589 --> 00:08:10.599 align:start position:0% rules but if you think about it this 00:08:10.599 --> 00:08:14.520 align:start position:0% rules but if you think about it this captures<00:08:11.310> everything<00:08:12.960> that<00:08:13.960> is<00:08:14.139> intended 00:08:14.520 --> 00:08:14.530 align:start position:0% captures everything that is intended 00:08:14.530 --> 00:08:19.409 align:start position:0% captures everything that is intended with<00:08:14.830> this<00:08:15.010> plane<00:08:16.289> so<00:08:17.289> if<00:08:17.560> you<00:08:18.000> if<00:08:19.000> you<00:08:19.210> haven't 00:08:19.409 --> 00:08:19.419 align:start position:0% with this plane so if you if you haven't 00:08:19.419 --> 00:08:21.839 align:start position:0% with this plane so if you if you haven't raced<00:08:19.750> it<00:08:19.990> that<00:08:20.830> satisfies<00:08:21.550> these 00:08:21.839 --> 00:08:21.849 align:start position:0% raced it that satisfies these 00:08:21.849 --> 00:08:24.749 align:start position:0% raced it that satisfies these constraints<00:08:22.860> you've<00:08:23.860> shown<00:08:24.190> the<00:08:24.400> display 00:08:24.749 --> 00:08:24.759 align:start position:0% constraints you've shown the display 00:08:24.759 --> 00:08:25.580 align:start position:0% constraints you've shown the display place 00:08:25.580 --> 00:08:25.590 align:start position:0% place 00:08:25.590 --> 00:08:28.540 align:start position:0% place so<00:08:26.220> now<00:08:26.370> we've<00:08:26.580> reduced<00:08:26.850> our<00:08:27.330> problem<00:08:27.780> from 00:08:28.540 --> 00:08:28.550 align:start position:0% so now we've reduced our problem from 00:08:28.550 --> 00:08:33.440 align:start position:0% so now we've reduced our problem from this<00:08:29.550> thing<00:08:29.820> here<00:08:30.530> to<00:08:31.530> this<00:08:31.680> thing<00:08:31.980> here<00:08:32.450> we 00:08:33.440 --> 00:08:33.450 align:start position:0% this thing here to this thing here we 00:08:33.450 --> 00:08:35.560 align:start position:0% this thing here to this thing here we still<00:08:33.630> have<00:08:33.840> a<00:08:33.870> major<00:08:34.140> trade<00:08:34.440> secret<00:08:35.130> but 00:08:35.560 --> 00:08:35.570 align:start position:0% still have a major trade secret but 00:08:35.570 --> 00:08:38.990 align:start position:0% still have a major trade secret but that's<00:08:36.570> part<00:08:36.840> of<00:08:36.930> the<00:08:37.080> star<00:08:37.469> protocol<00:08:37.919> but<00:08:38.849> in 00:08:38.990 --> 00:08:39.000 align:start position:0% that's part of the star protocol but in 00:08:39.000 --> 00:08:41.870 align:start position:0% that's part of the star protocol but in order<00:08:39.210> to<00:08:39.240> do<00:08:39.479> that<00:08:39.659> we<00:08:40.200> need<00:08:40.380> to<00:08:40.529> do<00:08:41.460> a<00:08:41.550> couple 00:08:41.870 --> 00:08:41.880 align:start position:0% order to do that we need to do a couple 00:08:41.880 --> 00:08:43.940 align:start position:0% order to do that we need to do a couple more<00:08:42.029> iterations<00:08:42.210> on<00:08:43.020> what<00:08:43.740> these 00:08:43.940 --> 00:08:43.950 align:start position:0% more iterations on what these 00:08:43.950 --> 00:08:46.910 align:start position:0% more iterations on what these constraints<00:08:44.580> look<00:08:44.760> like<00:08:44.940> and<00:08:45.529> the<00:08:46.529> next<00:08:46.800> thing 00:08:46.910 --> 00:08:46.920 align:start position:0% constraints look like and the next thing 00:08:46.920 --> 00:08:48.620 align:start position:0% constraints look like and the next thing we<00:08:47.040> need<00:08:47.070> to<00:08:47.220> do<00:08:47.490> is<00:08:47.760> we<00:08:47.940> need<00:08:48.029> to<00:08:48.089> tell<00:08:48.360> them 00:08:48.620 --> 00:08:48.630 align:start position:0% we need to do is we need to tell them 00:08:48.630 --> 00:08:50.990 align:start position:0% we need to do is we need to tell them into<00:08:48.990> multi<00:08:49.350> bright<00:08:49.529> mysteries<00:08:49.980> so<00:08:50.670> instead 00:08:50.990 --> 00:08:51.000 align:start position:0% into multi bright mysteries so instead 00:08:51.000 --> 00:08:53.510 align:start position:0% into multi bright mysteries so instead of<00:08:51.060> having<00:08:51.300> equalities<00:08:52.080> we<00:08:52.320> need<00:08:53.190> to<00:08:53.310> create 00:08:53.510 --> 00:08:53.520 align:start position:0% of having equalities we need to create 00:08:53.520 --> 00:08:58.340 align:start position:0% of having equalities we need to create expressions<00:08:54.500> that<00:08:55.500> are<00:08:55.800> 0<00:08:57.020> whenever<00:08:58.020> they 00:08:58.340 --> 00:08:58.350 align:start position:0% expressions that are 0 whenever they 00:08:58.350 --> 00:09:00.890 align:start position:0% expressions that are 0 whenever they hold<00:08:58.880> that<00:08:59.880> easy<00:09:00.150> whenever<00:09:00.570> you<00:09:00.690> have<00:09:00.810> an 00:09:00.890 --> 00:09:00.900 align:start position:0% hold that easy whenever you have an 00:09:00.900 --> 00:09:03.350 align:start position:0% hold that easy whenever you have an equality<00:09:01.140> sign<00:09:01.529> just<00:09:02.310> replace<00:09:03.000> it<00:09:03.029> with<00:09:03.330> a 00:09:03.350 --> 00:09:03.360 align:start position:0% equality sign just replace it with a 00:09:03.360 --> 00:09:07.700 align:start position:0% equality sign just replace it with a minus<00:09:03.810> so<00:09:04.460> this<00:09:05.460> thing<00:09:05.760> needs<00:09:06.000> to<00:09:06.150> be<00:09:06.240> 0<00:09:06.630> on<00:09:07.260> row 00:09:07.700 --> 00:09:07.710 align:start position:0% minus so this thing needs to be 0 on row 00:09:07.710 --> 00:09:12.920 align:start position:0% minus so this thing needs to be 0 on row 0<00:09:09.230> it's<00:09:10.230> only<00:09:10.440> 0<00:09:10.770> when<00:09:11.040> this<00:09:11.160> thing<00:09:11.339> is<00:09:11.460> 1<00:09:11.930> same 00:09:12.920 --> 00:09:12.930 align:start position:0% 0 it's only 0 when this thing is 1 same 00:09:12.930 --> 00:09:15.019 align:start position:0% 0 it's only 0 when this thing is 1 same here<00:09:13.230> this<00:09:13.650> thing<00:09:13.920> needs<00:09:14.130> to<00:09:14.220> be<00:09:14.279> 0<00:09:14.580> on<00:09:14.670> world 00:09:15.019 --> 00:09:15.029 align:start position:0% here this thing needs to be 0 on world 00:09:15.029 --> 00:09:19.460 align:start position:0% here this thing needs to be 0 on world 200<00:09:16.730> you<00:09:17.730> just<00:09:17.940> subtract<00:09:18.300> the<00:09:18.390> value<00:09:18.720> and<00:09:18.990> then 00:09:19.460 --> 00:09:19.470 align:start position:0% 200 you just subtract the value and then 00:09:19.470 --> 00:09:20.470 align:start position:0% 200 you just subtract the value and then it'll<00:09:19.620> be<00:09:19.680> 0 00:09:20.470 --> 00:09:20.480 align:start position:0% it'll be 0 00:09:20.480 --> 00:09:25.310 align:start position:0% it'll be 0 same<00:09:21.480> thing<00:09:21.779> for<00:09:21.860> us<00:09:22.860> needing<00:09:23.279> to<00:09:23.310> have<00:09:24.320> these 00:09:25.310 --> 00:09:25.320 align:start position:0% same thing for us needing to have these 00:09:25.320 --> 00:09:27.500 align:start position:0% same thing for us needing to have these two<00:09:25.500> values<00:09:25.710> equal<00:09:26.279> you<00:09:26.760> just<00:09:26.970> subtract<00:09:27.360> them 00:09:27.500 --> 00:09:27.510 align:start position:0% two values equal you just subtract them 00:09:27.510 --> 00:09:31.250 align:start position:0% two values equal you just subtract them and<00:09:28.010> again<00:09:29.180> what<00:09:30.180> we<00:09:30.330> need<00:09:30.540> to<00:09:30.720> have<00:09:30.900> the<00:09:31.050> sum 00:09:31.250 --> 00:09:31.260 align:start position:0% and again what we need to have the sum 00:09:31.260 --> 00:09:33.860 align:start position:0% and again what we need to have the sum we<00:09:31.620> just<00:09:32.030> subtract<00:09:33.030> it<00:09:33.180> left<00:09:33.540> hand<00:09:33.720> the 00:09:33.860 --> 00:09:33.870 align:start position:0% we just subtract it left hand the 00:09:33.870 --> 00:09:35.510 align:start position:0% we just subtract it left hand the expression<00:09:34.290> from<00:09:35.040> the<00:09:35.190> right<00:09:35.339> hand 00:09:35.510 --> 00:09:35.520 align:start position:0% expression from the right hand 00:09:35.520 --> 00:09:37.880 align:start position:0% expression from the right hand expression<00:09:36.000> ok<00:09:36.690> so<00:09:36.960> now<00:09:37.110> we've<00:09:37.320> done<00:09:37.350> that<00:09:37.650> we 00:09:37.880 --> 00:09:37.890 align:start position:0% expression ok so now we've done that we 00:09:37.890 --> 00:09:39.980 align:start position:0% expression ok so now we've done that we have<00:09:37.920> changed<00:09:38.160> our<00:09:38.460> constraints<00:09:39.089> such<00:09:39.750> that 00:09:39.980 --> 00:09:39.990 align:start position:0% have changed our constraints such that 00:09:39.990 --> 00:09:42.770 align:start position:0% have changed our constraints such that they<00:09:40.110> are<00:09:40.140> expressions<00:09:40.680> that<00:09:41.460> are<00:09:41.520> 0<00:09:41.940> whenever 00:09:42.770 --> 00:09:42.780 align:start position:0% they are expressions that are 0 whenever 00:09:42.780 --> 00:09:45.290 align:start position:0% they are expressions that are 0 whenever the<00:09:43.080> constraint<00:09:43.500> volts<00:09:43.860> now<00:09:44.850> we<00:09:44.910> didn't<00:09:45.210> need 00:09:45.290 --> 00:09:45.300 align:start position:0% the constraint volts now we didn't need 00:09:45.300 --> 00:09:47.960 align:start position:0% the constraint volts now we didn't need to<00:09:45.330> do<00:09:45.540> a<00:09:45.570> next<00:09:45.839> trick<00:09:46.310> the<00:09:47.310> reasons<00:09:47.700> for<00:09:47.760> this 00:09:47.960 --> 00:09:47.970 align:start position:0% to do a next trick the reasons for this 00:09:47.970 --> 00:09:49.970 align:start position:0% to do a next trick the reasons for this trigger<00:09:48.270> kind<00:09:48.540> of<00:09:48.600> mathematical<00:09:49.230> and<00:09:49.560> I<00:09:49.800> don't 00:09:49.970 --> 00:09:49.980 align:start position:0% trigger kind of mathematical and I don't 00:09:49.980 --> 00:09:51.829 align:start position:0% trigger kind of mathematical and I don't have<00:09:50.130> the<00:09:50.280> time<00:09:50.670> to<00:09:50.940> go<00:09:51.089> into<00:09:51.360> the<00:09:51.480> details<00:09:51.810> of 00:09:51.829 --> 00:09:51.839 align:start position:0% have the time to go into the details of 00:09:51.839 --> 00:09:55.100 align:start position:0% have the time to go into the details of exactly<00:09:52.220> why<00:09:53.220> it<00:09:53.280> is<00:09:53.520> the<00:09:53.640> way<00:09:53.760> it<00:09:53.820> is<00:09:53.970> but<00:09:54.810> if 00:09:55.100 --> 00:09:55.110 align:start position:0% exactly why it is the way it is but if 00:09:55.110 --> 00:09:57.500 align:start position:0% exactly why it is the way it is but if we<00:09:55.320> have<00:09:55.530> a<00:09:55.560> constraint<00:09:56.430> where<00:09:57.060> we<00:09:57.180> want<00:09:57.390> I 00:09:57.500 --> 00:09:57.510 align:start position:0% we have a constraint where we want I 00:09:57.510 --> 00:10:00.170 align:start position:0% we have a constraint where we want I equals<00:09:58.080> some<00:09:58.230> value<00:09:58.700> we<00:09:59.700> need<00:09:59.850> to<00:09:59.970> multiply 00:10:00.170 --> 00:10:00.180 align:start position:0% equals some value we need to multiply 00:10:00.180 --> 00:10:05.570 align:start position:0% equals some value we need to multiply this<00:10:00.630> by<00:10:01.200> a<00:10:01.920> thing<00:10:02.310> 1<00:10:02.910> over<00:10:03.300> X<00:10:03.600> minus<00:10:04.430> Omega<00:10:05.430> to 00:10:05.570 --> 00:10:05.580 align:start position:0% this by a thing 1 over X minus Omega to 00:10:05.580 --> 00:10:09.340 align:start position:0% this by a thing 1 over X minus Omega to the<00:10:05.610> power<00:10:06.410> Omega<00:10:07.410> is<00:10:07.680> a<00:10:07.920> constant<00:10:08.070> and 00:10:09.340 --> 00:10:09.350 align:start position:0% the power Omega is a constant and 00:10:09.350 --> 00:10:11.420 align:start position:0% the power Omega is a constant and similarly<00:10:10.350> if<00:10:10.620> we<00:10:10.740> want<00:10:10.920> a<00:10:10.980> repeating 00:10:11.420 --> 00:10:11.430 align:start position:0% similarly if we want a repeating 00:10:11.430 --> 00:10:13.310 align:start position:0% similarly if we want a repeating constraint<00:10:11.880> we<00:10:12.450> need<00:10:12.630> to<00:10:12.720> multiply<00:10:12.900> this 00:10:13.310 --> 00:10:13.320 align:start position:0% constraint we need to multiply this 00:10:13.320 --> 00:10:16.850 align:start position:0% constraint we need to multiply this thing<00:10:13.770> with<00:10:14.610> this<00:10:14.790> expression<00:10:15.120> here<00:10:15.800> when<00:10:16.800> you 00:10:16.850 --> 00:10:16.860 align:start position:0% thing with this expression here when you 00:10:16.860 --> 00:10:20.540 align:start position:0% thing with this expression here when you do<00:10:16.980> that<00:10:17.160> you<00:10:17.970> get<00:10:18.120> this<00:10:18.330> system 00:10:20.540 --> 00:10:20.550 align:start position:0% do that you get this system 00:10:20.550 --> 00:10:22.820 align:start position:0% do that you get this system it<00:10:21.510> looks<00:10:21.750> complicated<00:10:22.110> but<00:10:22.620> it's<00:10:22.770> really 00:10:22.820 --> 00:10:22.830 align:start position:0% it looks complicated but it's really 00:10:22.830 --> 00:10:26.329 align:start position:0% it looks complicated but it's really just<00:10:23.149> these<00:10:24.149> things<00:10:24.500> multiplied<00:10:25.500> by<00:10:26.279> these 00:10:26.329 --> 00:10:26.339 align:start position:0% just these things multiplied by these 00:10:26.339 --> 00:10:30.530 align:start position:0% just these things multiplied by these things<00:10:26.760> and<00:10:28.100> that's<00:10:29.100> pretty<00:10:29.459> much<00:10:29.640> it<00:10:30.149> what 00:10:30.530 --> 00:10:30.540 align:start position:0% things and that's pretty much it what 00:10:30.540 --> 00:10:33.860 align:start position:0% things and that's pretty much it what you<00:10:30.690> need<00:10:30.839> to<00:10:30.990> do<00:10:31.200> in<00:10:31.589> order<00:10:31.770> to<00:10:32.209> create<00:10:33.209> a 00:10:33.860 --> 00:10:33.870 align:start position:0% you need to do in order to create a 00:10:33.870 --> 00:10:36.380 align:start position:0% you need to do in order to create a constraint<00:10:34.620> system<00:10:35.190> for<00:10:35.880> the<00:10:35.940> people<00:10:36.240> that's 00:10:36.380 --> 00:10:36.390 align:start position:0% constraint system for the people that's 00:10:36.390 --> 00:10:39.320 align:start position:0% constraint system for the people that's you<00:10:36.480> start<00:10:36.750> so<00:10:37.380> let's<00:10:37.589> show<00:10:38.430> you<00:10:38.459> now<00:10:38.850> what<00:10:39.180> it 00:10:39.320 --> 00:10:39.330 align:start position:0% you start so let's show you now what it 00:10:39.330 --> 00:10:44.630 align:start position:0% you start so let's show you now what it looks<00:10:39.540> like<00:10:39.720> if<00:10:40.190> implemented<00:10:43.250> using<00:10:44.250> or 00:10:44.630 --> 00:10:44.640 align:start position:0% looks like if implemented using or 00:10:44.640 --> 00:10:48.889 align:start position:0% looks like if implemented using or vibrations<00:10:45.860> so<00:10:46.860> is<00:10:47.640> anyone<00:10:47.910> trying<00:10:48.270> to<00:10:48.390> code 00:10:48.889 --> 00:10:48.899 align:start position:0% vibrations so is anyone trying to code 00:10:48.899 --> 00:11:02.449 align:start position:0% vibrations so is anyone trying to code along<00:10:55.940> now<00:10:56.940> this<00:10:57.120> makes<00:10:57.330> sense<00:11:00.410> so<00:11:01.410> yeah<00:11:01.560> I'm 00:11:02.449 --> 00:11:02.459 align:start position:0% along now this makes sense so yeah I'm 00:11:02.459 --> 00:11:04.190 align:start position:0% along now this makes sense so yeah I'm hoping<00:11:02.790> you've<00:11:03.089> got<00:11:03.390> it<00:11:03.570> to<00:11:03.720> the<00:11:03.839> point<00:11:04.080> where 00:11:04.190 --> 00:11:04.200 align:start position:0% hoping you've got it to the point where 00:11:04.200 --> 00:11:05.870 align:start position:0% hoping you've got it to the point where you<00:11:04.410> can<00:11:04.589> do<00:11:04.680> the<00:11:04.830> build<00:11:05.220> release<00:11:05.580> and<00:11:05.820> you 00:11:05.870 --> 00:11:05.880 align:start position:0% you can do the build release and you 00:11:05.880 --> 00:11:26.960 align:start position:0% you can do the build release and you managed<00:11:06.180> to<00:11:06.209> download 00:11:26.960 --> 00:11:26.970 align:start position:0% 00:11:26.970 --> 00:11:43.010 align:start position:0% [Music] 00:11:43.010 --> 00:11:43.020 align:start position:0% 00:11:43.020 --> 00:11:53.130 align:start position:0% so<00:11:44.020> I<00:11:44.350> build<00:11:44.950> it<00:11:45.190> here<00:11:45.430> now<00:11:51.480> so<00:11:52.480> what<00:11:52.660> we<00:11:52.810> do<00:11:52.930> is 00:11:53.130 --> 00:11:53.140 align:start position:0% so I build it here now so what we do is 00:11:53.140 --> 00:11:56.010 align:start position:0% so I build it here now so what we do is we<00:11:53.380> take<00:11:53.560> the<00:11:53.830> ckp<00:11:54.610> start<00:11:55.149> package<00:11:55.630> and<00:11:55.960> we 00:11:56.010 --> 00:11:56.020 align:start position:0% we take the ckp start package and we 00:11:56.020 --> 00:11:58.800 align:start position:0% we take the ckp start package and we just<00:11:56.230> import<00:11:56.620> everything<00:11:57.149> we<00:11:58.149> also<00:11:58.300> employed 00:11:58.800 --> 00:11:58.810 align:start position:0% just import everything we also employed 00:11:58.810 --> 00:12:01.680 align:start position:0% just import everything we also employed the<00:11:59.020> prime<00:11:59.290> field<00:11:59.649> that<00:11:59.830> again<00:12:00.070> to<00:12:00.279> this<00:12:00.690> what 00:12:01.680 --> 00:12:01.690 align:start position:0% the prime field that again to this what 00:12:01.690 --> 00:12:03.810 align:start position:0% the prime field that again to this what a<00:12:01.720> great<00:12:01.779> example<00:12:02.110> it<00:12:02.680> doesn't<00:12:03.100> really<00:12:03.279> matter 00:12:03.810 --> 00:12:03.820 align:start position:0% a great example it doesn't really matter 00:12:03.820 --> 00:12:12.000 align:start position:0% a great example it doesn't really matter those<00:12:04.120> are<00:12:04.240> values<00:12:05.910> but<00:12:10.260> but<00:12:11.260> if<00:12:11.410> you're 00:12:12.000 --> 00:12:12.010 align:start position:0% those are values but but if you're 00:12:12.010 --> 00:12:13.590 align:start position:0% those are values but but if you're working<00:12:12.190> with<00:12:12.520> these<00:12:12.640> systems<00:12:13.089> in<00:12:13.330> like 00:12:13.590 --> 00:12:13.600 align:start position:0% working with these systems in like 00:12:13.600 --> 00:12:16.079 align:start position:0% working with these systems in like practical<00:12:14.529> applications<00:12:15.160> you<00:12:15.730> need<00:12:15.850> to<00:12:15.940> know 00:12:16.079 --> 00:12:16.089 align:start position:0% practical applications you need to know 00:12:16.089 --> 00:12:18.510 align:start position:0% practical applications you need to know that<00:12:16.390> every<00:12:17.110> operation<00:12:17.500> happens<00:12:18.040> in<00:12:18.279> some 00:12:18.510 --> 00:12:18.520 align:start position:0% that every operation happens in some 00:12:18.520 --> 00:12:22.920 align:start position:0% that every operation happens in some large<00:12:18.850> prime<00:12:19.209> field<00:12:21.000> applications<00:12:22.000> so<00:12:22.779> the 00:12:22.920 --> 00:12:22.930 align:start position:0% large prime field applications so the 00:12:22.930 --> 00:12:25.050 align:start position:0% large prime field applications so the first<00:12:23.140> thing<00:12:23.320> we<00:12:23.470> do<00:12:23.620> is<00:12:23.890> we<00:12:24.100> create<00:12:24.459> a<00:12:24.640> struts 00:12:25.050 --> 00:12:25.060 align:start position:0% first thing we do is we create a struts 00:12:25.060 --> 00:12:27.150 align:start position:0% first thing we do is we create a struts that<00:12:25.390> represents<00:12:25.990> our<00:12:26.080> plane<00:12:26.410> in<00:12:26.770> this<00:12:26.920> case 00:12:27.150 --> 00:12:27.160 align:start position:0% that represents our plane in this case 00:12:27.160 --> 00:12:28.920 align:start position:0% that represents our plane in this case the<00:12:27.399> greatest<00:12:27.910> article<00:12:28.360> tonight<00:12:28.570> she<00:12:28.720> claimed 00:12:28.920 --> 00:12:28.930 align:start position:0% the greatest article tonight she claimed 00:12:28.930 --> 00:12:31.889 align:start position:0% the greatest article tonight she claimed it<00:12:29.430> has<00:12:30.430> the<00:12:30.580> index<00:12:30.940> which<00:12:31.240> in<00:12:31.390> the<00:12:31.480> example<00:12:31.810> is 00:12:31.889 --> 00:12:31.899 align:start position:0% it has the index which in the example is 00:12:31.899 --> 00:12:34.110 align:start position:0% it has the index which in the example is 200<00:12:32.380> it<00:12:32.620> has<00:12:32.770> the<00:12:32.920> secret<00:12:33.220> value<00:12:33.760> which<00:12:34.000> was 00:12:34.110 --> 00:12:34.120 align:start position:0% 200 it has the secret value which was 00:12:34.120 --> 00:12:35.970 align:start position:0% 200 it has the secret value which was this<00:12:34.270> very<00:12:34.600> large<00:12:34.750> number<00:12:35.200> that<00:12:35.230> behind<00:12:35.680> and 00:12:35.970 --> 00:12:35.980 align:start position:0% this very large number that behind and 00:12:35.980 --> 00:12:38.280 align:start position:0% this very large number that behind and so<00:12:36.190> he<00:12:36.250> has<00:12:36.430> neat<00:12:36.630> public<00:12:37.630> Valeo<00:12:37.959> didn't 00:12:38.280 --> 00:12:38.290 align:start position:0% so he has neat public Valeo didn't 00:12:38.290 --> 00:12:39.090 align:start position:0% so he has neat public Valeo didn't complain 00:12:39.090 --> 00:12:39.100 align:start position:0% complain 00:12:39.100 --> 00:12:42.660 align:start position:0% complain large<00:12:39.760> numbers<00:12:40.320> and<00:12:41.320> now<00:12:41.500> we<00:12:41.560> implement<00:12:42.130> two 00:12:42.660 --> 00:12:42.670 align:start position:0% large numbers and now we implement two 00:12:42.670 --> 00:12:47.579 align:start position:0% large numbers and now we implement two trails<00:12:43.149> on<00:12:45.150> let's<00:12:46.150> start<00:12:46.420> the<00:12:46.600> provable<00:12:47.080> so 00:12:47.579 --> 00:12:47.589 align:start position:0% trails on let's start the provable so 00:12:47.589 --> 00:12:49.320 align:start position:0% trails on let's start the provable so what<00:12:47.740> do<00:12:47.830> we<00:12:47.860> need<00:12:48.040> to<00:12:48.190> do<00:12:48.339> you<00:12:48.580> need<00:12:48.730> to<00:12:48.880> create 00:12:49.320 --> 00:12:49.330 align:start position:0% what do we need to do you need to create 00:12:49.330 --> 00:12:57.660 align:start position:0% what do we need to do you need to create a<00:12:49.620> table<00:12:50.790> or<00:12:51.790> this<00:12:52.029> thing<00:12:55.589> like<00:12:56.589> we<00:12:56.800> said<00:12:57.310> so 00:12:57.660 --> 00:12:57.670 align:start position:0% a table or this thing like we said so 00:12:57.670 --> 00:13:00.660 align:start position:0% a table or this thing like we said so what<00:12:58.420> I<00:12:58.450> already<00:12:58.810> have<00:12:59.080> here<00:12:59.350> is<00:12:59.560> we<00:13:00.190> have<00:13:00.220> the 00:13:00.660 --> 00:13:00.670 align:start position:0% what I already have here is we have the 00:13:00.670 --> 00:13:03.690 align:start position:0% what I already have here is we have the Stars<00:13:01.270> itself<00:13:01.690> which<00:13:02.440> is<00:13:02.589> here<00:13:02.950> we<00:13:03.370> have<00:13:03.400> our 00:13:03.690 --> 00:13:03.700 align:start position:0% Stars itself which is here we have our 00:13:03.700 --> 00:13:07.140 align:start position:0% Stars itself which is here we have our secret<00:13:04.150> value<00:13:04.920> which<00:13:05.920> is<00:13:06.100> here<00:13:06.430> twenty<00:13:06.970> South 00:13:07.140 --> 00:13:07.150 align:start position:0% secret value which is here twenty South 00:13:07.150 --> 00:13:10.500 align:start position:0% secret value which is here twenty South were<00:13:07.360> to<00:13:07.420> trace<00:13:07.660> table<00:13:08.080> so<00:13:09.010> for<00:13:09.510> mathematical 00:13:10.500 --> 00:13:10.510 align:start position:0% were to trace table so for mathematical 00:13:10.510 --> 00:13:12.240 align:start position:0% were to trace table so for mathematical reasons<00:13:10.570> the<00:13:11.200> tri-state<00:13:11.620> will<00:13:11.740> always<00:13:12.040> needs 00:13:12.240 --> 00:13:12.250 align:start position:0% reasons the tri-state will always needs 00:13:12.250 --> 00:13:14.670 align:start position:0% reasons the tri-state will always needs to<00:13:12.310> have<00:13:12.520> a<00:13:12.550> power<00:13:12.790> of<00:13:12.910> two<00:13:13.209> sighs<00:13:13.540> so<00:13:14.320> we'll 00:13:14.670 --> 00:13:14.680 align:start position:0% to have a power of two sighs so we'll 00:13:14.680 --> 00:13:17.100 align:start position:0% to have a power of two sighs so we'll just<00:13:14.830> round<00:13:15.040> index<00:13:15.910> up<00:13:16.120> to<00:13:16.270> the<00:13:16.390> next<00:13:16.630> power<00:13:16.810> of 00:13:17.100 --> 00:13:17.110 align:start position:0% just round index up to the next power of 00:13:17.110 --> 00:13:19.019 align:start position:0% just round index up to the next power of two<00:13:17.290> don't<00:13:17.800> worry<00:13:17.950> we'll<00:13:18.190> still<00:13:18.400> get<00:13:18.610> brother 00:13:19.019 --> 00:13:19.029 align:start position:0% two don't worry we'll still get brother 00:13:19.029 --> 00:13:20.400 align:start position:0% two don't worry we'll still get brother two<00:13:19.180> hundred<00:13:19.540> out<00:13:19.630> of<00:13:19.660> it<00:13:19.930> we<00:13:20.050> just<00:13:20.200> need<00:13:20.320> to 00:13:20.400 --> 00:13:20.410 align:start position:0% two hundred out of it we just need to 00:13:20.410 --> 00:13:23.390 align:start position:0% two hundred out of it we just need to compute<00:13:20.650> two<00:13:20.890> hundred<00:13:21.160> into<00:13:21.370> the<00:13:21.520> safe<00:13:21.700> rows 00:13:23.390 --> 00:13:23.400 align:start position:0% compute two hundred into the safe rows 00:13:23.400 --> 00:13:25.130 align:start position:0% compute two hundred into the safe rows and<00:13:23.580> we<00:13:23.700> create<00:13:23.940> race<00:13:24.240> table<00:13:24.600> with<00:13:24.750> this<00:13:24.900> size 00:13:25.130 --> 00:13:25.140 align:start position:0% and we create race table with this size 00:13:25.140 --> 00:13:27.470 align:start position:0% and we create race table with this size into<00:13:25.530> the<00:13:25.620> columns<00:13:25.950> so<00:13:26.490> let's<00:13:26.670> initialize<00:13:26.970> it 00:13:27.470 --> 00:13:27.480 align:start position:0% into the columns so let's initialize it 00:13:27.480 --> 00:13:36.740 align:start position:0% into the columns so let's initialize it we<00:13:27.750> start<00:13:28.080> with<00:13:28.290> adding<00:13:30.530> almost<00:13:34.190> what<00:13:35.190> we<00:13:35.750> need 00:13:36.740 --> 00:13:36.750 align:start position:0% we start with adding almost what we need 00:13:36.750 --> 00:13:46.160 align:start position:0% we start with adding almost what we need to<00:13:36.900> hi<00:13:38.450> the<00:13:39.740> second<00:13:40.740> column<00:13:40.950> B<00:13:41.700> or<00:13:43.100> C<00:13:44.100> value<00:13:45.170> and 00:13:46.160 --> 00:13:46.170 align:start position:0% to hi the second column B or C value and 00:13:46.170 --> 00:13:52.630 align:start position:0% to hi the second column B or C value and then<00:13:46.650> we<00:13:46.680> have<00:13:46.980> mark<00:13:47.280> for<00:13:47.550> loop<00:13:50.840> where<00:13:51.840> we 00:13:52.630 --> 00:13:52.640 align:start position:0% then we have mark for loop where we 00:13:52.640 --> 00:13:59.270 align:start position:0% then we have mark for loop where we update<00:13:53.640> each<00:13:56.360> that<00:13:57.360> was<00:13:57.720> sort<00:13:57.960> of<00:13:58.020> the<00:13:58.860> first 00:13:59.270 --> 00:13:59.280 align:start position:0% update each that was sort of the first 00:13:59.280 --> 00:14:04.340 align:start position:0% update each that was sort of the first one<00:13:59.640> was<00:13:59.940> they<00:14:00.150> both<00:14:00.450> lead<00:14:01.010> all<00:14:02.480> by<00:14:03.480> minus<00:14:03.900> 1<00:14:04.080> to 00:14:04.340 --> 00:14:04.350 align:start position:0% one was they both lead all by minus 1 to 00:14:04.350 --> 00:14:14.210 align:start position:0% one was they both lead all by minus 1 to 1<00:14:04.380> and<00:14:09.200> the<00:14:10.200> second<00:14:10.920> value<00:14:11.580> or<00:14:12.030> Y<00:14:12.360> value<00:14:13.220> was 00:14:14.210 --> 00:14:14.220 align:start position:0% 1 and the second value or Y value was 00:14:14.220 --> 00:14:32.790 align:start position:0% 1 and the second value or Y value was equal<00:14:14.430> to<00:14:14.700> hit<00:14:15.090> some 00:14:32.790 --> 00:14:32.800 align:start position:0% 00:14:32.800 --> 00:14:37.450 align:start position:0% talk<00:14:33.800> louder<00:14:34.450> yes<00:14:35.450> then<00:14:35.920> semantics<00:14:36.920> so<00:14:37.190> if 00:14:37.450 --> 00:14:37.460 align:start position:0% talk louder yes then semantics so if 00:14:37.460 --> 00:14:39.250 align:start position:0% talk louder yes then semantics so if you're<00:14:37.820> not<00:14:37.940> familiar<00:14:38.090> with<00:14:38.540> us<00:14:38.750> you<00:14:39.020> can 00:14:39.250 --> 00:14:39.260 align:start position:0% you're not familiar with us you can 00:14:39.260 --> 00:14:41.530 align:start position:0% you're not familiar with us you can ignore<00:14:39.830> the<00:14:40.010> under<00:14:40.310> sons<00:14:40.550> and<00:14:40.850> diplomas<00:14:41.330> there 00:14:41.530 --> 00:14:41.540 align:start position:0% ignore the under sons and diplomas there 00:14:41.540 --> 00:14:43.620 align:start position:0% ignore the under sons and diplomas there just<00:14:41.840> to<00:14:41.960> satisfy<00:14:42.140> the<00:14:42.530> Bordeaux<00:14:42.920> checker 00:14:43.620 --> 00:14:43.630 align:start position:0% just to satisfy the Bordeaux checker 00:14:43.630 --> 00:14:49.900 align:start position:0% just to satisfy the Bordeaux checker let's<00:14:44.630> see<00:14:46.420> what's<00:14:47.420> happening<00:14:48.490> little<00:14:49.490> line 00:14:49.900 --> 00:14:49.910 align:start position:0% let's see what's happening little line 00:14:49.910 --> 00:14:56.850 align:start position:0% let's see what's happening little line where<00:14:50.300> we<00:14:50.540> say<00:14:50.870> that<00:14:50.900> the<00:14:51.380> value<00:14:51.710> equals 00:14:56.850 --> 00:14:56.860 align:start position:0% 00:14:56.860 --> 00:14:59.650 align:start position:0% that's<00:14:57.860> pretty<00:14:58.490> the<00:14:58.640> value<00:14:59.000> that<00:14:59.180> we<00:14:59.330> want<00:14:59.480> to 00:14:59.650 --> 00:14:59.660 align:start position:0% that's pretty the value that we want to 00:14:59.660 --> 00:15:07.660 align:start position:0% that's pretty the value that we want to play<00:15:01.300> doctor<00:15:02.320> and<00:15:03.320> is<00:15:03.500> larger<00:15:03.860> still<00:15:06.640> yeah 00:15:07.660 --> 00:15:07.670 align:start position:0% play doctor and is larger still yeah 00:15:07.670 --> 00:15:16.030 align:start position:0% play doctor and is larger still yeah here<00:15:14.050> just<00:15:15.050> the<00:15:15.170> programming<00:15:15.680> like<00:15:15.830> this 00:15:16.030 --> 00:15:16.040 align:start position:0% here just the programming like this 00:15:16.040 --> 00:15:17.730 align:start position:0% here just the programming like this interesting 00:15:17.730 --> 00:15:17.740 align:start position:0% interesting 00:15:17.740 --> 00:15:20.950 align:start position:0% interesting so<00:15:18.740> yes<00:15:18.920> let's<00:15:19.190> print<00:15:20.090> the<00:15:20.210> value<00:15:20.630> at<00:15:20.780> if<00:15:20.900> I 00:15:20.950 --> 00:15:20.960 align:start position:0% so yes let's print the value at if I 00:15:20.960 --> 00:15:32.830 align:start position:0% so yes let's print the value at if I trying<00:15:21.230> to<00:15:21.320> clean<00:15:21.590> there<00:15:21.980> we<00:15:22.010> go<00:15:22.220> okay<00:15:31.510> and<00:15:32.510> we 00:15:32.830 --> 00:15:32.840 align:start position:0% trying to clean there we go okay and we 00:15:32.840 --> 00:15:35.620 align:start position:0% trying to clean there we go okay and we have<00:15:32.870> already<00:15:33.230> playing<00:15:33.740> here<00:15:34.270> so<00:15:35.270> let's<00:15:35.450> go<00:15:35.570> to 00:15:35.620 --> 00:15:35.630 align:start position:0% have already playing here so let's go to 00:15:35.630 --> 00:15:36.940 align:start position:0% have already playing here so let's go to the<00:15:35.780> main<00:15:35.900> function<00:15:36.110> so<00:15:36.380> we<00:15:36.500> created<00:15:36.800> our 00:15:36.940 --> 00:15:36.950 align:start position:0% the main function so we created our 00:15:36.950 --> 00:15:39.250 align:start position:0% the main function so we created our playing<00:15:37.280> index<00:15:38.090> to<00:15:38.240> wonder<00:15:38.630> and<00:15:38.840> we<00:15:39.020> think 00:15:39.250 --> 00:15:39.260 align:start position:0% playing index to wonder and we think 00:15:39.260 --> 00:15:40.540 align:start position:0% playing index to wonder and we think that<00:15:39.410> the<00:15:39.500> value<00:15:39.860> is<00:15:40.010> this<00:15:40.190> is<00:15:40.310> just<00:15:40.460> a 00:15:40.540 --> 00:15:40.550 align:start position:0% that the value is this is just a 00:15:40.550 --> 00:15:43.360 align:start position:0% that the value is this is just a hexadecimal<00:15:40.880> will<00:15:41.390> be<00:15:41.570> large<00:15:41.930> number<00:15:42.370> the 00:15:43.360 --> 00:15:43.370 align:start position:0% hexadecimal will be large number the 00:15:43.370 --> 00:15:45.820 align:start position:0% hexadecimal will be large number the claim<00:15:43.580> of<00:15:43.730> those<00:15:43.850> secret<00:15:44.180> is<00:15:44.270> 42<00:15:44.830> regular 00:15:45.820 --> 00:15:45.830 align:start position:0% claim of those secret is 42 regular 00:15:45.830 --> 00:15:48.750 align:start position:0% claim of those secret is 42 regular playing<00:15:46.250> store<00:15:46.610> which<00:15:47.000> you<00:15:47.030> can<00:15:47.270> see<00:15:47.450> here<00:15:47.810> and 00:15:48.750 --> 00:15:48.760 align:start position:0% playing store which you can see here and 00:15:48.760 --> 00:15:52.090 align:start position:0% playing store which you can see here and let's<00:15:49.760> just<00:15:49.880> for<00:15:50.240> test<00:15:50.600> who<00:15:51.050> claims<00:15:51.590> on<00:15:51.890> each 00:15:52.090 --> 00:15:52.100 align:start position:0% let's just for test who claims on each 00:15:52.100 --> 00:16:01.030 align:start position:0% let's just for test who claims on each race<00:15:56.590> and<00:15:57.850> see<00:15:58.850> if<00:15:59.120> indeed<00:15:59.630> one<00:15:59.990> row<00:16:00.260> 200<00:16:00.920> we 00:16:01.030 --> 00:16:01.040 align:start position:0% race and see if indeed one row 200 we 00:16:01.040 --> 00:16:04.810 align:start position:0% race and see if indeed one row 200 we get<00:16:01.190> the<00:16:01.340> value<00:16:02.020> and<00:16:03.020> yes<00:16:03.380> we<00:16:03.950> get<00:16:04.130> the<00:16:04.430> value 00:16:04.810 --> 00:16:04.820 align:start position:0% get the value and yes we get the value 00:16:04.820 --> 00:16:07.270 align:start position:0% get the value and yes we get the value that<00:16:05.150> is<00:16:05.330> the<00:16:05.570> same<00:16:05.870> as<00:16:06.110> this<00:16:06.290> one<00:16:06.350> so<00:16:06.950> we 00:16:07.270 --> 00:16:07.280 align:start position:0% that is the same as this one so we 00:16:07.280 --> 00:16:13.720 align:start position:0% that is the same as this one so we implemented<00:16:07.790> by<00:16:07.940> trace<00:16:08.180> table<00:16:08.540> correctly<00:16:12.730> so 00:16:13.720 --> 00:16:13.730 align:start position:0% implemented by trace table correctly so 00:16:13.730 --> 00:16:15.190 align:start position:0% implemented by trace table correctly so that's<00:16:13.910> the<00:16:14.090> trade<00:16:14.300> stable<00:16:14.660> now<00:16:14.750> the<00:16:14.810> second 00:16:15.190 --> 00:16:15.200 align:start position:0% that's the trade stable now the second 00:16:15.200 --> 00:16:16.750 align:start position:0% that's the trade stable now the second thing<00:16:15.350> we<00:16:15.470> need<00:16:15.500> to<00:16:15.650> do<00:16:15.920> is<00:16:16.220> we<00:16:16.430> need<00:16:16.610> to 00:16:16.750 --> 00:16:16.760 align:start position:0% thing we need to do is we need to 00:16:16.760 --> 00:16:19.930 align:start position:0% thing we need to do is we need to implement<00:16:17.090> the<00:16:17.510> constraint<00:16:18.080> expressions<00:16:18.940> for 00:16:19.930 --> 00:16:19.940 align:start position:0% implement the constraint expressions for 00:16:19.940 --> 00:16:22.390 align:start position:0% implement the constraint expressions for that<00:16:20.000> we<00:16:20.390> have<00:16:20.540> a<00:16:20.570> little<00:16:20.810> genome<00:16:21.740> oppression 00:16:22.390 --> 00:16:22.400 align:start position:0% that we have a little genome oppression 00:16:22.400 --> 00:16:24.340 align:start position:0% that we have a little genome oppression expression<00:16:22.910> is<00:16:23.120> important<00:16:23.690> we<00:16:23.840> need<00:16:23.930> to<00:16:23.990> again 00:16:24.340 --> 00:16:24.350 align:start position:0% expression is important we need to again 00:16:24.350 --> 00:16:27.490 align:start position:0% expression is important we need to again have<00:16:25.160> a<00:16:25.220> number<00:16:25.630> of<00:16:26.630> rows<00:16:26.900> that<00:16:26.930> this<00:16:27.230> is<00:16:27.320> power 00:16:27.490 --> 00:16:27.500 align:start position:0% have a number of rows that this is power 00:16:27.500 --> 00:16:30.280 align:start position:0% have a number of rows that this is power of<00:16:27.680> 2<00:16:27.860> so<00:16:28.070> we<00:16:28.160> rounded<00:16:28.520> up<00:16:28.610> the<00:16:28.670> next<00:16:29.030> one<00:16:29.290> here 00:16:30.280 --> 00:16:30.290 align:start position:0% of 2 so we rounded up the next one here 00:16:30.290 --> 00:16:33.340 align:start position:0% of 2 so we rounded up the next one here I've<00:16:30.520> prepared<00:16:31.520> those<00:16:32.030> two<00:16:32.390> expressions<00:16:33.170> that 00:16:33.340 --> 00:16:33.350 align:start position:0% I've prepared those two expressions that 00:16:33.350 --> 00:16:37.870 align:start position:0% I've prepared those two expressions that do<00:16:34.310> one<00:16:34.760> off<00:16:34.940> and<00:16:35.330> repeated<00:16:35.900> constraints<00:16:36.880> so 00:16:37.870 --> 00:16:37.880 align:start position:0% do one off and repeated constraints so 00:16:37.880 --> 00:16:40.050 align:start position:0% do one off and repeated constraints so we<00:16:38.240> can<00:16:38.480> just<00:16:38.630> need<00:16:38.780> create<00:16:39.200> a<00:16:39.260> new<00:16:39.470> constraint 00:16:40.050 --> 00:16:40.060 align:start position:0% we can just need create a new constraint 00:16:40.060 --> 00:16:43.450 align:start position:0% we can just need create a new constraint object<00:16:41.060> from<00:16:41.570> expressions<00:16:42.260> we<00:16:42.950> give<00:16:43.100> the<00:16:43.220> size 00:16:43.450 --> 00:16:43.460 align:start position:0% object from expressions we give the size 00:16:43.460 --> 00:16:46.000 align:start position:0% object from expressions we give the size of<00:16:43.700> a<00:16:43.760> trace<00:16:44.000> table<00:16:44.420> which<00:16:44.570> is<00:16:44.600> n<00:16:44.870> by<00:16:45.050> two<00:16:45.110> we 00:16:46.000 --> 00:16:46.010 align:start position:0% of a trace table which is n by two we 00:16:46.010 --> 00:16:47.590 align:start position:0% of a trace table which is n by two we give<00:16:46.160> a<00:16:46.190> seed<00:16:46.460> which<00:16:46.940> in<00:16:47.120> this 00:16:47.590 --> 00:16:47.600 align:start position:0% give a seed which in this 00:16:47.600 --> 00:16:49.660 align:start position:0% give a seed which in this we're<00:16:47.720> not<00:16:47.839> really<00:16:48.019> using<00:16:48.440> and<00:16:48.920> now<00:16:49.250> I<00:16:49.279> know 00:16:49.660 --> 00:16:49.670 align:start position:0% we're not really using and now I know 00:16:49.670 --> 00:16:51.430 align:start position:0% we're not really using and now I know the<00:16:49.880> sector<00:16:50.269> where<00:16:50.540> I<00:16:50.600> just<00:16:50.899> can<00:16:51.110> just<00:16:51.139> enter 00:16:51.430 --> 00:16:51.440 align:start position:0% the sector where I just can just enter 00:16:51.440 --> 00:16:54.939 align:start position:0% the sector where I just can just enter these<00:16:51.800> expressions<00:16:52.519> so<00:16:53.199> does<00:16:54.199> anyone 00:16:54.939 --> 00:16:54.949 align:start position:0% these expressions so does anyone 00:16:54.949 --> 00:16:58.210 align:start position:0% these expressions so does anyone remember<00:16:55.130> or<00:16:55.699> constraints<00:16:56.800> there<00:16:57.800> you<00:16:57.949> go<00:16:58.040> the 00:16:58.210 --> 00:16:58.220 align:start position:0% remember or constraints there you go the 00:16:58.220 --> 00:17:00.970 align:start position:0% remember or constraints there you go the first<00:16:58.250> one<00:16:58.730> was<00:16:59.000> the<00:16:59.630> first<00:16:59.899> row<00:17:00.170> and<00:17:00.649> the 00:17:00.970 --> 00:17:00.980 align:start position:0% first one was the first row and the 00:17:00.980 --> 00:17:03.970 align:start position:0% first one was the first row and the first<00:17:01.009> column<00:17:01.310> needs<00:17:02.180> to<00:17:02.389> be<00:17:02.589> in<00:17:03.589> constant 00:17:03.970 --> 00:17:03.980 align:start position:0% first column needs to be in constant 00:17:03.980 --> 00:17:09.669 align:start position:0% first column needs to be in constant value<00:17:05.169> quantity<00:17:06.880> and<00:17:07.990> this<00:17:08.990> needs<00:17:09.289> to<00:17:09.470> hold 00:17:09.669 --> 00:17:09.679 align:start position:0% value quantity and this needs to hold 00:17:09.679 --> 00:17:13.299 align:start position:0% value quantity and this needs to hold for<00:17:10.100> the<00:17:10.910> first<00:17:11.209> row<00:17:11.510> so<00:17:11.959> we<00:17:12.079> say<00:17:12.260> on<00:17:12.530> row<00:17:12.740> zero 00:17:13.299 --> 00:17:13.309 align:start position:0% for the first row so we say on row zero 00:17:13.309 --> 00:17:16.689 align:start position:0% for the first row so we say on row zero and<00:17:13.880> for<00:17:14.150> second<00:17:15.110> constraint<00:17:15.500> very<00:17:16.280> similar 00:17:16.689 --> 00:17:16.699 align:start position:0% and for second constraint very similar 00:17:16.699 --> 00:17:20.890 align:start position:0% and for second constraint very similar to<00:17:16.819> the<00:17:16.910> first<00:17:17.150> one<00:17:17.410> except<00:17:18.410> that<00:17:19.240> we<00:17:20.240> now<00:17:20.510> need 00:17:20.890 --> 00:17:20.900 align:start position:0% to the first one except that we now need 00:17:20.900 --> 00:17:25.179 align:start position:0% to the first one except that we now need to<00:17:20.959> have<00:17:21.949> it<00:17:22.159> match<00:17:22.370> or<00:17:22.730> claims<00:17:23.240> invalid<00:17:24.189> and 00:17:25.179 --> 00:17:25.189 align:start position:0% to have it match or claims invalid and 00:17:25.189 --> 00:17:27.939 align:start position:0% to have it match or claims invalid and we<00:17:26.089> need<00:17:26.240> to<00:17:26.360> have<00:17:26.539> it<00:17:26.720> on<00:17:26.929> the<00:17:27.169> row<00:17:27.380> that<00:17:27.740> be 00:17:27.939 --> 00:17:27.949 align:start position:0% we need to have it on the row that be 00:17:27.949 --> 00:17:35.890 align:start position:0% we need to have it on the row that be plain<00:17:28.600> so<00:17:29.600> like<00:17:29.780> this<00:17:31.990> so<00:17:34.210> I<00:17:35.210> choose<00:17:35.690> the 00:17:35.890 --> 00:17:35.900 align:start position:0% plain so like this so I choose the 00:17:35.900 --> 00:17:39.710 align:start position:0% plain so like this so I choose the Southern<00:17:36.230> gentleman 00:17:39.710 --> 00:17:39.720 align:start position:0% 00:17:39.720 --> 00:17:43.690 align:start position:0% [Music] 00:17:43.690 --> 00:17:43.700 align:start position:0% 00:17:43.700 --> 00:17:47.240 align:start position:0% I'm<00:17:44.700> sorry<00:17:45.150> so<00:17:45.450> this<00:17:45.600> is<00:17:45.780> actually<00:17:46.200> this<00:17:46.920> is<00:17:46.980> an 00:17:47.240 --> 00:17:47.250 align:start position:0% I'm sorry so this is actually this is an 00:17:47.250 --> 00:17:52.670 align:start position:0% I'm sorry so this is actually this is an i<00:17:47.430> plus<00:17:47.580> you<00:17:48.560> but<00:17:50.570> so<00:17:51.570> it<00:17:51.660> means<00:17:51.840> that<00:17:51.960> on<00:17:52.260> on 00:17:52.670 --> 00:17:52.680 align:start position:0% i plus you but so it means that on on 00:17:52.680 --> 00:18:00.170 align:start position:0% i plus you but so it means that on on the<00:17:52.730> role<00:17:53.730> of<00:17:53.760> set<00:17:54.240> zero<00:17:54.630> versus<00:17:55.440> pro<00:17:55.620> upset<00:17:59.180> so 00:18:00.170 --> 00:18:00.180 align:start position:0% the role of set zero versus pro upset so 00:18:00.180 --> 00:18:03.320 align:start position:0% the role of set zero versus pro upset so this<00:18:01.530> where<00:18:02.070> it<00:18:02.160> like<00:18:02.430> this<00:18:02.640> now<00:18:02.940> it<00:18:03.150> have 00:18:03.320 --> 00:18:03.330 align:start position:0% this where it like this now it have 00:18:03.330 --> 00:18:05.930 align:start position:0% this where it like this now it have the<00:18:03.510> repeating<00:18:04.200> on<00:18:04.410> the<00:18:04.500> strain<00:18:04.770> but<00:18:05.640> before 00:18:05.930 --> 00:18:05.940 align:start position:0% the repeating on the strain but before 00:18:05.940 --> 00:18:07.330 align:start position:0% the repeating on the strain but before you<00:18:06.030> go<00:18:06.150> ahead 00:18:07.330 --> 00:18:07.340 align:start position:0% you go ahead 00:18:07.340 --> 00:18:09.950 align:start position:0% you go ahead the<00:18:08.340> on<00:18:08.520> row<00:18:08.700> and<00:18:08.850> every<00:18:09.060> row<00:18:09.210> of<00:18:09.240> functions 00:18:09.950 --> 00:18:09.960 align:start position:0% the on row and every row of functions 00:18:09.960 --> 00:18:13.220 align:start position:0% the on row and every row of functions and<00:18:10.230> omega<00:18:10.530> are<00:18:10.800> those<00:18:11.040> um<00:18:11.750> just<00:18:12.750> for<00:18:12.930> every 00:18:13.220 --> 00:18:13.230 align:start position:0% and omega are those um just for every 00:18:13.230 --> 00:18:14.600 align:start position:0% and omega are those um just for every table<00:18:13.740> or<00:18:13.860> are<00:18:13.920> they<00:18:14.010> specific<00:18:14.190> to<00:18:14.520> this 00:18:14.600 --> 00:18:14.610 align:start position:0% table or are they specific to this 00:18:14.610 --> 00:18:18.610 align:start position:0% table or are they specific to this example<00:18:15.890> they<00:18:16.890> would<00:18:17.130> work<00:18:17.340> for<00:18:17.610> every<00:18:17.970> table 00:18:18.610 --> 00:18:18.620 align:start position:0% example they would work for every table 00:18:18.620 --> 00:18:20.960 align:start position:0% example they would work for every table the<00:18:19.620> technical<00:18:20.130> thing<00:18:20.280> that<00:18:20.430> happens<00:18:20.760> is<00:18:20.940> that 00:18:20.960 --> 00:18:20.970 align:start position:0% the technical thing that happens is that 00:18:20.970 --> 00:18:24.650 align:start position:0% the technical thing that happens is that omega<00:18:21.570> is<00:18:21.840> a<00:18:22.200> root<00:18:22.950> of<00:18:23.130> unity<00:18:23.370> of<00:18:23.880> size<00:18:24.330> of<00:18:24.540> the 00:18:24.650 --> 00:18:24.660 align:start position:0% omega is a root of unity of size of the 00:18:24.660 --> 00:18:26.990 align:start position:0% omega is a root of unity of size of the trace<00:18:24.870> table<00:18:25.290> and<00:18:25.470> a<00:18:25.980> particular<00:18:26.310> prime<00:18:26.730> field 00:18:26.990 --> 00:18:27.000 align:start position:0% trace table and a particular prime field 00:18:27.000 --> 00:18:28.760 align:start position:0% trace table and a particular prime field that<00:18:27.180> we<00:18:27.300> have<00:18:27.480> as<00:18:27.780> roots<00:18:28.020> feud<00:18:28.380> is<00:18:28.470> the<00:18:28.590> only 00:18:28.760 --> 00:18:28.770 align:start position:0% that we have as roots feud is the only 00:18:28.770 --> 00:18:30.560 align:start position:0% that we have as roots feud is the only of<00:18:28.950> powers<00:18:29.280> of<00:18:29.400> two<00:18:29.550> which<00:18:29.940> is<00:18:30.120> why<00:18:30.300> these<00:18:30.360> have 00:18:30.560 --> 00:18:30.570 align:start position:0% of powers of two which is why these have 00:18:30.570 --> 00:18:33.560 align:start position:0% of powers of two which is why these have a<00:18:30.870> power<00:18:31.110> of<00:18:31.230> two<00:18:31.410> is<00:18:31.440> a<00:18:31.710> stable<00:18:32.040> name<00:18:32.160> but<00:18:32.940> this 00:18:33.560 --> 00:18:33.570 align:start position:0% a power of two is a stable name but this 00:18:33.570 --> 00:18:35.630 align:start position:0% a power of two is a stable name but this these<00:18:34.050> three<00:18:34.320> lines<00:18:34.530> here<00:18:34.980> you<00:18:35.460> can 00:18:35.630 --> 00:18:35.640 align:start position:0% these three lines here you can 00:18:35.640 --> 00:18:37.340 align:start position:0% these three lines here you can essentially<00:18:36.030> copy-paste<00:18:36.630> in<00:18:36.930> in<00:18:37.200> any 00:18:37.340 --> 00:18:37.350 align:start position:0% essentially copy-paste in in any 00:18:37.350 --> 00:18:44.840 align:start position:0% essentially copy-paste in in any constraint<00:18:37.830> system<00:18:38.160> and<00:18:38.340> I<00:18:38.400> should<00:18:43.850> know 00:18:44.840 --> 00:18:44.850 align:start position:0% constraint system and I should know 00:18:44.850 --> 00:18:49.610 align:start position:0% constraint system and I should know because<00:18:44.880> if<00:18:45.480> you<00:18:45.630> go<00:18:45.900> to<00:18:45.960> any<00:18:46.440> X<00:18:48.140> you<00:18:49.140> see<00:18:49.170> here 00:18:49.610 --> 00:18:49.620 align:start position:0% because if you go to any X you see here 00:18:49.620 --> 00:18:54.020 align:start position:0% because if you go to any X you see here that<00:18:49.650> we<00:18:49.860> do<00:18:50.130> I<00:18:50.400> and<00:18:50.820> I<00:18:51.180> plus<00:18:51.660> 1<00:18:52.280> so<00:18:53.280> the<00:18:53.820> I<00:18:53.850> plus 00:18:54.020 --> 00:18:54.030 align:start position:0% that we do I and I plus 1 so the I plus 00:18:54.030 --> 00:18:57.110 align:start position:0% that we do I and I plus 1 so the I plus is<00:18:54.750> sort<00:18:54.960> of<00:18:55.050> implicit<00:18:55.410> here<00:18:55.890> in<00:18:56.430> this<00:18:56.670> case<00:18:56.880> we 00:18:57.110 --> 00:18:57.120 align:start position:0% is sort of implicit here in this case we 00:18:57.120 --> 00:19:00.350 align:start position:0% is sort of implicit here in this case we have<00:18:57.270> I<00:18:57.420> plus<00:18:57.660> 0<00:18:57.960> I<00:18:58.050> plus<00:18:58.290> 0<00:18:59.030> which<00:19:00.030> matches 00:19:00.350 --> 00:19:00.360 align:start position:0% have I plus 0 I plus 0 which matches 00:19:00.360 --> 00:19:02.330 align:start position:0% have I plus 0 I plus 0 which matches what<00:19:00.690> we're<00:19:00.870> doing<00:19:01.080> here<00:19:01.380> this<00:19:01.560> is<00:19:01.890> like<00:19:02.160> I 00:19:02.330 --> 00:19:02.340 align:start position:0% what we're doing here this is like I 00:19:02.340 --> 00:19:07.160 align:start position:0% what we're doing here this is like I plus<00:19:02.730> 0<00:19:03.030> and<00:19:03.150> this<00:19:03.420> is<00:19:03.600> either<00:19:03.720> 0<00:19:05.180> the<00:19:06.180> actual 00:19:07.160 --> 00:19:07.170 align:start position:0% plus 0 and this is either 0 the actual 00:19:07.170 --> 00:19:10.730 align:start position:0% plus 0 and this is either 0 the actual did<00:19:07.680> the<00:19:08.220> number<00:19:08.520> 200<00:19:09.000> itself<00:19:09.360> comes<00:19:10.320> into 00:19:10.730 --> 00:19:10.740 align:start position:0% did the number 200 itself comes into 00:19:10.740 --> 00:19:12.890 align:start position:0% did the number 200 itself comes into this<00:19:10.890> on<00:19:11.130> world<00:19:11.400> expression<00:19:12.030> that's<00:19:12.690> where 00:19:12.890 --> 00:19:12.900 align:start position:0% this on world expression that's where 00:19:12.900 --> 00:19:16.610 align:start position:0% this on world expression that's where the<00:19:13.490> 200<00:19:14.490> is<00:19:14.670> implying<00:19:15.210> it<00:19:16.200> becomes<00:19:16.500> a<00:19:16.530> little 00:19:16.610 --> 00:19:16.620 align:start position:0% the 200 is implying it becomes a little 00:19:16.620 --> 00:19:18.470 align:start position:0% the 200 is implying it becomes a little bit<00:19:16.710> more<00:19:16.920> clearer<00:19:17.280> with<00:19:17.580> the<00:19:17.760> repeating 00:19:18.470 --> 00:19:18.480 align:start position:0% bit more clearer with the repeating 00:19:18.480 --> 00:19:20.180 align:start position:0% bit more clearer with the repeating constraints<00:19:19.020> so<00:19:19.170> the<00:19:19.260> first<00:19:19.470> one<00:19:19.680> will<00:19:19.860> do<00:19:19.980> is 00:19:20.180 --> 00:19:20.190 align:start position:0% constraints so the first one will do is 00:19:20.190 --> 00:19:25.390 align:start position:0% constraints so the first one will do is the<00:19:20.310> pokemons<00:19:20.700> strength 00:19:25.390 --> 00:19:25.400 align:start position:0% 00:19:25.400 --> 00:19:29.560 align:start position:0% we'll<00:19:25.730> do<00:19:25.880> a<00:19:25.910> trace<00:19:27.460> and<00:19:28.460> here<00:19:28.760> we<00:19:28.880> want<00:19:29.090> I<00:19:29.270> plus 00:19:29.560 --> 00:19:29.570 align:start position:0% we'll do a trace and here we want I plus 00:19:29.570 --> 00:19:33.490 align:start position:0% we'll do a trace and here we want I plus one<00:19:29.840> so<00:19:30.110> we<00:19:30.200> say<00:19:30.380> one<00:19:30.620> year<00:19:30.650> and<00:19:31.220> zero<00:19:31.610> and<00:19:32.500> we 00:19:33.490 --> 00:19:33.500 align:start position:0% one so we say one year and zero and we 00:19:33.500 --> 00:19:38.010 align:start position:0% one so we say one year and zero and we need<00:19:33.710> to<00:19:33.890> subtract<00:19:34.580> Trey's<00:19:36.190> zero<00:19:37.190> comma<00:19:37.730> one 00:19:38.010 --> 00:19:38.020 align:start position:0% need to subtract Trey's zero comma one 00:19:38.020 --> 00:19:42.870 align:start position:0% need to subtract Trey's zero comma one so<00:19:39.490> one<00:19:40.490> row<00:19:40.700> down<00:19:41.030> and<00:19:41.420> coma<00:19:41.960> zero 00:19:42.870 --> 00:19:42.880 align:start position:0% so one row down and coma zero 00:19:42.880 --> 00:19:49.360 align:start position:0% so one row down and coma zero -<00:19:43.880> same<00:19:44.780> room<00:19:45.140> whole<00:19:45.650> month<00:19:47.500> and<00:19:48.500> we<00:19:49.040> want<00:19:49.160> this 00:19:49.360 --> 00:19:49.370 align:start position:0% - same room whole month and we want this 00:19:49.370 --> 00:19:55.530 align:start position:0% - same room whole month and we want this on<00:19:50.530> every<00:19:51.530> row<00:19:51.710> and<00:19:54.010> then<00:19:55.010> there<00:19:55.190> is<00:19:55.280> one<00:19:55.490> more 00:19:55.530 --> 00:19:55.540 align:start position:0% on every row and then there is one more 00:19:55.540 --> 00:19:58.990 align:start position:0% on every row and then there is one more repeating<00:19:56.540> strength<00:19:56.990> that<00:19:57.110> we<00:19:57.260> have<00:19:57.440> and<00:19:58.000> in 00:19:58.990 --> 00:19:59.000 align:start position:0% repeating strength that we have and in 00:19:59.000 --> 00:20:00.310 align:start position:0% repeating strength that we have and in fact<00:19:59.030> this<00:19:59.360> is<00:19:59.420> the<00:19:59.540> constraint<00:19:59.960> whether<00:20:00.230> it's 00:20:00.310 --> 00:20:00.320 align:start position:0% fact this is the constraint whether it's 00:20:00.320 --> 00:20:01.990 align:start position:0% fact this is the constraint whether it's on<00:20:00.470> or<00:20:00.680> it's<00:20:01.070> all<00:20:01.190> about<00:20:01.400> because<00:20:01.700> this<00:20:01.820> is<00:20:01.880> the 00:20:01.990 --> 00:20:02.000 align:start position:0% on or it's all about because this is the 00:20:02.000 --> 00:20:03.430 align:start position:0% on or it's all about because this is the one<00:20:02.150> that<00:20:02.240> I<00:20:02.420> should<00:20:02.480> be<00:20:02.750> implements<00:20:03.230> that<00:20:03.260> you 00:20:03.430 --> 00:20:03.440 align:start position:0% one that I should be implements that you 00:20:03.440 --> 00:20:04.950 align:start position:0% one that I should be implements that you will<00:20:03.560> not<00:20:03.650> see<00:20:03.890> there<00:20:04.130> is<00:20:04.250> this<00:20:04.400> sort<00:20:04.640> of<00:20:04.730> like 00:20:04.950 --> 00:20:04.960 align:start position:0% will not see there is this sort of like 00:20:04.960 --> 00:20:09.580 align:start position:0% will not see there is this sort of like boiler<00:20:05.960> plate<00:20:06.200> and<00:20:06.380> plumbing<00:20:06.710> and<00:20:08.470> this<00:20:09.470> is 00:20:09.580 --> 00:20:09.590 align:start position:0% boiler plate and plumbing and this is 00:20:09.590 --> 00:20:13.170 align:start position:0% boiler plate and plumbing and this is the<00:20:09.710> line<00:20:09.890> that<00:20:09.920> says<00:20:10.310> that<00:20:10.610> it<00:20:10.850> is<00:20:10.880> the<00:20:11.150> sum<00:20:11.420> of 00:20:13.170 --> 00:20:13.180 align:start position:0% the line that says that it is the sum of 00:20:13.180 --> 00:20:16.540 align:start position:0% the line that says that it is the sum of the<00:20:14.180> next<00:20:14.510> row<00:20:14.660> first<00:20:15.020> column<00:20:15.110> is<00:20:15.860> the<00:20:16.070> sum<00:20:16.280> of 00:20:16.540 --> 00:20:16.550 align:start position:0% the next row first column is the sum of 00:20:16.550 --> 00:20:19.540 align:start position:0% the next row first column is the sum of the<00:20:16.850> previous<00:20:17.300> row<00:20:17.450> both<00:20:17.720> columns<00:20:18.460> there<00:20:19.460> we 00:20:19.540 --> 00:20:19.550 align:start position:0% the previous row both columns there we 00:20:19.550 --> 00:20:26.860 align:start position:0% the previous row both columns there we go 00:20:26.860 --> 00:20:26.870 align:start position:0% 00:20:26.870 --> 00:20:30.490 align:start position:0% here<00:20:27.440> right<00:20:27.740> right<00:20:27.950> yes<00:20:28.490> so<00:20:29.240> next<00:20:29.660> row<00:20:29.840> second 00:20:30.490 --> 00:20:30.500 align:start position:0% here right right yes so next row second 00:20:30.500 --> 00:20:35.980 align:start position:0% here right right yes so next row second column<00:20:30.530> sum<00:20:31.460> of<00:20:31.610> previous<00:20:32.300> row<00:20:34.090> okay<00:20:35.090> let's 00:20:35.980 --> 00:20:35.990 align:start position:0% column sum of previous row okay let's 00:20:35.990 --> 00:20:36.490 align:start position:0% column sum of previous row okay let's see<00:20:36.200> it 00:20:36.490 --> 00:20:36.500 align:start position:0% see it 00:20:36.500 --> 00:20:37.490 align:start position:0% see it runs 00:20:37.490 --> 00:20:37.500 align:start position:0% runs 00:20:37.500 --> 00:20:47.390 align:start position:0% runs [Music] 00:20:47.390 --> 00:20:47.400 align:start position:0% 00:20:47.400 --> 00:21:10.860 align:start position:0% I<00:20:47.960> expected 00:21:10.860 --> 00:21:10.870 align:start position:0% 00:21:10.870 --> 00:21:17.970 align:start position:0% missing<00:21:11.560> parentheses<00:21:16.620> successful<00:21:17.620> people 00:21:17.970 --> 00:21:17.980 align:start position:0% missing parentheses successful people 00:21:17.980 --> 00:21:23.370 align:start position:0% missing parentheses successful people not<00:21:18.220> see<00:21:18.430> proof<00:21:18.640> in<00:21:19.680> 32<00:21:20.680> it<00:21:20.860> opens<00:21:22.140> it<00:21:23.140> gets 00:21:23.370 --> 00:21:23.380 align:start position:0% not see proof in 32 it opens it gets 00:21:23.380 --> 00:21:25.380 align:start position:0% not see proof in 32 it opens it gets better<00:21:23.950> the<00:21:24.700> crew<00:21:24.880> size<00:21:25.120> grows 00:21:25.380 --> 00:21:25.390 align:start position:0% better the crew size grows 00:21:25.390 --> 00:21:27.090 align:start position:0% better the crew size grows logarithmically<00:21:25.630> so-called<00:21:26.620> larger<00:21:26.950> and 00:21:27.090 --> 00:21:27.100 align:start position:0% logarithmically so-called larger and 00:21:27.100 --> 00:21:29.340 align:start position:0% logarithmically so-called larger and larger<00:21:27.190> examples<00:21:27.940> it's<00:21:28.350> significantly 00:21:29.340 --> 00:21:29.350 align:start position:0% larger examples it's significantly 00:21:29.350 --> 00:21:31.980 align:start position:0% larger examples it's significantly better<00:21:29.940> now<00:21:30.940> I'll<00:21:31.150> show<00:21:31.360> you<00:21:31.420> what<00:21:31.750> what 00:21:31.980 --> 00:21:31.990 align:start position:0% better now I'll show you what what 00:21:31.990 --> 00:21:33.780 align:start position:0% better now I'll show you what what exactly<00:21:32.530> happened<00:21:32.860> here<00:21:33.010> so<00:21:33.430> we're<00:21:33.580> creating 00:21:33.780 --> 00:21:33.790 align:start position:0% exactly happened here so we're creating 00:21:33.790 --> 00:21:36.570 align:start position:0% exactly happened here so we're creating now<00:21:34.300> an<00:21:34.750> instance<00:21:35.650> of<00:21:35.800> this<00:21:35.980> people<00:21:36.280> massive 00:21:36.570 --> 00:21:36.580 align:start position:0% now an instance of this people massive 00:21:36.580 --> 00:21:39.150 align:start position:0% now an instance of this people massive flame<00:21:36.790> of<00:21:37.030> yet<00:21:37.240> with<00:21:37.960> the<00:21:38.170> values<00:21:38.650> that<00:21:38.980> we 00:21:39.150 --> 00:21:39.160 align:start position:0% flame of yet with the values that we 00:21:39.160 --> 00:21:41.370 align:start position:0% flame of yet with the values that we want<00:21:39.280> to<00:21:39.460> prove<00:21:39.700> we<00:21:40.480> have<00:21:40.690> our<00:21:40.810> secret<00:21:41.170> value 00:21:41.370 --> 00:21:41.380 align:start position:0% want to prove we have our secret value 00:21:41.380 --> 00:21:44.820 align:start position:0% want to prove we have our secret value that<00:21:41.650> we<00:21:41.740> want<00:21:41.860> to<00:21:42.010> hide<00:21:42.210> we<00:21:43.260> created<00:21:44.260> proof<00:21:44.500> by 00:21:44.820 --> 00:21:44.830 align:start position:0% that we want to hide we created proof by 00:21:44.830 --> 00:21:47.640 align:start position:0% that we want to hide we created proof by saying<00:21:45.130> play<00:21:45.580> monkey<00:21:45.910> act<00:21:46.060> dog<00:21:46.480> proof<00:21:46.750> with 00:21:47.640 --> 00:21:47.650 align:start position:0% saying play monkey act dog proof with 00:21:47.650 --> 00:21:50.310 align:start position:0% saying play monkey act dog proof with our<00:21:47.770> secret<00:21:48.250> and<00:21:48.630> unwrap<00:21:49.630> as<00:21:49.810> a<00:21:49.840> technicality 00:21:50.310 --> 00:21:50.320 align:start position:0% our secret and unwrap as a technicality 00:21:50.320 --> 00:21:52.880 align:start position:0% our secret and unwrap as a technicality here<00:21:50.860> for<00:21:51.100> trust<00:21:52.090> error<00:21:52.300> handling 00:21:52.880 --> 00:21:52.890 align:start position:0% here for trust error handling 00:21:52.890 --> 00:21:54.990 align:start position:0% here for trust error handling they<00:21:53.890> basically<00:21:54.070> throws<00:21:54.460> an<00:21:54.640> error<00:21:54.790> in 00:21:54.990 --> 00:21:55.000 align:start position:0% they basically throws an error in 00:21:55.000 --> 00:21:58.380 align:start position:0% they basically throws an error in anything<00:21:55.270> fails<00:21:56.610> then<00:21:57.610> we<00:21:57.730> can<00:21:57.880> compare<00:21:58.210> this 00:21:58.380 --> 00:21:58.390 align:start position:0% anything fails then we can compare this 00:21:58.390 --> 00:22:00.870 align:start position:0% anything fails then we can compare this proof<00:21:58.690> -<00:21:58.990> it's<00:21:59.170> like<00:21:59.500> binary<00:21:59.880> representation 00:22:00.870 --> 00:22:00.880 align:start position:0% proof - it's like binary representation 00:22:00.880 --> 00:22:02.910 align:start position:0% proof - it's like binary representation we<00:22:01.150> can<00:22:01.300> show<00:22:01.480> that<00:22:01.630> it's<00:22:01.810> about<00:22:02.020> 32<00:22:02.380> kilobytes 00:22:02.910 --> 00:22:02.920 align:start position:0% we can show that it's about 32 kilobytes 00:22:02.920 --> 00:22:05.280 align:start position:0% we can show that it's about 32 kilobytes and<00:22:03.310> what<00:22:04.150> we<00:22:04.240> can<00:22:04.360> also<00:22:04.480> do<00:22:04.720> is<00:22:04.870> we<00:22:04.900> can<00:22:05.050> do 00:22:05.280 --> 00:22:05.290 align:start position:0% and what we can also do is we can do 00:22:05.290 --> 00:22:07.920 align:start position:0% and what we can also do is we can do plain<00:22:05.680> thought<00:22:06.490> verify<00:22:07.180> and<00:22:07.540> give<00:22:07.720> it<00:22:07.840> the 00:22:07.920 --> 00:22:07.930 align:start position:0% plain thought verify and give it the 00:22:07.930 --> 00:22:11.780 align:start position:0% plain thought verify and give it the proof<00:22:08.170> and<00:22:08.410> make<00:22:08.740> sure<00:22:08.890> it's<00:22:09.070> okay<00:22:10.110> and<00:22:11.110> I<00:22:11.320> mean 00:22:11.780 --> 00:22:11.790 align:start position:0% proof and make sure it's okay and I mean 00:22:11.790 --> 00:22:16.530 align:start position:0% proof and make sure it's okay and I mean print<00:22:12.790> valid<00:22:13.210> which<00:22:13.600> you<00:22:13.780> see<00:22:14.290> here<00:22:15.450> what<00:22:16.450> we 00:22:16.530 --> 00:22:16.540 align:start position:0% print valid which you see here what we 00:22:16.540 --> 00:22:18.960 align:start position:0% print valid which you see here what we can<00:22:16.690> also<00:22:16.780> do<00:22:17.050> is<00:22:17.320> create<00:22:17.890> an<00:22:18.100> incorrect<00:22:18.640> thing 00:22:18.960 --> 00:22:18.970 align:start position:0% can also do is create an incorrect thing 00:22:18.970 --> 00:22:22.080 align:start position:0% can also do is create an incorrect thing so<00:22:19.420> let's<00:22:19.930> take<00:22:20.140> the<00:22:20.260> same<00:22:20.290> index<00:22:20.890> and<00:22:21.190> let's 00:22:22.080 --> 00:22:22.090 align:start position:0% so let's take the same index and let's 00:22:22.090 --> 00:22:23.730 align:start position:0% so let's take the same index and let's not<00:22:22.270> change<00:22:22.510> the<00:22:22.660> value<00:22:22.780> to<00:22:23.170> something 00:22:23.730 --> 00:22:23.740 align:start position:0% not change the value to something 00:22:23.740 --> 00:22:24.720 align:start position:0% not change the value to something completely<00:22:24.070> different 00:22:24.720 --> 00:22:24.730 align:start position:0% completely different 00:22:24.730 --> 00:22:27.750 align:start position:0% completely different and<00:22:25.050> if<00:22:26.050> we<00:22:26.170> take<00:22:26.320> a<00:22:26.380> wrong<00:22:26.680> plane<00:22:27.010> and<00:22:27.340> try<00:22:27.700> to 00:22:27.750 --> 00:22:27.760 align:start position:0% and if we take a wrong plane and try to 00:22:27.760 --> 00:22:30.180 align:start position:0% and if we take a wrong plane and try to verify<00:22:28.300> it<00:22:28.360> using<00:22:28.540> this<00:22:29.020> proof<00:22:29.320> it<00:22:29.890> will 00:22:30.180 --> 00:22:30.190 align:start position:0% verify it using this proof it will 00:22:30.190 --> 00:22:36.830 align:start position:0% verify it using this proof it will actually<00:22:30.880> print<00:22:31.620> invalid<00:22:34.020> so 00:22:36.830 --> 00:22:36.840 align:start position:0% actually print invalid so 00:22:36.840 --> 00:22:41.180 align:start position:0% actually print invalid so so<00:22:37.409> much<00:22:37.529> for<00:22:37.710> the<00:22:37.769> life<00:22:37.950> coding<00:22:38.309> part<00:22:40.190> in 00:22:41.180 --> 00:22:41.190 align:start position:0% so much for the life coding part in 00:22:41.190 --> 00:22:45.889 align:start position:0% so much for the life coding part in contusion<00:22:43.249> so<00:22:44.249> we<00:22:44.340> started<00:22:44.669> this<00:22:44.759> open<00:22:45.120> CPU 00:22:45.889 --> 00:22:45.899 align:start position:0% contusion so we started this open CPU 00:22:45.899 --> 00:22:47.720 align:start position:0% contusion so we started this open CPU project<00:22:46.320> to<00:22:46.470> experiment<00:22:47.159> and<00:22:47.279> learn<00:22:47.340> and 00:22:47.720 --> 00:22:47.730 align:start position:0% project to experiment and learn and 00:22:47.730 --> 00:22:50.749 align:start position:0% project to experiment and learn and study<00:22:47.940> different<00:22:48.210> root<00:22:48.600> systems<00:22:49.519> like<00:22:50.519> I<00:22:50.549> said 00:22:50.749 --> 00:22:50.759 align:start position:0% study different root systems like I said 00:22:50.759 --> 00:22:52.039 align:start position:0% study different root systems like I said we're<00:22:50.970> currently<00:22:51.149> having<00:22:51.330> only<00:22:51.720> a<00:22:51.840> very 00:22:52.039 --> 00:22:52.049 align:start position:0% we're currently having only a very 00:22:52.049 --> 00:22:53.779 align:start position:0% we're currently having only a very partial<00:22:52.320> implementation<00:22:52.740> one<00:22:53.399> of<00:22:53.519> the<00:22:53.610> things 00:22:53.779 --> 00:22:53.789 align:start position:0% partial implementation one of the things 00:22:53.789 --> 00:22:55.940 align:start position:0% partial implementation one of the things we<00:22:53.970> would<00:22:54.179> like<00:22:54.389> to<00:22:54.419> implement<00:22:55.049> next<00:22:55.409> from<00:22:55.830> the 00:22:55.940 --> 00:22:55.950 align:start position:0% we would like to implement next from the 00:22:55.950 --> 00:22:58.669 align:start position:0% we would like to implement next from the start<00:22:56.249> proof<00:22:56.669> protocol<00:22:57.240> is<00:22:57.679> having 00:22:58.669 --> 00:22:58.679 align:start position:0% start proof protocol is having 00:22:58.679 --> 00:23:01.789 align:start position:0% start proof protocol is having constraints<00:22:59.370> that<00:22:59.749> span<00:23:00.749> offsets<00:23:01.289> different 00:23:01.789 --> 00:23:01.799 align:start position:0% constraints that span offsets different 00:23:01.799 --> 00:23:03.019 align:start position:0% constraints that span offsets different from<00:23:01.950> one<00:23:02.100> leg<00:23:02.309> right<00:23:02.340> now<00:23:02.519> we<00:23:02.730> have 00:23:03.019 --> 00:23:03.029 align:start position:0% from one leg right now we have 00:23:03.029 --> 00:23:05.779 align:start position:0% from one leg right now we have constraints<00:23:03.360> between<00:23:03.809> rows<00:23:04.080> between<00:23:04.950> one<00:23:05.610> row 00:23:05.779 --> 00:23:05.789 align:start position:0% constraints between rows between one row 00:23:05.789 --> 00:23:07.669 align:start position:0% constraints between rows between one row in<00:23:05.940> the<00:23:06.029> next<00:23:06.450> if<00:23:06.659> you<00:23:07.169> want<00:23:07.379> to<00:23:07.499> do 00:23:07.669 --> 00:23:07.679 align:start position:0% in the next if you want to do 00:23:07.679 --> 00:23:09.649 align:start position:0% in the next if you want to do interesting<00:23:08.190> things<00:23:08.399> you<00:23:08.940> really<00:23:09.330> need<00:23:09.509> to 00:23:09.649 --> 00:23:09.659 align:start position:0% interesting things you really need to 00:23:09.659 --> 00:23:12.230 align:start position:0% interesting things you really need to have<00:23:10.279> offsets<00:23:11.279> that<00:23:11.460> are<00:23:11.730> more<00:23:11.909> complicated 00:23:12.230 --> 00:23:12.240 align:start position:0% have offsets that are more complicated 00:23:12.240 --> 00:23:13.940 align:start position:0% have offsets that are more complicated than<00:23:12.659> one<00:23:12.990> row<00:23:13.139> in<00:23:13.289> the<00:23:13.379> next<00:23:13.590> you<00:23:13.649> want<00:23:13.799> to<00:23:13.860> be 00:23:13.940 --> 00:23:13.950 align:start position:0% than one row in the next you want to be 00:23:13.950 --> 00:23:16.070 align:start position:0% than one row in the next you want to be able<00:23:14.009> to<00:23:14.129> reference<00:23:14.549> multiple<00:23:15.029> rows<00:23:15.480> back<00:23:15.749> for 00:23:16.070 --> 00:23:16.080 align:start position:0% able to reference multiple rows back for 00:23:16.080 --> 00:23:18.350 align:start position:0% able to reference multiple rows back for example<00:23:16.639> we<00:23:17.639> want<00:23:17.789> to<00:23:17.850> add<00:23:17.909> many<00:23:18.269> more 00:23:18.350 --> 00:23:18.360 align:start position:0% example we want to add many more 00:23:18.360 --> 00:23:21.019 align:start position:0% example we want to add many more examples<00:23:18.990> that<00:23:19.230> is<00:23:19.470> we<00:23:20.159> have<00:23:20.309> for<00:23:20.519> example<00:23:20.549> an 00:23:21.019 --> 00:23:21.029 align:start position:0% examples that is we have for example an 00:23:21.029 --> 00:23:22.940 align:start position:0% examples that is we have for example an implementation<00:23:21.690> of<00:23:21.840> the<00:23:22.289> mimsy<00:23:22.679> hash 00:23:22.940 --> 00:23:22.950 align:start position:0% implementation of the mimsy hash 00:23:22.950 --> 00:23:25.940 align:start position:0% implementation of the mimsy hash function<00:23:23.519> we<00:23:24.240> are<00:23:24.269> working<00:23:24.720> on<00:23:24.960> technology 00:23:25.940 --> 00:23:25.950 align:start position:0% function we are working on technology 00:23:25.950 --> 00:23:31.389 align:start position:0% function we are working on technology proposal<00:23:26.789> for<00:23:28.580> proof<00:23:29.580> of<00:23:29.759> data<00:23:30.059> availability 00:23:31.389 --> 00:23:31.399 align:start position:0% proposal for proof of data availability 00:23:31.399 --> 00:23:35.359 align:start position:0% proposal for proof of data availability we<00:23:32.399> are<00:23:32.580> working<00:23:33.119> on<00:23:33.419> the<00:23:33.539> example<00:23:34.259> from<00:23:34.710> Aneta 00:23:35.359 --> 00:23:35.369 align:start position:0% we are working on the example from Aneta 00:23:35.369 --> 00:23:37.190 align:start position:0% we are working on the example from Aneta labs<00:23:35.700> where<00:23:36.029> they<00:23:36.059> do<00:23:36.210> a<00:23:36.240> verifiable<00:23:36.749> tool<00:23:37.080> a 00:23:37.190 --> 00:23:37.200 align:start position:0% labs where they do a verifiable tool a 00:23:37.200 --> 00:23:40.119 align:start position:0% labs where they do a verifiable tool a function<00:23:37.679> using<00:23:38.070> MC<00:23:38.429> so<00:23:38.909> that's<00:23:39.059> a<00:23:39.149> lot<00:23:39.269> of<00:23:39.299> fun 00:23:40.119 --> 00:23:40.129 align:start position:0% function using MC so that's a lot of fun 00:23:40.129 --> 00:23:43.820 align:start position:0% function using MC so that's a lot of fun we're<00:23:41.129> working<00:23:41.429> on<00:23:41.580> or<00:23:41.999> we<00:23:42.629> won't<00:23:43.019> be<00:23:43.320> working 00:23:43.820 --> 00:23:43.830 align:start position:0% we're working on or we won't be working 00:23:43.830 --> 00:23:44.450 align:start position:0% we're working on or we won't be working on 00:23:44.450 --> 00:23:44.460 align:start position:0% on 00:23:44.460 --> 00:23:46.730 align:start position:0% on evn<00:23:44.940> fairly<00:23:45.360> minor<00:23:45.570> contract<00:23:46.200> so<00:23:46.470> that<00:23:46.499> you 00:23:46.730 --> 00:23:46.740 align:start position:0% evn fairly minor contract so that you 00:23:46.740 --> 00:23:49.340 align:start position:0% evn fairly minor contract so that you can<00:23:46.950> not<00:23:47.369> only<00:23:47.519> like<00:23:47.879> right<00:23:48.059> now<00:23:48.240> we<00:23:49.200> can 00:23:49.340 --> 00:23:49.350 align:start position:0% can not only like right now we can 00:23:49.350 --> 00:23:51.950 align:start position:0% can not only like right now we can verify<00:23:49.590> your<00:23:49.830> proof<00:23:50.159> in<00:23:50.460> rust<00:23:50.759> our<00:23:51.480> rest<00:23:51.720> code 00:23:51.950 --> 00:23:51.960 align:start position:0% verify your proof in rust our rest code 00:23:51.960 --> 00:23:54.649 align:start position:0% verify your proof in rust our rest code base<00:23:52.169> compiles<00:23:52.889> to<00:23:52.980> webassembly<00:23:53.789> so<00:23:54.419> we 00:23:54.649 --> 00:23:54.659 align:start position:0% base compiles to webassembly so we 00:23:54.659 --> 00:23:57.529 align:start position:0% base compiles to webassembly so we already<00:23:55.529> have<00:23:55.679> verifiers<00:23:56.249> in<00:23:56.490> the<00:23:56.580> browser<00:23:56.789> we 00:23:57.529 --> 00:23:57.539 align:start position:0% already have verifiers in the browser we 00:23:57.539 --> 00:23:59.570 align:start position:0% already have verifiers in the browser we also<00:23:57.749> managed<00:23:58.259> to<00:23:58.289> verify<00:23:58.830> it<00:23:58.889> inside<00:23:59.369> of<00:23:59.519> the 00:23:59.570 --> 00:23:59.580 align:start position:0% also managed to verify it inside of the 00:23:59.580 --> 00:24:03.499 align:start position:0% also managed to verify it inside of the substrate<00:24:00.470> note<00:24:01.470> so<00:24:02.190> any<00:24:02.580> like<00:24:02.909> webassembly 00:24:03.499 --> 00:24:03.509 align:start position:0% substrate note so any like webassembly 00:24:03.509 --> 00:24:06.470 align:start position:0% substrate note so any like webassembly enabled<00:24:04.639> 2.0<00:24:05.639> blockchains 00:24:06.470 --> 00:24:06.480 align:start position:0% enabled 2.0 blockchains 00:24:06.480 --> 00:24:10.070 align:start position:0% enabled 2.0 blockchains will<00:24:06.960> be<00:24:07.110> able<00:24:07.230> to<00:24:07.350> verify<00:24:07.590> the<00:24:07.799> exposure<00:24:09.419> one 00:24:10.070 --> 00:24:10.080 align:start position:0% will be able to verify the exposure one 00:24:10.080 --> 00:24:11.749 align:start position:0% will be able to verify the exposure one thing<00:24:10.230> you<00:24:10.320> noticed<00:24:10.710> in<00:24:10.919> this<00:24:11.039> language<00:24:11.340> right 00:24:11.749 --> 00:24:11.759 align:start position:0% thing you noticed in this language right 00:24:11.759 --> 00:24:13.489 align:start position:0% thing you noticed in this language right now<00:24:11.879> is<00:24:12.090> it<00:24:12.210> feels<00:24:12.509> really<00:24:12.720> low<00:24:12.960> level<00:24:13.350> like 00:24:13.489 --> 00:24:13.499 align:start position:0% now is it feels really low level like 00:24:13.499 --> 00:24:15.080 align:start position:0% now is it feels really low level like we're<00:24:13.649> literally<00:24:13.950> writing<00:24:14.249> the<00:24:14.460> assembly 00:24:15.080 --> 00:24:15.090 align:start position:0% we're literally writing the assembly 00:24:15.090 --> 00:24:16.700 align:start position:0% we're literally writing the assembly language<00:24:15.539> that<00:24:15.690> those<00:24:15.809> brain<00:24:16.080> systems<00:24:16.289> and 00:24:16.700 --> 00:24:16.710 align:start position:0% language that those brain systems and 00:24:16.710 --> 00:24:18.470 align:start position:0% language that those brain systems and what<00:24:16.830> you<00:24:16.950> want<00:24:17.249> is<00:24:17.490> a<00:24:17.519> higher-level<00:24:17.879> language 00:24:18.470 --> 00:24:18.480 align:start position:0% what you want is a higher-level language 00:24:18.480 --> 00:24:21.379 align:start position:0% what you want is a higher-level language where<00:24:19.139> you<00:24:19.230> just<00:24:19.409> write<00:24:20.159> the<00:24:20.369> program<00:24:21.029> in 00:24:21.379 --> 00:24:21.389 align:start position:0% where you just write the program in 00:24:21.389 --> 00:24:24.350 align:start position:0% where you just write the program in moralistic<00:24:22.249> Python<00:24:23.249> s<00:24:23.429> language<00:24:24.029> that<00:24:24.330> I 00:24:24.350 --> 00:24:24.360 align:start position:0% moralistic Python s language that I 00:24:24.360 --> 00:24:26.869 align:start position:0% moralistic Python s language that I showed<00:24:25.009> and<00:24:26.009> then<00:24:26.129> demo<00:24:26.340> automatically 00:24:26.869 --> 00:24:26.879 align:start position:0% showed and then demo automatically 00:24:26.879 --> 00:24:29.210 align:start position:0% showed and then demo automatically generate<00:24:27.269> the<00:24:27.960> logic<00:24:28.320> put<00:24:28.529> a<00:24:28.559> trace<00:24:28.799> table<00:24:29.159> a 00:24:29.210 --> 00:24:29.220 align:start position:0% generate the logic put a trace table a 00:24:29.220 --> 00:24:31.220 align:start position:0% generate the logic put a trace table a little<00:24:29.279> spaces<00:24:29.639> for<00:24:30.179> you<00:24:30.330> that's<00:24:31.049> an 00:24:31.220 --> 00:24:31.230 align:start position:0% little spaces for you that's an 00:24:31.230 --> 00:24:34.609 align:start position:0% little spaces for you that's an interesting<00:24:31.820> field<00:24:32.820> to<00:24:32.940> explore 00:24:34.609 --> 00:24:34.619 align:start position:0% interesting field to explore 00:24:34.619 --> 00:24:38.149 align:start position:0% interesting field to explore performance<00:24:35.220> is<00:24:35.340> pretty<00:24:35.519> decent<00:24:36.529> but<00:24:37.529> still 00:24:38.149 --> 00:24:38.159 align:start position:0% performance is pretty decent but still 00:24:38.159 --> 00:24:39.380 align:start position:0% performance is pretty decent but still has<00:24:38.279> room<00:24:38.490> for 00:24:39.380 --> 00:24:39.390 align:start position:0% has room for 00:24:39.390 --> 00:24:41.820 align:start position:0% has room for so<00:24:40.390> that's<00:24:40.540> something<00:24:40.840> we<00:24:40.960> can<00:24:41.080> work<00:24:41.110> on<00:24:41.380> and 00:24:41.820 --> 00:24:41.830 align:start position:0% so that's something we can work on and 00:24:41.830 --> 00:24:44.190 align:start position:0% so that's something we can work on and we're<00:24:42.010> interested<00:24:42.610> in<00:24:42.929> implementing<00:24:43.929> all 00:24:44.190 --> 00:24:44.200 align:start position:0% we're interested in implementing all 00:24:44.200 --> 00:24:49.560 align:start position:0% we're interested in implementing all sorts<00:24:44.650> of<00:24:44.830> crazy<00:24:45.340> new<00:24:48.059> serie<00:24:49.059> knowledge<00:24:49.360> proof 00:24:49.560 --> 00:24:49.570 align:start position:0% sorts of crazy new serie knowledge proof 00:24:49.570 --> 00:24:51.150 align:start position:0% sorts of crazy new serie knowledge proof protocols<00:24:50.140> that<00:24:50.320> have<00:24:50.380> been<00:24:50.650> released<00:24:50.950> over 00:24:51.150 --> 00:24:51.160 align:start position:0% protocols that have been released over 00:24:51.160 --> 00:24:53.190 align:start position:0% protocols that have been released over the<00:24:51.340> past<00:24:51.520> couple<00:24:51.730> of<00:24:51.940> months<00:24:52.000> a<00:24:52.419> lot<00:24:52.900> of<00:24:53.020> them 00:24:53.190 --> 00:24:53.200 align:start position:0% the past couple of months a lot of them 00:24:53.200 --> 00:24:55.500 align:start position:0% the past couple of months a lot of them have<00:24:53.590> a<00:24:54.070> meaningful<00:24:54.520> equivalent<00:24:55.330> that<00:24:55.450> is 00:24:55.500 --> 00:24:55.510 align:start position:0% have a meaningful equivalent that is 00:24:55.510 --> 00:24:57.510 align:start position:0% have a meaningful equivalent that is very<00:24:55.750> similar<00:24:56.110> to<00:24:56.320> Starks<00:24:56.890> in<00:24:57.040> the<00:24:57.130> sense<00:24:57.400> that 00:24:57.510 --> 00:24:57.520 align:start position:0% very similar to Starks in the sense that 00:24:57.520 --> 00:25:01.230 align:start position:0% very similar to Starks in the sense that you<00:24:57.730> have<00:24:57.760> transparency<00:24:58.570> and<00:24:59.010> yet<00:25:00.010> no<00:25:00.820> trusted 00:25:01.230 --> 00:25:01.240 align:start position:0% you have transparency and yet no trusted 00:25:01.240 --> 00:25:03.840 align:start position:0% you have transparency and yet no trusted said<00:25:01.450> you<00:25:02.020> use<00:25:02.460> polynomial<00:25:03.460> commitment 00:25:03.840 --> 00:25:03.850 align:start position:0% said you use polynomial commitment 00:25:03.850 --> 00:25:06.780 align:start position:0% said you use polynomial commitment schemes<00:25:04.260> so<00:25:05.260> you<00:25:05.650> can<00:25:05.799> look<00:25:05.950> into<00:25:06.100> Aurora<00:25:06.549> I'm 00:25:06.780 --> 00:25:06.790 align:start position:0% schemes so you can look into Aurora I'm 00:25:06.790 --> 00:25:11.730 align:start position:0% schemes so you can look into Aurora I'm Marlene<00:25:07.210> plumb<00:25:08.040> fractal<00:25:09.040> etc<00:25:09.640> and<00:25:10.740> we're 00:25:11.730 --> 00:25:11.740 align:start position:0% Marlene plumb fractal etc and we're 00:25:11.740 --> 00:25:13.500 align:start position:0% Marlene plumb fractal etc and we're trying<00:25:11.950> to<00:25:12.100> do<00:25:12.610> is<00:25:12.700> there<00:25:13.030> is<00:25:13.059> a<00:25:13.120> nice 00:25:13.500 --> 00:25:13.510 align:start position:0% trying to do is there is a nice 00:25:13.510 --> 00:25:15.330 align:start position:0% trying to do is there is a nice community<00:25:14.169> within<00:25:14.470> the<00:25:14.679> theorem<00:25:14.950> block<00:25:15.100> chain 00:25:15.330 --> 00:25:15.340 align:start position:0% community within the theorem block chain 00:25:15.340 --> 00:25:17.730 align:start position:0% community within the theorem block chain of<00:25:15.549> people<00:25:15.730> researching<00:25:16.510> this<00:25:16.660> and<00:25:16.929> our<00:25:17.530> hope 00:25:17.730 --> 00:25:17.740 align:start position:0% of people researching this and our hope 00:25:17.740 --> 00:25:19.500 align:start position:0% of people researching this and our hope is<00:25:17.950> that<00:25:18.220> by<00:25:18.280> contributing<00:25:18.790> this<00:25:19.240> and 00:25:19.500 --> 00:25:19.510 align:start position:0% is that by contributing this and 00:25:19.510 --> 00:25:22.680 align:start position:0% is that by contributing this and inviting<00:25:19.929> owners<00:25:20.290> to<00:25:20.500> contribute<00:25:20.919> to<00:25:21.040> us<00:25:21.690> we 00:25:22.680 --> 00:25:22.690 align:start position:0% inviting owners to contribute to us we 00:25:22.690 --> 00:25:25.380 align:start position:0% inviting owners to contribute to us we look<00:25:22.840> at<00:25:22.990> an<00:25:23.309> exchange<00:25:24.309> of<00:25:24.490> ideas<00:25:24.669> and<00:25:25.210> help 00:25:25.380 --> 00:25:25.390 align:start position:0% look at an exchange of ideas and help 00:25:25.390 --> 00:25:38.750 align:start position:0% look at an exchange of ideas and help each<00:25:25.540> other<00:25:25.660> move<00:25:25.900> this<00:25:26.140> field<00:25:26.320> forward 00:25:38.750 --> 00:25:38.760 align:start position:0% 00:25:38.760 --> 00:25:41.750 align:start position:0% yes<00:25:39.390> so<00:25:39.840> what<00:25:40.020> about<00:25:40.080> Annie<00:25:40.530> do<00:25:40.770> we<00:25:40.950> have<00:25:41.220> the 00:25:41.750 --> 00:25:41.760 align:start position:0% yes so what about Annie do we have the 00:25:41.760 --> 00:25:44.810 align:start position:0% yes so what about Annie do we have the distinct<00:25:42.180> it<00:25:42.270> is<00:25:42.420> not<00:25:42.680> legally<00:25:43.680> hey<00:25:44.580> in<00:25:44.700> this 00:25:44.810 --> 00:25:44.820 align:start position:0% distinct it is not legally hey in this 00:25:44.820 --> 00:25:47.360 align:start position:0% distinct it is not legally hey in this case<00:25:45.090> yeah<00:25:45.450> absolutely<00:25:46.290> none<00:25:46.980> because<00:25:47.280> you 00:25:47.360 --> 00:25:47.370 align:start position:0% case yeah absolutely none because you 00:25:47.370 --> 00:25:49.940 align:start position:0% case yeah absolutely none because you can<00:25:47.520> just<00:25:47.610> compute<00:25:47.880> Fibonacci<00:25:48.060> reversed<00:25:48.950> the 00:25:49.940 --> 00:25:49.950 align:start position:0% can just compute Fibonacci reversed the 00:25:49.950 --> 00:25:51.800 align:start position:0% can just compute Fibonacci reversed the other<00:25:50.070> thing<00:25:50.340> I<00:25:50.700> briefly<00:25:51.090> mentioned<00:25:51.210> it<00:25:51.660> what 00:25:51.800 --> 00:25:51.810 align:start position:0% other thing I briefly mentioned it what 00:25:51.810 --> 00:25:53.270 align:start position:0% other thing I briefly mentioned it what one<00:25:51.930> of<00:25:52.080> the<00:25:52.170> things<00:25:52.350> we<00:25:52.500> don't<00:25:52.770> have<00:25:53.010> right 00:25:53.270 --> 00:25:53.280 align:start position:0% one of the things we don't have right 00:25:53.280 --> 00:25:55.370 align:start position:0% one of the things we don't have right now<00:25:53.310> is<00:25:53.670> perfect<00:25:54.090> server<00:25:54.240> knowledge<00:25:54.600> you<00:25:55.230> need 00:25:55.370 --> 00:25:55.380 align:start position:0% now is perfect server knowledge you need 00:25:55.380 --> 00:25:56.780 align:start position:0% now is perfect server knowledge you need to<00:25:55.590> you<00:25:55.800> need<00:25:55.890> to<00:25:55.950> implement<00:25:56.190> a<00:25:56.400> couple<00:25:56.640> more 00:25:56.780 --> 00:25:56.790 align:start position:0% to you need to implement a couple more 00:25:56.790 --> 00:25:58.820 align:start position:0% to you need to implement a couple more things<00:25:56.970> to<00:25:57.150> get<00:25:57.300> them<00:25:57.570> so<00:25:57.900> right<00:25:58.080> now<00:25:58.260> we<00:25:58.710> don't 00:25:58.820 --> 00:25:58.830 align:start position:0% things to get them so right now we don't 00:25:58.830 --> 00:26:00.890 align:start position:0% things to get them so right now we don't have<00:25:58.950> enough<00:25:59.220> zero<00:25:59.730> knowledge<00:25:59.970> we<00:26:00.600> just<00:26:00.780> have 00:26:00.890 --> 00:26:00.900 align:start position:0% have enough zero knowledge we just have 00:26:00.900 --> 00:26:03.560 align:start position:0% have enough zero knowledge we just have Cygnus<00:26:01.500> which<00:26:02.190> means<00:26:02.430> that<00:26:02.670> your<00:26:02.820> proof<00:26:03.180> only 00:26:03.560 --> 00:26:03.570 align:start position:0% Cygnus which means that your proof only 00:26:03.570 --> 00:26:06.110 align:start position:0% Cygnus which means that your proof only grows<00:26:03.870> logarithmically<00:26:04.680> in<00:26:05.490> the<00:26:05.580> size<00:26:05.820> of<00:26:06.030> the 00:26:06.110 --> 00:26:06.120 align:start position:0% grows logarithmically in the size of the 00:26:06.120 --> 00:26:08.420 align:start position:0% grows logarithmically in the size of the fact<00:26:06.360> that<00:26:06.420> it<00:26:06.600> would<00:26:06.750> instantly<00:26:07.080> and<00:26:07.800> he 00:26:08.420 --> 00:26:08.430 align:start position:0% fact that it would instantly and he 00:26:08.430 --> 00:26:11.510 align:start position:0% fact that it would instantly and he became<00:26:08.670> protector<00:26:09.330> proof<00:26:09.630> or<00:26:10.160> we<00:26:11.160> should<00:26:11.340> do 00:26:11.510 --> 00:26:11.520 align:start position:0% became protector proof or we should do 00:26:11.520 --> 00:26:13.610 align:start position:0% became protector proof or we should do you<00:26:11.790> can<00:26:11.880> check<00:26:12.240> the<00:26:12.360> food<00:26:12.600> and<00:26:13.290> you<00:26:13.380> can<00:26:13.530> I 00:26:13.610 --> 00:26:13.620 align:start position:0% you can check the food and you can I 00:26:13.620 --> 00:26:16.640 align:start position:0% you can check the food and you can I just<00:26:13.890> do<00:26:14.220> not<00:26:14.250> young<00:26:14.580> rhythm<00:26:14.970> and<00:26:15.330> and<00:26:16.170> check 00:26:16.640 --> 00:26:16.650 align:start position:0% just do not young rhythm and and check 00:26:16.650 --> 00:26:19.520 align:start position:0% just do not young rhythm and and check that<00:26:16.740> it<00:26:16.860> block<00:26:17.040> that<00:26:17.220> way<00:26:17.540> I<00:26:18.540> know<00:26:19.140> it's<00:26:19.380> more 00:26:19.520 --> 00:26:19.530 align:start position:0% that it block that way I know it's more 00:26:19.530 --> 00:26:22.460 align:start position:0% that it block that way I know it's more efficient<00:26:19.920> so<00:26:20.670> is<00:26:21.060> this<00:26:21.270> instrument<00:26:21.780> it's 00:26:22.460 --> 00:26:22.470 align:start position:0% efficient so is this instrument it's 00:26:22.470 --> 00:26:27.590 align:start position:0% efficient so is this instrument it's it's<00:26:22.800> logarithmic<00:26:23.310> in<00:26:23.730> the<00:26:23.880> original<00:26:26.450> in<00:26:27.450> the 00:26:27.590 --> 00:26:27.600 align:start position:0% it's logarithmic in the original in the 00:26:27.600 --> 00:26:36.030 align:start position:0% it's logarithmic in the original in the number<00:26:27.950> yes<00:26:28.950> yeah<00:26:29.760> yeah 00:26:36.030 --> 00:26:36.040 align:start position:0% 00:26:36.040 --> 00:26:40.470 align:start position:0% here<00:26:37.030> for<00:26:37.600> example<00:26:37.660> gonna<00:26:38.910> like<00:26:39.910> this<00:26:40.150> seed 00:26:40.470 --> 00:26:40.480 align:start position:0% here for example gonna like this seed 00:26:40.480 --> 00:26:43.650 align:start position:0% here for example gonna like this seed straight<00:26:41.070> somewhere<00:26:42.100> what<00:26:42.820> was<00:26:42.970> that<00:26:43.150> for 00:26:43.650 --> 00:26:43.660 align:start position:0% straight somewhere what was that for 00:26:43.660 --> 00:26:49.740 align:start position:0% straight somewhere what was that for yes<00:26:44.440> so<00:26:45.870> what<00:26:46.870> you<00:26:47.020> want<00:26:47.380> is<00:26:47.740> to<00:26:48.750> initialize 00:26:49.740 --> 00:26:49.750 align:start position:0% yes so what you want is to initialize 00:26:49.750 --> 00:26:52.590 align:start position:0% yes so what you want is to initialize the<00:26:50.530> proof<00:26:50.830> with<00:26:51.280> the<00:26:51.850> shared<00:26:52.150> information 00:26:52.590 --> 00:26:52.600 align:start position:0% the proof with the shared information 00:26:52.600 --> 00:26:54.840 align:start position:0% the proof with the shared information between<00:26:53.140> the<00:26:53.380> approver<00:26:53.590> and<00:26:53.770> the<00:26:53.890> verifier<00:26:54.340> so 00:26:54.840 --> 00:26:54.850 align:start position:0% between the approver and the verifier so 00:26:54.850 --> 00:26:56.400 align:start position:0% between the approver and the verifier so if<00:26:54.970> I'm<00:26:55.120> creating<00:26:55.390> a<00:26:55.690> prove<00:26:55.870> and<00:26:56.049> I'm<00:26:56.140> giving 00:26:56.400 --> 00:26:56.410 align:start position:0% if I'm creating a prove and I'm giving 00:26:56.410 --> 00:26:57.720 align:start position:0% if I'm creating a prove and I'm giving it<00:26:56.470> to<00:26:56.620> you 00:26:57.720 --> 00:26:57.730 align:start position:0% it to you 00:26:57.730 --> 00:27:00.870 align:start position:0% it to you ideally<00:26:58.480> it<00:26:59.169> would<00:26:59.380> improve<00:26:59.740> security<00:27:00.130> is<00:27:00.610> all 00:27:00.870 --> 00:27:00.880 align:start position:0% ideally it would improve security is all 00:27:00.880 --> 00:27:02.549 align:start position:0% ideally it would improve security is all are<00:27:01.090> you<00:27:01.179> all<00:27:01.510> on<00:27:01.780> knowledge<00:27:01.990> we<00:27:02.290> have<00:27:02.440> in 00:27:02.549 --> 00:27:02.559 align:start position:0% are you all on knowledge we have in 00:27:02.559 --> 00:27:03.120 align:start position:0% are you all on knowledge we have in common 00:27:03.120 --> 00:27:03.130 align:start position:0% common 00:27:03.130 --> 00:27:04.799 align:start position:0% common what's<00:27:03.460> encoded<00:27:03.940> in<00:27:04.059> there<00:27:04.240> so<00:27:04.600> what<00:27:04.750> you 00:27:04.799 --> 00:27:04.809 align:start position:0% what's encoded in there so what you 00:27:04.809 --> 00:27:06.900 align:start position:0% what's encoded in there so what you could<00:27:05.049> do<00:27:05.230> is<00:27:05.500> take<00:27:05.679> a<00:27:05.740> hash<00:27:06.040> of<00:27:06.400> your<00:27:06.580> claim 00:27:06.900 --> 00:27:06.910 align:start position:0% could do is take a hash of your claim 00:27:06.910 --> 00:27:10.409 align:start position:0% could do is take a hash of your claim put<00:27:07.540> it<00:27:07.660> in<00:27:07.809> there<00:27:08.049> and<00:27:08.410> then<00:27:09.040> it<00:27:09.880> prove<00:27:10.210> is 00:27:10.409 --> 00:27:10.419 align:start position:0% put it in there and then it prove is 00:27:10.419 --> 00:27:13.260 align:start position:0% put it in there and then it prove is more<00:27:10.690> constraints<00:27:11.590> cryptographically<00:27:12.520> to<00:27:13.090> be 00:27:13.260 --> 00:27:13.270 align:start position:0% more constraints cryptographically to be 00:27:13.270 --> 00:27:23.159 align:start position:0% more constraints cryptographically to be for<00:27:13.510> that<00:27:13.630> particular<00:27:20.309> so<00:27:21.309> adds<00:27:22.299> to<00:27:22.600> security 00:27:23.159 --> 00:27:23.169 align:start position:0% for that particular so adds to security 00:27:23.169 --> 00:27:25.260 align:start position:0% for that particular so adds to security by<00:27:23.380> committing<00:27:24.309> you<00:27:24.549> to<00:27:24.760> this<00:27:24.880> particular 00:27:25.260 --> 00:27:25.270 align:start position:0% by committing you to this particular 00:27:25.270 --> 00:27:32.660 align:start position:0% by committing you to this particular instance<00:27:25.809> of<00:27:25.900> the<00:27:26.020> problem 00:27:32.660 --> 00:27:32.670 align:start position:0% 00:27:32.670 --> 00:27:35.560 align:start position:0% like<00:27:33.270> I<00:27:33.480> get<00:27:33.720> back<00:27:33.930> to<00:27:34.020> my<00:27:34.140> motivational<00:27:34.890> shirt 00:27:35.560 --> 00:27:35.570 align:start position:0% like I get back to my motivational shirt 00:27:35.570 --> 00:27:38.390 align:start position:0% like I get back to my motivational shirt so<00:27:36.570> suppose<00:27:37.260> I<00:27:37.290> do<00:27:37.590> people<00:27:38.040> actually<00:27:38.160> did 00:27:38.390 --> 00:27:38.400 align:start position:0% so suppose I do people actually did 00:27:38.400 --> 00:27:40.970 align:start position:0% so suppose I do people actually did something<00:27:38.610> else<00:27:38.910> yes<00:27:39.510> so<00:27:39.900> again<00:27:40.350> what<00:27:40.830> can 00:27:40.970 --> 00:27:40.980 align:start position:0% something else yes so again what can 00:27:40.980 --> 00:27:46.040 align:start position:0% something else yes so again what can people<00:27:41.340> do<00:27:41.760> by<00:27:42.180> this<00:27:44.300> you<00:27:45.300> know<00:27:45.420> the<00:27:45.570> study<00:27:45.810> but 00:27:46.040 --> 00:27:46.050 align:start position:0% people do by this you know the study but 00:27:46.050 --> 00:27:53.540 align:start position:0% people do by this you know the study but yeah<00:27:51.110> so<00:27:52.110> this<00:27:52.260> these<00:27:52.800> two<00:27:52.980> things<00:27:53.250> to<00:27:53.430> this 00:27:53.540 --> 00:27:53.550 align:start position:0% yeah so this these two things to this 00:27:53.550 --> 00:28:02.360 align:start position:0% yeah so this these two things to this question<00:27:54.060> the<00:27:54.300> first<00:27:54.660> is<00:27:59.990> yes<00:28:00.990> it's<00:28:01.200> okay<00:28:01.470> so 00:28:02.360 --> 00:28:02.370 align:start position:0% question the first is yes it's okay so 00:28:02.370 --> 00:28:05.120 align:start position:0% question the first is yes it's okay so the<00:28:02.850> guarantee<00:28:03.330> that<00:28:03.540> you<00:28:03.720> get<00:28:03.960> is<00:28:04.320> that<00:28:04.350> the 00:28:05.120 --> 00:28:05.130 align:start position:0% the guarantee that you get is that the 00:28:05.130 --> 00:28:07.610 align:start position:0% the guarantee that you get is that the verifier<00:28:05.790> will<00:28:06.540> not<00:28:06.810> be<00:28:06.960> able<00:28:07.080> to<00:28:07.260> learn 00:28:07.610 --> 00:28:07.620 align:start position:0% verifier will not be able to learn 00:28:07.620 --> 00:28:09.890 align:start position:0% verifier will not be able to learn anything<00:28:08.100> more<00:28:08.430> and<00:28:08.820> can<00:28:09.060> be<00:28:09.180> learned<00:28:09.450> from 00:28:09.890 --> 00:28:09.900 align:start position:0% anything more and can be learned from 00:28:09.900 --> 00:28:13.880 align:start position:0% anything more and can be learned from the<00:28:10.080> public<00:28:10.350> input<00:28:10.500> and<00:28:11.420> if<00:28:12.420> on<00:28:13.380> paper<00:28:13.740> by 00:28:13.880 --> 00:28:13.890 align:start position:0% the public input and if on paper by 00:28:13.890 --> 00:28:16.070 align:start position:0% the public input and if on paper by somebody<00:28:14.220> other<00:28:14.510> absolutely<00:28:15.510> yeah<00:28:15.660> that<00:28:15.930> is 00:28:16.070 --> 00:28:16.080 align:start position:0% somebody other absolutely yeah that is 00:28:16.080 --> 00:28:18.890 align:start position:0% somebody other absolutely yeah that is that<00:28:16.110> is<00:28:16.380> a<00:28:16.500> proof<00:28:16.800> done<00:28:17.130> by<00:28:17.570> elements<00:28:18.570> person 00:28:18.890 --> 00:28:18.900 align:start position:0% that is a proof done by elements person 00:28:18.900 --> 00:28:21.110 align:start position:0% that is a proof done by elements person at<00:28:19.020> all<00:28:19.140> I<00:28:19.350> know<00:28:19.530> but<00:28:20.040> what<00:28:20.490> do<00:28:20.580> you<00:28:20.670> what<00:28:21.000> do 00:28:21.110 --> 00:28:21.120 align:start position:0% at all I know but what do you what do 00:28:21.120 --> 00:28:22.340 align:start position:0% at all I know but what do you what do you<00:28:21.180> your<00:28:21.780> proof 00:28:22.340 --> 00:28:22.350 align:start position:0% you your proof 00:28:22.350 --> 00:28:27.680 align:start position:0% you your proof you<00:28:23.280> think<00:28:23.610> they<00:28:25.640> yeah<00:28:26.640> which<00:28:27.030> is<00:28:27.060> essentially 00:28:27.680 --> 00:28:27.690 align:start position:0% you think they yeah which is essentially 00:28:27.690 --> 00:28:30.440 align:start position:0% you think they yeah which is essentially what<00:28:27.840> happens<00:28:28.200> in<00:28:28.410> in<00:28:28.710> the<00:28:28.890> Fibonacci<00:28:29.760> example 00:28:30.440 --> 00:28:30.450 align:start position:0% what happens in in the Fibonacci example 00:28:30.450 --> 00:28:31.730 align:start position:0% what happens in in the Fibonacci example because<00:28:30.720> you<00:28:30.810> know<00:28:30.930> the<00:28:31.080> output<00:28:31.230> is<00:28:31.560> just 00:28:31.730 --> 00:28:31.740 align:start position:0% because you know the output is just 00:28:31.740 --> 00:28:33.770 align:start position:0% because you know the output is just defined<00:28:32.130> buddy<00:28:32.400> by<00:28:32.730> the<00:28:32.790> secret<00:28:33.180> values<00:28:33.540> so 00:28:33.770 --> 00:28:33.780 align:start position:0% defined buddy by the secret values so 00:28:33.780 --> 00:28:35.660 align:start position:0% defined buddy by the secret values so you<00:28:33.840> can<00:28:34.050> just<00:28:34.200> compute<00:28:34.500> it<00:28:34.650> backwards<00:28:35.010> it's 00:28:35.660 --> 00:28:35.670 align:start position:0% you can just compute it backwards it's 00:28:35.670 --> 00:28:38.090 align:start position:0% you can just compute it backwards it's not<00:28:35.820> hard<00:28:36.210> algebra<00:28:36.750> I<00:28:36.780> hate<00:28:36.990> to<00:28:37.110> do<00:28:37.230> this<00:28:37.260> but 00:28:38.090 --> 00:28:38.100 align:start position:0% not hard algebra I hate to do this but 00:28:38.100 --> 00:28:40.220 align:start position:0% not hard algebra I hate to do this but you<00:28:38.220> can<00:28:38.250> also<00:28:38.400> do<00:28:38.730> is<00:28:38.940> just<00:28:39.180> like<00:28:39.390> iterate 00:28:40.220 --> 00:28:40.230 align:start position:0% you can also do is just like iterate 00:28:40.230 --> 00:28:42.230 align:start position:0% you can also do is just like iterate through<00:28:40.470> all<00:28:40.560> the<00:28:40.740> values<00:28:41.220> if<00:28:41.490> you<00:28:41.850> know<00:28:42.000> that 00:28:42.230 --> 00:28:42.240 align:start position:0% through all the values if you know that 00:28:42.240 --> 00:28:43.550 align:start position:0% through all the values if you know that there<00:28:42.360> is<00:28:42.450> only<00:28:42.570> a<00:28:42.720> small<00:28:42.840> set<00:28:43.170> of<00:28:43.200> them<00:28:43.350> and 00:28:43.550 --> 00:28:43.560 align:start position:0% there is only a small set of them and 00:28:43.560 --> 00:28:46.220 align:start position:0% there is only a small set of them and this<00:28:43.950> is<00:28:44.130> why<00:28:44.280> the<00:28:44.360> is<00:28:45.360> really<00:28:45.660> important<00:28:46.110> to 00:28:46.220 --> 00:28:46.230 align:start position:0% this is why the is really important to 00:28:46.230 --> 00:28:48.500 align:start position:0% this is why the is really important to know<00:28:46.470> what<00:28:46.710> the<00:28:46.800> exact<00:28:47.100> truth<00:28:47.310> is<00:28:47.520> and<00:28:47.790> the 00:28:48.500 --> 00:28:48.510 align:start position:0% know what the exact truth is and the 00:28:48.510 --> 00:28:50.240 align:start position:0% know what the exact truth is and the exact<00:28:48.870> thing<00:28:49.020> is<00:28:49.140> you<00:28:49.260> cannot<00:28:49.500> learn<00:28:49.800> anything 00:28:50.240 --> 00:28:50.250 align:start position:0% exact thing is you cannot learn anything 00:28:50.250 --> 00:28:53.210 align:start position:0% exact thing is you cannot learn anything more<00:28:50.610> than<00:28:50.790> you<00:28:50.880> can<00:28:51.030> already<00:28:51.420> learn<00:28:51.860> from<00:28:52.860> the 00:28:53.210 --> 00:28:53.220 align:start position:0% more than you can already learn from the 00:28:53.220 --> 00:28:56.750 align:start position:0% more than you can already learn from the claim<00:28:53.490> itself<00:28:54.020> if<00:28:55.020> the<00:28:55.170> claim<00:28:55.710> contains<00:28:56.610> your 00:28:56.750 --> 00:28:56.760 align:start position:0% claim itself if the claim contains your 00:28:56.760 --> 00:28:59.350 align:start position:0% claim itself if the claim contains your private<00:28:57.240> into<00:28:57.540> it<00:28:57.660> or<00:28:57.870> something<00:28:58.070> that<00:28:59.070> allows 00:28:59.350 --> 00:28:59.360 align:start position:0% private into it or something that allows 00:28:59.360 --> 00:29:02.780 align:start position:0% private into it or something that allows you<00:29:00.360> to<00:29:00.420> derive<00:29:00.720> the<00:29:00.930> private<00:29:01.260> input<00:29:01.640> then<00:29:02.640> you 00:29:02.780 --> 00:29:02.790 align:start position:0% you to derive the private input then you 00:29:02.790 --> 00:29:04.580 align:start position:0% you to derive the private input then you have<00:29:02.970> no<00:29:03.120> zero<00:29:03.330> knowledge<00:29:03.540> guarantees<00:29:03.990> so 00:29:04.580 --> 00:29:04.590 align:start position:0% have no zero knowledge guarantees so 00:29:04.590 --> 00:29:06.620 align:start position:0% have no zero knowledge guarantees so this<00:29:05.160> is<00:29:05.310> something<00:29:05.490> to<00:29:05.730> keep<00:29:05.850> in<00:29:06.000> mind<00:29:06.270> if<00:29:06.510> you 00:29:06.620 --> 00:29:06.630 align:start position:0% this is something to keep in mind if you 00:29:06.630 --> 00:29:08.150 align:start position:0% this is something to keep in mind if you want<00:29:06.810> to<00:29:06.840> use<00:29:07.080> these<00:29:07.290> things<00:29:07.350> for<00:29:07.710> is<00:29:07.980> your 00:29:08.150 --> 00:29:08.160 align:start position:0% want to use these things for is your 00:29:08.160 --> 00:29:10.640 align:start position:0% want to use these things for is your actual<00:29:08.640> zero<00:29:08.820> knowledge<00:29:09.210> and<00:29:09.390> privacy<00:29:09.810> be 00:29:10.640 --> 00:29:10.650 align:start position:0% actual zero knowledge and privacy be 00:29:10.650 --> 00:29:12.200 align:start position:0% actual zero knowledge and privacy be careful<00:29:11.130> about<00:29:11.280> what<00:29:11.460> you<00:29:11.580> put<00:29:11.700> in<00:29:11.850> the<00:29:11.940> public 00:29:12.200 --> 00:29:12.210 align:start position:0% careful about what you put in the public 00:29:12.210 --> 00:29:14.630 align:start position:0% careful about what you put in the public input<00:29:12.360> because<00:29:13.040> you<00:29:14.040> might<00:29:14.280> be<00:29:14.460> able<00:29:14.520> to 00:29:14.630 --> 00:29:14.640 align:start position:0% input because you might be able to 00:29:14.640 --> 00:29:16.190 align:start position:0% input because you might be able to derive<00:29:14.880> the<00:29:15.090> private<00:29:15.390> input<00:29:15.660> from<00:29:15.810> this<00:29:15.990> if 00:29:16.190 --> 00:29:16.200 align:start position:0% derive the private input from this if 00:29:16.200 --> 00:29:17.590 align:start position:0% derive the private input from this if you're<00:29:16.320> not<00:29:16.470> careful 00:29:17.590 --> 00:29:17.600 align:start position:0% you're not careful 00:29:17.600 --> 00:29:19.820 align:start position:0% you're not careful another<00:29:18.600> big<00:29:18.840> room<00:29:19.080> are<00:29:19.230> going<00:29:19.350> to<00:29:19.530> make<00:29:19.680> is 00:29:19.820 --> 00:29:19.830 align:start position:0% another big room are going to make is 00:29:19.830 --> 00:29:21.650 align:start position:0% another big room are going to make is that<00:29:19.860> right<00:29:20.250> now<00:29:20.430> we<00:29:20.490> don't<00:29:20.940> have<00:29:21.090> perfect 00:29:21.650 --> 00:29:21.660 align:start position:0% that right now we don't have perfect 00:29:21.660 --> 00:29:23.810 align:start position:0% that right now we don't have perfect your<00:29:22.020> knowledge<00:29:22.380> we<00:29:22.800> only<00:29:22.950> have<00:29:23.130> sickness<00:29:23.640> in 00:29:23.810 --> 00:29:23.820 align:start position:0% your knowledge we only have sickness in 00:29:23.820 --> 00:29:25.310 align:start position:0% your knowledge we only have sickness in the<00:29:23.910> system<00:29:24.240> that<00:29:24.270> we<00:29:24.420> have<00:29:24.510> so<00:29:24.990> like<00:29:25.140> the 00:29:25.310 --> 00:29:25.320 align:start position:0% the system that we have so like the 00:29:25.320 --> 00:29:26.810 align:start position:0% the system that we have so like the system<00:29:25.650> we<00:29:25.740> have<00:29:25.920> is<00:29:26.100> not<00:29:26.280> soon 00:29:26.810 --> 00:29:26.820 align:start position:0% system we have is not soon 00:29:26.820 --> 00:29:29.629 align:start position:0% system we have is not soon at<00:29:26.880> the<00:29:26.970> moment<00:29:27.149> for<00:29:27.570> any<00:29:28.190> hard<00:29:29.190> privacy 00:29:29.629 --> 00:29:29.639 align:start position:0% at the moment for any hard privacy 00:29:29.639 --> 00:29:34.129 align:start position:0% at the moment for any hard privacy requirements<00:29:31.700> but<00:29:32.700> again<00:29:33.049> contributions<00:29:34.049> of 00:29:34.129 --> 00:29:34.139 align:start position:0% requirements but again contributions of 00:29:34.139 --> 00:29:37.129 align:start position:0% requirements but again contributions of weapons<00:29:35.419> though<00:29:36.419> so<00:29:36.720> something<00:29:36.960> that<00:29:36.990> you 00:29:37.129 --> 00:29:37.139 align:start position:0% weapons though so something that you 00:29:37.139 --> 00:29:38.600 align:start position:0% weapons though so something that you could<00:29:37.320> committee<00:29:37.590> group<00:29:37.799> with<00:29:38.039> this<00:29:38.190> is<00:29:38.429> that 00:29:38.600 --> 00:29:38.610 align:start position:0% could committee group with this is that 00:29:38.610 --> 00:29:42.710 align:start position:0% could committee group with this is that given<00:29:39.360> the<00:29:39.870> output<00:29:40.559> being<00:29:41.190> a<00:29:41.789> hash<00:29:42.240> function 00:29:42.710 --> 00:29:42.720 align:start position:0% given the output being a hash function 00:29:42.720 --> 00:29:45.019 align:start position:0% given the output being a hash function it<00:29:43.110> was<00:29:43.259> verified<00:29:43.529> that<00:29:43.710> there<00:29:43.860> was<00:29:44.100> an<00:29:44.610> input 00:29:45.019 --> 00:29:45.029 align:start position:0% it was verified that there was an input 00:29:45.029 --> 00:29:47.269 align:start position:0% it was verified that there was an input that<00:29:45.299> did<00:29:45.899> get<00:29:46.080> a<00:29:46.110> rate<00:29:46.320> that<00:29:46.470> actually<00:29:47.159> we 00:29:47.269 --> 00:29:47.279 align:start position:0% that did get a rate that actually we 00:29:47.279 --> 00:29:49.789 align:start position:0% that did get a rate that actually we have<00:29:47.309> an<00:29:47.610> example<00:29:47.970> of<00:29:48.299> a<00:29:48.539> machine<00:29:49.259> Ashley 00:29:49.789 --> 00:29:49.799 align:start position:0% have an example of a machine Ashley 00:29:49.799 --> 00:29:52.249 align:start position:0% have an example of a machine Ashley image<00:29:50.269> you<00:29:51.269> can<00:29:51.419> see<00:29:51.450> you<00:29:51.600> can<00:29:51.720> find<00:29:51.870> it<00:29:52.049> in<00:29:52.169> the 00:29:52.249 --> 00:29:52.259 align:start position:0% image you can see you can find it in the 00:29:52.259 --> 00:30:01.290 align:start position:0% image you can see you can find it in the repo 00:30:01.290 --> 00:30:01.300 align:start position:0% 00:30:01.300 --> 00:30:07.640 align:start position:0% [Applause]