1. Gabatarwa

Wannan takarda ta magance wani gibi na asali a cikin tsaron blockchain: rashin iyakoki na tsaro na ainihi, waɗanda ba su ƙare ba don yarjejeniya ta tushen aiki na shawara (PoW), musamman ga nau'ikan da ba na jere ba. Yayin da aka yi bincike kan yarjejeniyar Nakamoto ta Bitcoin a matsayin ƙarshe, yanayin sa na yiwuwa ya bar masu amfani cikin shakku game da ƙarshe. Aikin kwanan nan na Li da sauransu (AFT '21) ya ba da iyakoki na ainihi don PoW na jere. Wannan aikin ya faɗaɗa wannan ƙaƙƙarfan zuwa aiki na shawara mai haɗin gwiwa, yana gabatar da sabon iyali na tsare-tsaren sake haɓaka jihohi (Ak) waɗanda ke amfani da k wasanin gwada ilimi masu zaman kansu a kowane toshe maimakon sarkar guda ɗaya.

Alƙawarin asali shine ba da damar ƙarshen toshe guda ɗaya tare da ƙididdigewa, ƙananan yiwuwar kasa sosai, yana magance kai tsaye haɗarin kashe kuɗi sau biyu waɗanda ke addabar tsarin kamar Bitcoin.

2. Ra'ayoyi na Asali & Bayanan Baya

2.1 Aiki na Shawara na Jere vs. Haɗin Gwiwa

Aiki na Shawara na Jere (Bitcoin): Kowane toshe yana ƙunshe da mafita ɗaya ta wasan gwada ilimi wacce ke nuni da toshe ɗaya da ya gabata ta hanyar sirri, yana samar da sarkar layi. Tsaro ya dogara da ka'idar "sarkar mafi tsayi" da jira don tabbatar da yawa (misali, tubalan 6).

Aiki na Shawara mai Haɗin Gwiwa (An Gabatar): Kowane toshe yana ƙunshe da k mafita na wasanin gwada ilimi masu zaman kansu. Ana tattara waɗannan mafita don samar da toshe, yana ƙirƙirar tsari inda yawancin hanyoyin aiki na shawara ke ba da gudummawa ga sabunta jiha guda ɗaya (duba Hoto na 1 a cikin PDF). Wannan ƙira tana nufin samar da lokutan isowar tubalan da suka fi dacewa da ƙwaƙƙwaran aikin shawara a kowane raka'a na lokaci.

2.2 Bukatar Iyakoki na Tsaro na Ainihi

Hujjojin tsaro na ƙarshe (misali, "mai tsaro don n mai girma isasshe") ba su isa ba don turawa a duniyar gaske. Ba sa gaya masu amfani har yaushe su jira ko menene ainihin haɗarin. Iyakoki na ainihi suna ba da matsakaicin yiwuwar kasa (misali, $2.2 \times 10^{-4}$) idan aka yi la'akari da takamaiman sigogin cibiyar sadarwa (jinkiri $Δ$) da ƙarfin maharin ($\beta$). Wannan yana da mahimmanci ga aikace-aikacen kuɗi waɗanda ke buƙatar sarrafa haɗari daidai.

3. Tsarin da aka Gabatar: Ak

3.1 Ƙirar Tsari & Ƙaramin Tsarin Yarjejeniya

An gina dangin tsarin Ak daga ƙasa zuwa sama daga wani ƙaramin tsarin yarjejeniya na asali. Wannan ƙaramin tsarin yana ba da damar ƙwararrun nodes su yarda da yanayin yanzu tare da iyakataccen yiwuwar kasa. Ta hanyar maimaita wannan hanyar yarjejeniya, an gina cikakken tsarin sake haɓaka jihohi wanda ya gaji iyakar kuskure na ainihi.

Mahimmin ƙa'idar ƙira: Yi amfani da k wasanin gwada ilimi masu zaman kansu don samar da toshe. Wannan yana ƙara "yawan aiki" a kowane tazara na toshe, yana sa ya zama da wahalar ƙididdiga ga mahari don ƙirƙirar sarkar gasa ta sirri daidai da nauyi.

3.2 Zaɓin Sigogi & Ingantawa

Takardar tana ba da jagora don zaɓar mafi kyawun sigogi (musamman k da wahalar wasan gwada ilimi) don yawancin zato:

  • Haɗin Kai na Cibiyar Sadarwa: Matsakaicin jinkirin yaɗa saƙo ($Δ$).
  • Ƙarfin Mahari: Kashi na jimlar ƙimar hash da mahari ke sarrafa ($\beta$).
  • Matakin Tsaro da ake nema: Iyakar sama da ake so akan yiwuwar kasa ($\epsilon$).
  • Manufofin Gudanarwa/Jinkiri: Lokacin toshe da ake tsammani.

Misali, don kiyaye lokacin toshe na Bitcoin na mintuna 10 da ake tsammani amma tare da tsaro mafi girma, mutum na iya zaɓar k=51 wasanin gwada ilimi a kowane toshe, tare da kowane wasan gwada ilimi yana da sauƙin warwarewa.

4. Binciken Tsaro & Iyakoki na Ainihi

4.1 Iyakoki na Sama na Yiwuwar Kasa

Babbar gudummawar ka'idar ita ce samo iyakoki na sama don matsakaicin yiwuwar kasa na tsarin Ak. An ayyana kasa a matsayin keta tsaro (misali, kashe kuɗi sau biyu) ko rayuwa. An bayyana iyakoki a matsayin aiki na $k$, $\beta$, $Δ$, da sigar wahalar wasan gwada ilimi.

Binciken yana iya ginuwa akan da faɗaɗa samfuran "harin sirri" da "harin daidaitawa" da aka yi amfani da su don PoW na jere, yana daidaita su zuwa yanayin haɗin gwiwa inda maharin dole ne ya warware wasannin gwada ilimi da yawa a lokaci guda don yin gasa.

4.2 Kwatanta da Aiki na Shawara na Jere (Bitcoin)

Kwatancin Tsaro: PoW mai Haɗin Gwiwa (k=51) vs. "Bitcoin Mai Sauri"

Yanayi: Mahari tare da ƙimar hash 25% ($\beta=0.25$), jinkirin cibiyar sadarwa $Δ=2s$.

  • PoW mai Haɗin Gwiwa (An Gabatar): Yiwuwar kasa don daidaito bayan toshe 1 ≈ $2.2 \times 10^{-4}$.
  • PoW na Jere ("Bitcoin Mai Sauri" a tubalan 7/min): Yiwuwar kasa bayan toshe 1 ≈ 9%.

Fassara: Mahari zai yi nasara wajen kashe kuɗi sau biyu kusan sau ɗaya a cikin sa'o'i 2 a kan Bitcoin mai sauri, amma zai buƙaci yin aiki akan "tubalan dubu ba tare da nasara ba" a kan tsarin haɗin gwiwa.

5. Sakamakon Gwaji & Kwaikwayo

Takardar ta haɗa da kwaikwayo don tabbatar da iyakokin ka'idar da gwada ƙarfi.

  • Tabbatar da Iyakoki: Kwaikwayo a ƙarƙashin zato na samfurin sun tabbatar da iyakoki na ainihi da aka samo suna riƙe.
  • Gwajin Ƙarfi: Kwaikwayo a ƙarƙashin keta ɓangaren zato na ƙira (misali, haɗin kai mara kyau, ɗan bambancin hali na mahari) sun nuna ginin da aka gabatar ya kasance mai ƙarfi. Wannan yana da mahimmanci don turawa a duniyar gaske inda samfuran ingantattu ba su taɓa riƙewa sosai ba.
  • Bayanin Chati (An fayyace): Babban chati zai iya zana Yiwuwar Kasa (ma'auni na log) akan Ƙarfin Hash na Mahari ($\beta$) don ƙimar k daban-daban. Wannan chati zai nuna faɗuwa mai zurfi, mai kama da ƙari a cikin yiwuwar kasa yayin da k ya ƙaru, musamman ga matsakaicin $\beta$, yana nuna fa'idar tsaro akan PoW na jere (layi ɗaya don k=1).

6. Cikakkun Bayanai na Fasaha & Tsarin Lissafi

Binciken tsaro ya dogara ne akan samfurin yiwuwar tseren PoW. Bari:

  • $\lambda_h$: Yadda ƙungiyar gaskiya ke warware wasannin gwada ilimi.
  • $\lambda_a = \beta \lambda_h$: Yadda mahari ke warware wasannin gwada ilimi.
  • $k$: Adadin wasannin gwada ilimi a kowane toshe.
  • $Δ$: Iyakar jinkirin cibiyar sadarwa.

Asalin samo iyaka ya ƙunshi bincika tseren tsarin binomial ko Poisson tsakanin cibiyar sadarwa ta gaskiya da mahari. Yiwuwar cewa maharin zai iya warware k wasannin gwada ilimi a asirce (don ƙirƙirar toshe mai gasa) kafin cibiyar sadarwa ta gaskiya ta warware adadin isasshe a cikin nodes ɗinta ana iyakance ta ta amfani da rashin daidaiton wutsiya (misali, iyakokin Chernoff). Tsarin haɗin gwiwa ya juya matsalar zuwa ɗaya daga cikin maharin da ke buƙatar k nasarori kafin cibiyar sadarwa ta gaskiya ta sami wani jagora, wanda ga k mai girma ya zama mai yiwuwa sosai idan $\beta < 0.5$. Wani sauƙaƙan iyaka na ra'ayi zai iya zama kamar haka: $$P_{\text{kasa}} \leq \exp(-k \cdot f(\beta, \Delta \lambda_h))$$ inda $f$ aiki ne da ke ɗaukar fa'idar ƙwararrun nodes. Wannan yana nuna ingantaccen tsaro na ƙari tare da k.

7. Tsarin Bincike: Fahimta ta Asali & Kwararar Hankali

Fahimta ta Asali: Cigaban takardar ba kawai wasannin gwada ilimi masu haɗin gwiwa ba ne—shi ne tabbataccen ƙididdiga da yake saya. Yayin da wasu (misali, Bobtail) suka yi jayayya da hanyar PoW mai haɗin gwiwa yana inganta tsaro, wannan aikin shine farkon lissafin ainihin ciniki tsakanin haɗin gwiwa (k), ƙimar aiki, da lokacin ƙarshe. Yana canza tsaro daga wasan "jira da bege" zuwa sigar injiniya.

Kwararar Hankali:

  1. Matsala: PoW na jere (Bitcoin) yana da ƙarshe mara iyaka, mai yiwuwa. Iyakoki na ƙarshe ba su da amfani ga masu aiki.
  2. Lura: Haɗa aiki a cikin toshe yana ƙara "tsantsar" ƙididdiga na sarkar, yana sa ya fi wahala a wuce ta a asirce.
  3. Ƙirar Hanyoyi: Gina ƙaramin tsarin yarjejeniya (Ak) wanda ke amfani da wannan tsantsar. Tsaronsa ana iya bincika shi a cikin samfurin haɗin kai.
  4. Lissafi: Samo iyakoki na ainihi, waɗanda ake iya ƙididdigewa na sama don yiwuwar kasa na Ak.
  5. Ƙaddamar da Tsari: Maimaita Ak don gina cikakken blockchain. Iyakar tsaro ta wuce.
  6. Ingantawa & Tabbatarwa: Bayar da hanyar zaɓin k da wahala, da kuma yin kwaikwayo don nuna ƙarfi.
Wannan kwararar tana kama da ƙaƙƙarfan injiniyan tsaro da ake gani a cikin tsarin rarraba na al'ada (misali, dangin Paxos), yanzu an yi amfani da shi ga yarjejeniya mara izini.

8. Ƙarfafawa, Kurakurai & Fahimta mai Aiki

Ƙarfafawa:

  • Tsaro na Ainihi: Wannan shine kambin sarauta. Yana ba da damar turawa daidaita haɗari. Ƙofar biyan kuɗi yanzu na iya cewa, "Muna karɓar ma'amaloli bayan toshe 1 saboda haɗarin kashe kuɗi sau biyu daidai 0.022%, wanda ya fi ƙaramin ƙimar zamba na katin bashi."
  • Yuwuwar Ƙarshen Toshe Guda: Yana rage jinkirin daidaitawa sosai don ma'amaloli masu ƙima, wani babban cikas ga karɓar blockchain a cikin kuɗi.
  • Ƙira mai Sigogi: Yana ba da maɓalli mai daidaitawa (k) don ciniki tsakanin tsaro, gudanarwa, da ƙaddamarwa (kamar yadda wasannin gwada ilimi masu sauƙi na iya rage shingen hakar ma'adinai).
  • Tushe mai Ƙarfi: Gina kai tsaye akan kafaffen samfurin haɗin kai na Pass da sauransu da aikin iyakoki na ainihi na Li da sauransu, yana ba shi amincin ilimi.

Kurakurai & Tambayoyi masu Muhimmanci:

  • Samfurin Haɗin Kai na Ƙarfafawa: Duk binciken ya dogara ne akan sanannen $Δ$. A duniyar gaske (intanet), $Δ$ mai canzawa ne mai yiwuwa, ba iyaka ba. "Ƙarfin" kwaikwayon ga keta zato yana da ban gamsu amma ba hujja ba. Wannan babban tashin hankali ne a cikin duk hujjojin blockchain na haɗin kai.
  • Wuce Gona da Irin Sadarwa: Tattara k mafita a kowane toshe yana ƙara girman toshe da nauyin tabbatarwa. Don k=51, wannan ba ƙaramin abu bane. Takardar tana buƙatar tattaunawa mai haske kan iya haɓaka wannan wuce gona da iri.
  • Dabarun Ma'adinai & Ƙaddamarwa: Shin PoW mai haɗin gwiwa yana canza ka'idar wasan hakar ma'adinai? Shin zai iya ƙarfafa taro (kamar yadda aka gani a Bitcoin) ta hanyoyi sababbi? Binciken yana ɗauka mafi rinjaye na gaskiya suna bin tsari—ma'auni amma sau da yawa ana keta shi.
  • Tushen Kwatanta: Yin bambanci da "Bitcoin mai sauri" (tubalan 7/min) ɗan rashin adalci ne. Kwatanta mai adalci zai iya zama akan PoW na jere tare da irin wannan jimlar ƙimar hash a kowane raka'a na lokaci. Duk da haka, batun su game da saurin ƙarshe ya tsaya.

Fahimta mai Aiki:

  1. Ga Masu Ƙirar Tsari: Wannan shiri ne. Dangin Ak yakamata ya zama farkon farawa ga kowane sabon sarkar PoW da ke buƙatar ƙarshe mai sauri, musamman a cikin yanayi da aka sarrafa (misali, sarƙoƙin ƙungiya) inda za a iya iyakance $Δ$ da kyau.
  2. Ga Kamfanoni: Daina amfani da "tabbatar da 6" a matsayin mantra. Yi amfani da wannan tsarin don ƙididdige zurfin tabbatarwar ku bisa ga juriyar haɗarin ku, ƙimar ƙarfin maharin da aka ƙiyasta, da jinkirin cibiyar sadarwa.
  3. Ga Masu Bincike: Babbar tambayar da aka buɗe ita ce gada zuwa ɓangaren haɗin kai ko rashin haɗin kai. Shin ana iya samun irin wannan iyakoki na ainihi a cikin waɗannan samfuran da suka fi dacewa da gaske? Haka nan, bincika ƙira masu haɗawa da haɗa PoW mai haɗin gwiwa tare da wasu kayan aikin ƙarshe (kamar Casper na Ethereum).
  4. Mataki na Gaba mai Muhimmanci: Aiwatar da wannan a cikin hanyar gwaji (kamar cokali mai yatsu na Bitcoin Core) kuma a gwada shi a ƙarƙashin yanayin cibiyar sadarwa na duniyar gaske. Ka'idar tana da ban sha'awa; yanzu tana buƙatar tabo na yaƙi.

9. Aikace-aikace na Gaba & Hanyoyin Bincike

  • Daidaituwar Ciniki mai Yawan Mita (HFT): HFT na tushen blockchain yana buƙatar ƙarshe ƙasa da daƙiƙa tare da haɗari kusan sifili. Sarkar PoW mai haɗin gwiwa da aka daidaita a cikin cibiyar sadarwa mai ƙarancin jinkiri, wanda aka sarrafa, zai iya zama mafita mai yuwuwa.
  • Kuɗin Bankin Tsakiya na Digital (CBDCs): Don CBDCs na jama'a, inda mahalarta aka sani kuma ana iya sarrafa yanayin cibiyar sadarwa, PoW mai haɗin gwiwa yana ba da yarjejeniya mai bayyanawa, mai dacewa da bincike tare da haɗarin daidaitawa da ake iya ƙididdigewa.
  • Gadoji & Oracle na Tsakanin Sarƙoƙi: Waɗannan muhimman sassa na kayayyaki suna buƙatar tsaro mai ƙarfi sosai don ƙarshen jiha. Wani gefen sarkar PoW mai haɗin gwiwa da aka keɓe don yarjejeniyar gada zai iya ba da garantin mafi ƙarfi fiye da yawancin ƙira na yanzu.
  • Haɗuwa tare da Tabbacin Hannun Jari (PoS): Bincike zai iya bincika nau'ikan PoS "masu haɗin gwiwa" ko samfuran haɗawa inda tsaro ya samo asali daga ƙungiyoyin masu tabbatarwa masu zaman kansu da yawa a kowane rami, kwatankwacin wasannin gwada ilimi da yawa a kowane toshe.
  • La'akari da Bayan Quantum: Yayin da PoW ke da juriya na bayan quantum a asali (don nemo, ba don tabbatarwa ba), tsarin wasannin gwada ilimi masu haɗin gwiwa na iya ba da ƙarin juriya ga abokan gaba na quantum ta hanyar buƙatar hare-hare masu haɗin gwiwa akan matsalolin sirri masu zaman kansu da yawa.

10. Nassoshi

  1. Keller, P., & Böhme, R. (2022). Aiki na Shawara tare da Iyakoki na Ainihi. A cikin Proceedings of the 4th ACM Conference on Advances in Financial Technologies (AFT '22).
  2. Nakamoto, S. (2008). Bitcoin: Tsarin Kuɗin Lantarki na Peer-to-Peer.
  3. Li, J., da sauransu. (2021). Tsaron Bitcoin a cikin Samfurin Haɗin Kai: Bincike na Ainihi. A cikin Proceedings of AFT '21.
  4. Pass, R., Seeman, L., & Shelat, A. (2017). Binciken Tsarin Blockchain a Cibiyoyin Sadarwa marasa Haɗin Kai. A cikin EUROCRYPT.
  5. Garay, J., Kiayias, A., & Leonardos, N. (2015). Tsarin Ƙarshen Bitcoin: Bincike da Aikace-aikace. A cikin EUROCRYPT.
  6. Bobtail: Tsarin Aiki na Shawara wanda ya Cimma Manufar Lokacin Toshe da Ƙananan Lokutan Tabbatar da Ma'amaloli (Takarda Fari).
  7. Buterin, V., & Griffith, V. (2019). Casper the Friendly Finality Gadget. arXiv preprint arXiv:1710.09437.
  8. Lamport, L. (1998). Majalisar Wakilai na ɓangare. ACM Transactions on Computer Systems.