UClaude uhlukanise i-RSA-896. Nansi indlela i-RSA ephuka ngayo

Lokho okuhlanganiswa yile vidiyo

• I-RSA-896 iyawa: izinombolo ezingama-270, ama-GPU angama-2,048, izinsuku eziyishumi
• 1977 → 1994: iminyaka engamakhulu amane eziqhingi, amavolontiya angamakhulu ayisithupha
• 2009 → 2020: irekhodi elilodwa ngeshumi leminyaka, konke kuma-CPU
• Septhemba 2026: UDevin, bese kuba uClaude, amarekhodi amabili ezinsukwini eziyishumi nesithupha
• I-sieve: polynomial → sieving → umugqa wama-million angama-656 → i-square root

Umbhalo obhaliwe ohunyushwe

Kuhunyushwe kusuka ekulandiseni kokuqala kwesiNgisi. Umsindo namazwibela atholakalayo alawulwa yi-YouTube.

I-RSA-896 iyawa: izinombolo ezingama-270, ama-GPU angama-2,048, izinsuku eziyishumi

0:00 NgoMgqibelo unjiniyela e-Anthropic uhlukanise i-RSA eyisishiyagalombili namashumi ayisishiyagalolunye nesithupha, inombolo enezinombolo ezingamakhulu amabili namashumi ayisikhombisa ehloselwe ukuba isebenze impilo yonke, ngoClaude kanye nama-GPU angasebenzi angamakhulu amabili, okuyindlela ebiza kakhulu eyake yatholakala ukuqinisekisa ukuthi ukhiye wakho we-SSH cishe ulungile. Izinombolo ezintathu. Ama-GPU-years angamashumi amathathu ezinsukwini eziyishumi. Amadola ayizinkulungwane ezingamashumi ayisikhombisa nanhlanu emali yomklomelo yale nombolo ngqo, ayikhishwe ngonyaka ka-two thousand seven. Nentengo yokwenza lokho kukhiye ose-laptop yakho,

0:24 amadola ayizigidigidi ezingamashumi amathathu nesikhombisa. Emizuzwini emithathu, ukuthi irekhodi lokuhlukanisa libekwa kanjani, kungani i-algorithm iyi-sieve eneminyaka engamashumi amathathu futhi kungesona isikhulumi, nokuthi yimaphi okhiye bakho okufanele bakhathazeke. Lena i-The Daily Diff, ngaphansi kwesembozo.

1977 → 1994: iminyaka engamakhulu amane eziqhingi, amavolontiya angamakhulu ayisithupha

0:38 Nonyaka ka-1977. UMartin Gardner uprinta inombolo enezinombolo eziyikhulu namashumi amabili nesishiyagalolunye ku-Scientific American, futhi uRon Rivest ulinganisa ukuthi ukuyihlukanisa kuthatha iminyaka engamakhulu amane eziqhingi. Kuthatha amashumi ayisikhombisa, amavolontiya angamakhulu ayisithupha nemishini emibili ye-fax, futhi umyalezo oyimfihlo yigama lemilingo elithi squeamish ossifrage. Nonyaka ka-2009, i-RSA eyisikhombisa namashumi ayisithupha nesishiyagalombili, ama-core-years angamakhulu amabili.

2009 → 2020: irekhodi elilodwa ngeshumi leminyaka, konke kuma-CPU

0:58 Nonyaka ka-2020, i-RSA engamakhulu amabili namashumi amahlanu, ama-core-years angamakhulu amabili namashumi asikhombisa kuma- sieve ye-open-source ebizwa nge-Cado NFS, evela elabhulabhu yaseFrance. Irekhodi elilodwa ngeshumi leminyaka, ijubane labantu abaneminyaka yesipiliyoni.

Septhemba 2026: UDevin, bese kuba uClaude, amarekhodi amabili ezinsukwini eziyishumi nesithupha

1:10 Bese kuba uSepthemba. U-Eric Lu waseCognition utshela uDevin, i-coding agent yabo, ukuthi afake i-sieve kuma-GPU bese elala. Emasontweni amathathu namadola ayizinkulungwane ezingamakhulu amane zesikhathi esishiyekile se-cluster kamuva, i-RSA engamakhulu amabili namashumi ayisithupha isiqedile. Ezinsukwini eziyishumi nesithupha kamuva, uSteve Weis wase-Anthropic uphinda leli qhinga ngoClaude. Iminyaka eyisithupha phakathi kwamarekhodi, bese kuba amabili ngeviki, elilodwa lisuka kumuntu onentshisekelo ene- coding agent, elilodwa lisuka kumkhiqizi wezimfihlo onama-GPU angasebenzi. Indlela. Izigaba ezine.

I-sieve: polynomial → sieving → umugqa wama-million angama-656 → i-square root

1:36 Khetha i-polynomial. I-Sieve, okusho ukufuna izigidigidi zezinombolo ezinama-factors amancane kuphela, isikhundla ngasinye sizimele, ngakho-ke leso yisona siyingi esadlulela kuma-GPU. Bese kuba i-linear algebra, lapho izinto eziyisigidigidi eziyisishiyagalombili ziba yi-matrix engamakhulu ayisithupha namashumi amahlanu ezinkulungwane zemigqa ngasohlangothini, futhi i-node ngayinye ikhuluma nenye i-node kuze kube kube kukhona ovinjelwe. Bese kuba i-square root, leyo okwakhungatheka ngayo ukuphatha kwe-Cognition futhi yabhalwa kabusha kathathu.

Kungani i-2048 isabamba: $30M nge-RSA-1024, $38 quadrillion nge-RSA-2048

1:59 Kungani ukhiye wakho wamabhithi amabili namashumi amane nesishiyagalombili uyisilwane esihlukile. I-sieve iyi-subexponential, ngakho-ke ibhithi elengeziwe ngalinye libiza ngaphansi kokuphindwa kabili, kodwa iyahlanganiswa. I-RSA eyishumi namashumi amabili nane ingamashumi ayisikhombisa nesishiyagalombili esikhathi somsebenzi we-RSA engamakhulu amabili namashumi asithupha, biza lokho ngamadola ayizigidi ezingamashumi amathathu, imali yokuhlala phansi ye-hyperscaler. I-RSA eyizinkulungwane ezimbili namashumi amane nesishiyagalombili inzima kakhulu ngokuphindwe kabili, amadola ayizigidigidi ezingamashumi amathathu nesikhombisa, okuyisilinganiso sikaRivest esineyunithi lishintshiwe kusuka eminyakeni kuye kumadola.

Ukuphikisana vs ukufunda: 'UClaude wephule i-RSA' vs 'ayikho i-algorithm entsha'

2:24 Isimangalo vs ukufunda. Isihloko sithi uClaude wephule i-RSA. UClaude ngokwakhe uncoma abantu abakha i-sieve emashumini eminyaka, futhi uWeis wengeza imigqa emithathu. Ayikho i-algorithm entsha, isekhona i-exponential, okwathi kamuva wayilungisa yaba i-subexponential, futhi ayikho ingozi entsha kokhiye abasetshenzisiwe. Kokubili kuyiqiniso. Izibalo azizange zishintshe.

2:41 Inani lishintshile, ngoba ama-GPU angasebenzi kanye ne-agent efaka i-C endala ku-Cuda ngobusuku obubodwa kwenza umsebenzi weshumi leminyaka ube impelasonto ende. IHacker News ithi awudingi i-AI ngalokhu, nje i-compute. Iqiniso, kuze kube yilapho umuntu ephawula ukuthi i-Instagram isasayina i-imeyili yayo ngokhiye wamabhithi ayisikhombisa namashumi ayisithupha nesishiyagalombili, manje osewumsebenzi wempelasonto. Impendulo engcono kakhulu, evela ku-Allan Peng. Amabili ayi-factor ye-RSA eyisishiyagalombili namashumi ayisishiyagalolunye nesithupha kanye nokukodwa.

NgoMsombuluko: ssh-keygen -l, okhiye bakho bokusayina i-imeyili, umugqa we-NIST ka-2030

3:04 NgoMsombuluko. Qalisa i-ssh keygen dash L kokhiye bakho bomphakathi, nanoma yini ephrinta amashumi amabili nane inkinga ka-two thousand thirteen oyigcinile. Imali yakho yokusayina i-imeyili ngendlela efanayo. Futhi funda uhlaka lwe-Nist, ngoba i-RSA eyizinkulungwane ezimbili namashumi amane nesishiyagalombili isiphelelwe yisikhathi ngemuva konyaka ka-2030, hhayi ngama-sieve, ngama-qubits angakabi khona

Isinqumo, ngaphansi kwesembozo

3:21 nokho. Isinqumo, ngaphansi kwesembozo. Kudinga ukubuyekezwa. Amabhithi angamakhulu amabili namashumi amane nesishiyagalombili alungile. Amabhithi ayisikhombisa namashumi ayisithupha nesishiyagalombili ku-DNS yakho akulungile, futhi umhlaseli akasenawo ilabhulabhu, kuphela ama-GPU angasebenzi newindi lengxoxo. Ngitshele ukuthi yini okufanele ngiyivule ngokulandelayo kumazwana. Futhi lo ngumhlahlandlela wanamuhla. NginguNiko wase-Axrisi. Hlanganisa ngokuzibophezela.

Imithombo

1. Stephen A. Weis, "RSA-896" (N, p, q)saweis.net
2. Weis on X — the run (2,048 GPUs, 30 GPU-years, 10 days)x.com
3. Weis on X — Claude's statement: https://x.com/sweis/status/2101492820028895607 · the three clarifications: https://x.com/sweis/status/2101494688528400792 · "GNFS is subexponential"x.com
4. Allan Peng: "2 is a factor of (RSA-896 + 1)"x.com
5. Hacker News threadnews.ycombinator.com
6. Eric Lu / Cognition, "Factoring RSA-260" (GPU siever, cost ladder, 656M-row matrix, sqrt rewritten 3×)cognition.com
7. CADO-NFS (INRIA)cado-nfs.gitlabpages.inria.fr
8. RSA numbers (RSA-129 … RSA-2048, prizes): https://en.wikipedia.org/wiki/RSA_numbers · "The Magic Words are Squeamish Ossifrage"en.wikipedia.org
9. NIST IR 8547 (initial public draft), transition timelinenvlpubs.nist.gov
10. Instagram DKIM recorddns.google