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naehrwert: Joo. Kiitos 
yleisölle ja kiitos että tulitte.Kiitos

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myös kongressille 
mahdollisuudesta olla täällä tänä iltana

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kertomassa teille vähän post-kvanttikryptografiasta ja isogeneeseistä.

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Tarkoitan, että koulutan ihmisiä 
hieman siitä, mitä se tarkoittaa, 
koska en ole

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aivan varma kuinka moni teistä 
on kuullut siitä aiemmin. 
Joo, siirrytään suoraan asiaan.

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Päivätyönäni olen matematiikan tohtoriopiskelija salassa 
pidetyssä yliopistossa.

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Voit kysyä yksityisesti, jos 
olet kiinnostunut. Aiemmin olen opiskellut fysiikkaa.

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Olin myös tai ehkä olen edelleen hieman aktiivinen konsolihakkerointipiireissä.

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Ja jos olette kiinnostuneita siitä niin häpeämätön mainos, voitte
löytää meidät Nintenbros

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Assemblysta myöhemmin. Voitte 
kysyä meiltä kaikenlaisista konsolihakkerointiprojekteistamme.

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Mutta tarpeeksi siitä. 
Toin teille joitain kuvia, 
kuvankaappauksia websivuilta.

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En tiedä, oletko huomannut viimeaikaista keskustelua sosiaalisessa mediassa ja blogeissa

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Googlen paperista kvanttiherruudesta.
Siitä on Nature-lehdessä artikkeli

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"Beyond Quantum Supremacy" ja The Verge -lehdessä artikkeli, että Google

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vahvistaa kvanttiherruuden ja läpimurron, mitä se sitten tarkoittaakaan.

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Googlella on myös oma blogikirjoitus aiheesta. Huomaa, että niissä on aina näitä kiiltäviä kuvia

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valtavista heliumilla täytetyistä 
säiliöistä, joissa näitä 
kvanttitietokoneita pidetään.

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Herruus tarkoittaa ylivertaisuutta muihin nähden auktoriteetin,

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vallan tai aseman suhteen. Joten jonkun kutsuminen kvanttiherruudeksi, se huutaa jonkun olevan

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jotain melko uskomatonta. Mutta mitä tämä oikeastaan tarkoittaa meille? Mitä

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se tarkoittaa kryptografialle?
Ja uskon, että voin lievittää

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joitain teidän pelkoja käytännön osalta. Ehkä tänään se ei

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vielä tarkoita mitään. Kryptografian kannalta mikään perustavaa laatua olevista oletuksistamme,

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mitä ne sitten tarkoittavatkin tällä hetkellä, ei ole vielä tietääksemme aktiivisesti rikottu.

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Mutta teoriassa ne ovat rikottavissa. Okei. Ja koska ne ovat rikottavissa vain

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teoriassa, se on melko hyvä asia. Voimme edelleen syyttää suunnittelijoita ja toteuttajia,

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kun asiat menevät pieleen. Se on myös mukavaa. Mutta kuten jo

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kirjoitin tämän esityksen tiivistelmässä, meidän olisi jotenkin

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parempi olla varmoja. 
Joten sen sijaan, että odotamme, kunnes

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kvanttitietokoneet ovat jollain tavalla kykeneviä murtamaan kryptografiamme, meidän pitäisi ehkä

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tutkia sitä tänään. Se on vähän kuin ilmastonmuutoksen kanssa, eikö niin? 
On järkevää

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pelastaa ilmastomme tänään sen sijaan, että odotamme liian myöhään. Joten jos

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haluamme tehdä saman kryptografialle. Täällä on myös kolme tulevaa esitystä,

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joita haluan mainostaa hieman. En muista tarkkaa päivää,

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mutta kuvaukset näyttävät melko kiinnostavilta. Jätän ne esille muutamaksi

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sekunniksi. Niistä yksi on nimeltään "Provable Insecurity", yksi on

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"Cryptography Demystified" ja yksi "High Assurance Cryptography Software".

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Olen varma, että ne ovat kiinnostavia. OK, palataan siihen, mistä haluan puhua.

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Minulla on jotain, mitä kutsun leikillisesti Post-Kvantin Kryptografian Eläintarhaksi.

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Siellä on muutamia kuumia puheenaiheita. Ette oikeastaan tarvitse tietää, mitä ne tarkoittavat.

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Sanon ne vain ääneen. Ristikot, koodit, monimuuttujaiset polynomijärjestelmät.

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Se on myös melko pitkä sana. Ja tiivistepohjaiset kryptografiat. Ja sitten on

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yksi, josta haluan puhua lyhyesti tänä iltana, nimeltään supersingulaariset elliptisen käyrän

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isogeenit. OK, tämä on se juttu, mistä todella pidän. Isogeenit, ne ovat mahtavia.

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Ja nyt aion kertoa teille, miksi ne ovat niin mahtavia. Hyvä. En tiedä, kuinka monella

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teistä on matemaattinen tausta. Ehkä voin tehdä testin. Voitteko nostaa

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kätenne, jos teillä on jonkinlaista virallista koulutusta esimerkiksi algebraan? Kyllä. Okei.

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Joten kerron teille hieman siitä. On desimaalilukuja.

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Tämä on pii. Sitten on rationaalisia lukuja, kuten puolikas,

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kolmasosa ja niin edelleen. Sitten on kokonaislukuja miinus ääretön ja plus ääretön välillä, ja ne etenevät mukavasti kokonaisin askelin. Mutta työskentelyä varten ja kryptografiaa varten haluamme jotain käyttäytymiseltään parempaa. Haluamme jonkinlaisen rajallisen joukon. OK. Tämä on tärkeää toteutuksen kannalta. Ja ne, joiden kanssa haluamme työskennellä, muistutan teitä, ovat luvut modulo N, joten otamme jonkin positiivisen kokonaisluvun N, ison N, ja sitten tarkastelemme joukkoa nollasta N miinus yksi. OK. Nämä luvut noudattavat tiettyjä lisäys- ja kertolaskusääntöjä, ja se toimii melkein kuin kellotaulu. Valitsin tähän N:ksi 12, ja, olkaa kärsivällisiä, kuvitelkaa, että kellotauluni ulottuu nollasta yhteenstoista sen sijaan, että se menisi yhdestä kahteentoista. Mutta se on oikeastaan sama asia. Esimerkiksi jos yritän lisätä kymmenen viiteen. OK, aloitan kymmenestä. Menen kaksi askelta, ja sitten saavun nollaan. Tässä kohtaa kellotauluni vaihtaa päivää. Oikein.

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00:27:43,580 --> 00:27:50,120


307
00:27:50,120 --> 00:27:55,669


308
00:27:55,669 --> 00:28:01,919


309
00:28:01,919 --> 00:28:09,099


310
00:28:09,099 --> 00:28:17,080


311
00:28:17,080 --> 00:28:22,400


312
00:28:22,400 --> 00:28:26,540


313
00:28:26,540 --> 00:28:30,740


314
00:28:30,740 --> 00:28:35,179


315
00:28:35,179 --> 00:28:42,169


316
00:28:42,169 --> 00:28:47,660


317
00:28:47,660 --> 00:28:51,830


318
00:28:51,830 --> 00:28:54,620


319
00:28:54,620 --> 00:28:58,669


320
00:28:58,669 --> 00:29:04,320


321
00:29:04,320 --> 00:29:09,779


322
00:29:09,779 --> 00:29:16,139


323
00:29:16,139 --> 00:29:21,490


324
00:29:21,490 --> 00:29:27,549


325
00:29:27,549 --> 00:29:30,700


326
00:29:30,700 --> 00:29:38,510


327
00:29:38,510 --> 00:29:43,759


328
00:29:43,759 --> 00:29:48,840


329
00:29:48,840 --> 00:29:52,369


330
00:29:52,369 --> 00:29:59,850


331
00:29:59,850 --> 00:30:07,159


332
00:30:07,159 --> 00:30:16,240


333
00:30:16,240 --> 00:30:23,130


334
00:30:23,130 --> 00:30:28,630


335
00:30:28,630 --> 00:30:33,120


336
00:30:33,120 --> 00:30:37,880


337
00:30:37,880 --> 00:30:42,750


338
00:30:42,750 --> 00:30:47,700


339
00:30:47,700 --> 00:30:52,679


340
00:30:52,679 --> 00:30:58,000


341
00:30:58,000 --> 00:31:03,060


342
00:31:03,060 --> 00:31:07,910


343
00:31:07,910 --> 00:31:14,960


344
00:31:14,960 --> 00:31:21,350


345
00:31:21,350 --> 00:31:26,019


346
00:31:26,019 --> 00:31:35,539


347
00:31:35,539 --> 00:31:40,940


348
00:31:40,940 --> 00:31:45,459


349
00:31:45,459 --> 00:31:50,830


350
00:31:50,830 --> 00:31:58,190


351
00:31:58,190 --> 00:32:04,520


352
00:32:04,520 --> 00:32:12,129


353
00:32:12,129 --> 00:32:16,419


354
00:32:16,419 --> 00:32:23,090


355
00:32:23,090 --> 00:32:32,610


356
00:32:32,610 --> 00:32:36,929


357
00:32:36,929 --> 00:32:42,030


358
00:32:42,030 --> 00:32:48,669


359
00:32:48,669 --> 00:32:53,370


360
00:32:53,370 --> 00:32:57,600


361
00:32:57,600 --> 00:33:02,039


362
00:33:02,039 --> 00:33:06,549


363
00:33:06,549 --> 00:33:12,039


364
00:33:12,039 --> 00:33:17,320


365
00:33:17,320 --> 00:33:23,260


366
00:33:23,260 --> 00:33:30,390


367
00:33:30,390 --> 00:33:34,335


368
00:33:34,335 --> 00:33:38,440


369
00:33:38,440 --> 00:33:45,960


370
00:33:45,960 --> 00:33:54,101


371
00:33:54,101 --> 00:34:01,370


372
00:34:01,370 --> 00:34:07,730


373
00:34:07,730 --> 00:34:14,760


374
00:34:14,760 --> 00:34:22,720


375
00:34:22,720 --> 00:34:27,750


376
00:34:27,750 --> 00:34:34,490


377
00:34:34,490 --> 00:34:40,110


378
00:34:40,110 --> 00:34:44,860


379
00:34:44,860 --> 00:34:51,881


380
00:34:51,881 --> 00:34:59,660


381
00:34:59,660 --> 00:35:06,520


382
00:35:06,520 --> 00:35:13,290


383
00:35:13,290 --> 00:35:18,840


384
00:35:18,840 --> 00:35:26,090


385
00:35:26,090 --> 00:35:30,460


386
00:35:30,460 --> 00:35:40,511


387
00:35:40,511 --> 00:35:44,950


388
00:35:44,950 --> 00:35:49,960


389
00:35:49,960 --> 00:35:55,210


390
00:35:55,210 --> 00:36:01,500


391
00:36:01,500 --> 00:36:05,290


392
00:36:05,290 --> 00:36:10,410


393
00:36:10,410 --> 00:36:15,950


394
00:36:15,950 --> 00:36:22,680


395
00:36:22,680 --> 00:36:29,110


396
00:36:29,110 --> 00:36:36,660


397
00:36:36,660 --> 00:36:39,900


398
00:36:39,900 --> 00:36:45,240


399
00:36:45,240 --> 00:36:50,370


400
00:36:50,370 --> 00:36:58,380


401
00:36:58,380 --> 00:37:01,440


402
00:37:01,440 --> 00:37:14,870


403
00:37:14,870 --> 00:37:22,600


404
00:37:22,600 --> 00:37:27,640


405
00:37:27,640 --> 00:37:33,280


406
00:37:33,280 --> 00:37:41,510


407
00:37:41,510 --> 00:37:46,050


408
00:37:46,050 --> 00:37:53,180


409
00:37:53,180 --> 00:38:00,940


410
00:38:00,940 --> 00:38:07,400


411
00:38:07,400 --> 00:38:11,380


412
00:38:11,380 --> 00:38:17,500


413
00:38:17,500 --> 00:38:22,590


414
00:38:22,590 --> 00:38:26,670


415
00:38:26,670 --> 00:38:30,830


416
00:38:30,830 --> 00:38:32,730


417
00:38:32,730 --> 00:38:35,790


418
00:38:35,790 --> 00:38:44,500


419
00:38:44,500 --> 00:38:54,700


420
00:38:54,700 --> 00:39:02,770


421
00:39:02,770 --> 00:39:10,980


422
00:39:10,980 --> 00:39:14,890


423
00:39:14,890 --> 00:39:21,280


424
00:39:21,280 --> 00:39:26,220


425
00:39:26,220 --> 00:39:34,001


426
00:39:34,001 --> 00:39:40,650


427
00:39:40,650 --> 00:39:46,170


428
00:39:46,170 --> 00:39:51,700


429
00:39:51,700 --> 00:39:57,670


430
00:39:57,670 --> 00:40:03,910


431
00:40:03,910 --> 00:40:09,100


432
00:40:09,100 --> 00:40:15,020


433
00:40:15,020 --> 00:40:20,720


434
00:40:20,720 --> 00:40:28,910


435
00:40:28,910 --> 00:40:37,010


436
00:40:37,010 --> 00:40:39,931


437
00:40:39,931 --> 00:40:46,980


438
00:40:46,980 --> 00:40:52,950


439
00:40:52,950 --> 00:40:59,160


440
00:40:59,160 --> 00:41:03,510


441
00:41:03,510 --> 00:41:07,020


442
00:41:07,020 --> 00:41:10,740


443
00:41:10,740 --> 00:41:15,350


444
00:41:15,350 --> 00:41:19,810


445
00:41:19,810 --> 00:41:26,200


446
00:41:26,200 --> 00:41:35,240


447
00:41:35,240 --> 00:41:40,980


448
00:41:40,980 --> 00:41:47,321


449
00:41:47,321 --> 00:41:51,810


450
00:41:51,810 --> 00:41:59,610


451
00:41:59,610 --> 00:42:06,380


452
00:42:06,380 --> 00:42:16,500


453
00:42:16,500 --> 00:42:20,850


454
00:42:20,850 --> 00:42:25,600


455
00:42:25,600 --> 00:42:31,340


456
00:42:31,340 --> 00:42:37,650


457
00:42:37,650 --> 00:42:44,120


458
00:42:44,120 --> 00:42:48,480


459
00:42:48,480 --> 00:42:54,320


460
00:42:54,320 --> 00:42:59,310


461
00:42:59,310 --> 00:43:03,410


462
00:43:03,410 --> 00:43:07,400


463
00:43:07,400 --> 00:43:11,950


464
00:43:11,950 --> 00:43:16,030


465
00:43:16,030 --> 00:43:21,480


466
00:43:21,480 --> 00:43:28,430


467
00:43:28,430 --> 00:43:33,060


468
00:43:33,060 --> 00:43:38,500


469
00:43:38,500 --> 00:43:43,370


470
00:43:43,370 --> 00:43:51,180


471
00:43:51,180 --> 00:43:56,140


472
00:43:56,140 --> 00:44:01,660


473
00:44:01,660 --> 00:44:08,830


474
00:44:08,830 --> 00:44:14,261


475
00:44:14,261 --> 00:44:23,820


476
00:44:23,820 --> 00:44:27,600


477
00:44:27,600 --> 00:44:32,640


478
00:44:32,640 --> 00:44:33,900


479
00:44:33,900 --> 00:44:39,390


480
00:44:39,390 --> 00:44:43,330


481
00:44:43,330 --> 00:44:49,600


482
00:44:49,600 --> 00:44:53,560


483
00:44:53,560 --> 00:44:58,690


484
00:44:58,690 --> 00:45:03,400


485
00:45:03,400 --> 00:45:10,400


486
00:45:10,400 --> 00:45:16,170


487
00:45:16,170 --> 00:45:22,080


488
00:45:22,080 --> 00:45:27,440


489
00:45:27,440 --> 00:45:33,190


490
00:45:33,190 --> 00:45:37,180


491
00:45:37,180 --> 00:45:41,400


492
00:45:41,400 --> 00:45:49,990


493
00:45:49,990 --> 00:45:56,730


494
00:45:56,730 --> 00:46:03,580


495
00:46:03,580 --> 00:46:05,040


496
00:46:05,040 --> 00:46:10,170


497
00:46:10,170 --> 00:46:15,720


498
00:46:15,720 --> 00:46:20,290


499
00:46:20,290 --> 00:46:23,450


500
00:46:23,450 --> 00:46:29,500


501
00:46:29,500 --> 00:46:34,140


502
00:46:34,140 --> 00:46:41,440


503
00:46:41,440 --> 00:46:46,420


504
00:46:46,420 --> 00:46:50,240


505
00:46:50,240 --> 00:46:56,670


506
00:46:56,670 --> 00:47:00,940


507
00:47:00,940 --> 00:47:05,430


508
00:47:05,430 --> 00:47:08,940


509
00:47:08,940 --> 00:47:15,270


510
00:47:15,270 --> 00:47:19,440


511
00:47:19,440 --> 00:47:24,160


512
00:47:24,160 --> 00:47:26,430


513
00:47:26,430 --> 00:47:30,510


514
00:47:30,510 --> 00:47:35,760


515
00:47:35,760 --> 00:47:41,270


516
00:47:41,270 --> 00:47:45,720


517
00:47:45,720 --> 00:47:51,210


518
00:47:51,210 --> 00:47:55,570


519
00:47:55,570 --> 00:48:01,231


520
00:48:01,231 --> 00:48:06,170


521
00:48:06,170 --> 00:48:10,250


522
00:48:10,250 --> 00:48:14,570


523
00:48:14,570 --> 00:48:17,860


524
00:48:17,860 --> 00:48:23,260


525
00:48:23,260 --> 00:48:27,510


526
00:48:27,510 --> 00:48:32,670


527
00:48:32,670 --> 00:48:40,090


528
00:48:40,090 --> 00:48:45,890


529
00:48:45,890 --> 00:48:50,850


530
00:48:50,850 --> 00:48:55,810


531
00:48:55,810 --> 00:49:00,300


532
00:49:00,300 --> 00:49:07,260


533
00:49:07,260 --> 00:49:11,600


534
00:49:11,600 --> 00:49:17,600


535
00:49:17,600 --> 00:49:24,260


536
00:49:24,260 --> 00:49:31,440


537
00:49:31,440 --> 00:49:35,650


538
00:49:35,650 --> 00:49:40,860


539
00:49:40,860 --> 00:49:45,440


540
00:49:45,440 --> 00:49:51,030


541
00:49:51,030 --> 00:49:55,840


542
00:49:55,840 --> 00:50:00,120


543
00:50:00,120 --> 00:50:07,490


544
00:50:07,490 --> 00:50:12,110


545
00:50:12,110 --> 00:50:16,020


546
00:50:16,020 --> 00:50:18,870


547
00:50:18,870 --> 00:50:22,960


548
00:50:22,960 --> 00:50:28,560


549
00:50:28,560 --> 00:50:36,860


550
00:50:36,860 --> 00:50:44,110


551
00:50:44,110 --> 00:50:47,670


552
00:50:47,670 --> 00:50:55,130


553
00:50:55,130 --> 00:50:59,050


554
00:50:59,050 --> 00:51:02,680


555
00:51:02,680 --> 00:51:09,000


556
00:51:09,000 --> 00:51:14,510


557
00:51:14,510 --> 00:51:19,770


558
00:51:19,770 --> 00:51:25,670


559
00:51:25,670 --> 00:51:29,600


560
00:51:29,600 --> 00:51:34,600


561
00:51:34,600 --> 00:51:40,190


562
00:51:40,190 --> 00:51:45,970


563
00:51:45,970 --> 00:51:49,260


564
00:51:49,260 --> 00:51:54,860


565
00:51:54,860 --> 00:51:58,800


566
00:51:58,800 --> 00:52:23,000