LAMBA MAI LAMBOBI 155 DA AKA RARRABA A KAN KATUNAN ZANE (GPU)

Raba babbar lamba zuwa abubuwan farko da suka haɗa ta yana da wuya, kuma wannan wahalar tana da muhimmanci ga ɓoye bayanai (cryptography) — shi ya sa takardar ta kula ta faɗi abin da sakamakonta ba ya barazana gare shi. Lambobin “ƙalubalen RSA” na jama’a suna zama ma’auni ga hanyoyin rarrabawa. RSA-155 ɗaya ce daga cikinsu: lambobi 155, ko bit 512.

Matatu biyu, tarihi ɗaya kowanne

Iyalai biyu na tsarin lissafi (algorithms) ne suka mamaye fagen. Number field sieve ita ce zakara ga manyan lambobi ƙwarai: ta rarraba RSA-155 tun a 1999, kuma, a cewar takardar, tarihin gaba ɗaya yanzu yana kan wata lamba mai lambobi 270, RSA-896, a 2026. Tsohuwar quadratic sieve tana da jinkiri a dogon zango kuma, a kalaman marubutan da kansu, “kayan aikin da bai dace ba” ce ga tarihin gaba ɗaya. Duk da haka tana da nata jerin tarihin: lamba mafi girma da aka rarraba da ita ita ce RSA-150, a watan Yunin 2025, ta amfani da awannin core na CPU 11,664.

Quadratic sieve tana farautar ƙananan lambobi da yawa da ke rabuwa gaba ɗaya a kan wani tarin ƙananan lambobin farko, sannan ta yi amfani da algebra na layi (linear algebra) don haɗa su zuwa murabba’ai biyu x² da y² da suke daidai idan aka raba da N (modulo N). Daga nan babban mai raba lamba na bai ɗaya (greatest common divisor) yana bayyana wani abu daga cikin abubuwan da suka haɗa ta. A kwamfuta, wannan mafarki ne mai ban tsoro ga na’urorin sarrafa zane (GPUs): samun damar ƙwaƙwalwa yana warwatse nesa da duk wani cache, gwaje-gwajen cike suke da rassa (branches), kuma algebra na ƙarshe yana aiki a cikin lissafin binary da babu wani ɗakin karatu na kamfani da ke goyon bayansa. Ƙoƙarin GPU na baya sun hanzarta wasu matakai ɗai-ɗai kawai.

Komai a kan katin zane

Fabian Januszewski da Christoph Heinrichs, na cibiyar lissafi ta Jami’ar Paderborn a Jamus, sun gina CUDA-MPQS, wata quadratic sieve ta buɗaɗɗen tushe wadda a cikinta kowane mataki — shirya polynomials, tacewa, duba waɗanda za a iya zaɓa, haɗa sakamakon ɓangare, gina matrix, warware ta da ɗaukar tushen murabba’i na ƙarshe — yana gudana a kan GPU. Na’urar sarrafawa ta yau da kullum (CPU) tana tsarawa kawai, tana shiryawa kuma tana kula da shigarwa da fitarwa; marubutan sun lissafa ƙananan matakan da suka rage a ɓangaren mai masaukin (host) a fili. A gwaji na lamba mai lambobi 100, GPU ɗin yana aiki kashi 99.9% na lokacin tacewa, ba tare da tsayawa don jiran na’urar sarrafawa ba.

Ƙara girma ya bayyana wata ɓoyayyiyar kuskure (bug). A girman RSA-155, wani ma’auni (counter) mai bit 8 da ake amfani da shi wajen tacewa ya cika ya zube daidai a kan waɗanda suka fi daraja, yana watsar da kashi 98 zuwa 99.5% daga cikinsu ba tare da an sani ba. Tawagar ta maye gurbinsa da ma’auni mai tsayawa a iyaka (saturating counter) wanda suka tabbatar yana ba da sakamako iri ɗaya.

RSA-155 cikin kusan yini ɗaya

A ranar 14 ga Yulin 2026, tsarin ya rarraba RSA-155 zuwa lambobin farko biyu masu lambobi 78 kowanne, an duba su duka a kan GPU da kuma a kan mai masaukin:

• Tacewa: GPUs NVIDIA H100 guda 64 a cikin nodes 16, awanni 10.8, sun tattara kusan dangantaka (relations) miliyan 17.3.
• Algebra na layi: H100 guda ɗaya na awanni 10.9, a kan matrix mai layuka miliyan 16.7 da abubuwa marasa sifili miliyan 684.
• Jimilla: awannin GPU 700.6 da kilowatt-hour 242, kusan awanni 24 daga farko zuwa samun abubuwan. Tacewa ta kai kashi 98.4% na kuɗin.

A iya sanin marubutan, wannan ita ce lamba mafi girma da aka taɓa rarrabawa da quadratic sieve, lambobi biyar fiye da tarihin baya — kuma an cimma shi da mafi sauƙin nau’in hanyar, wanda ke riƙe “babbar lambar farko” ɗaya kawai a kowace dangantaka inda tarihin baya-bayan nan suka yi amfani da uku.

Mafi sauri fiye da mafi kyawun na’urorin sarrafawa

A kan lamba mai lambobi 100, H100 guda ɗaya yana kammalawa cikin daƙiƙa 29.2, kuma RTX 5070 Ti na masu amfani na yau da kullum cikin daƙiƙa 51. A cikin kwatancen da aka sarrafa a kan lamba ɗaya, da aka auna makamashi a ɓangarorin biyu, H100 ɗaya ya fi sauri sau 3.6 zuwa 4.2 fiye da quadratic sieve mafi sauri ta CPU da ke gudana a kan cores 96 na na’urar sarrafawa AMD EPYC, kuma kusan sau tara zuwa goma fiye da wani shiri na yau da kullum. Sun kuma sake rarraba RSA-150 cikin awannin GPU 302.9, idan aka kwatanta da awannin core 11,664 na tarihin baya — rabo da marubutan suka jaddada ba hanzari ne na kwatanta abu da irinsa ba.

Babu barazana ga ɓoye bayanai

Marubutan sun bayyana a fili: an riga an rarraba RSA-155, wannan ba tarihin rarrabawa na gaba ɗaya ba ne, kuma “babu abin da ke nan da ya rage gefen tsaro”. An kuma iyakance code ɗin da gangan zuwa kusan lambobi 155. Sha’awarsu tana wani wuri dabam: nuna cewa tsarin lissafi mara tsari, mai cike da rassa zai iya rayuwa gaba ɗaya a kan GPU. Sun nuna matatar lattice ta GPU da ke cikin zuciyar number field sieve a matsayin buri na gaba na zahiri — aikin da, sun lura, wasu sun fara tun daga lokacin, suna rarraba RSA-260 da RSA-896 da sauyin GPU na wani shiri da ake da shi, na ƙarshen da aka yi da Claude.

Rikicin moriya. Marubutan sun bayyana cewa an yi amfani da AI mai samarwa (generative AI) da kayan aikin rubuta code na wakilai (agentic coding tools): samfuran Claude na Anthropic (ta Claude Code) tare da samfuran GPT na OpenAI da Gemini na Google wajen haɓaka manhaja, da samfuran Claude wajen shirya bayanai da rubutun takarda. Sun bayyana cewa an duba kuma an tabbatar da duk abin da AI ta fitar da hannu. Claude ne kuma ya rubuta wannan labarin.