Bincike Kan Cin Zuba Kudi Sau Biyu A Cikin Bitcoin Ta Hanyar Amfani Da Hashrate

1. Gabatarwa

Tsarin tsaro na Bitcoin ya dogara ne akan hana cin zuba kudi sau biyu—aikin mugunta na kashe tsabar kuɗin dijital ɗaya sau biyu. Wannan takarda tana ba da bincike mai ma'ana, na stochastic game da hare-haren cin zuba kudi sau biyu bisa ga hashrate na mai kai hari. Tana fayyacewa kuma tana faɗaɗa kan tsarin ƙididdiga na asali da aka gabatar a cikin takarda mai farin fata ta asali ta Satoshi Nakamoto, tana motsawa daga fahimtar inganci zuwa tsarin yuwuwar daidaitacce.

2. Blockchain da Zaɓin Reshe

Blockchain na Bitcoin bishiya ce ta tubalan, kowanne yana nuni ga wanda ya gabace shi. Yarjejeniyar cibiyar sadarwa tana zaɓar sarkar mafi tsayi (ko sarkar da ke da mafi yawan tarin aikin shaida) a matsayin tarihi mai inganci. Sabani na ɗan lokaci (fork) ana warware su lokacin da wani sabon tubale ya faɗaɗa wani reshe, ya sa ya zama mafi tsayi. Wannan tsari shine fagen yaƙi don hare-haren cin zuba kudi sau biyu, inda mai kai hari a ɓoye yake gina madadin sarkar.

3. Yin Kamawa

Wannan sashe yana ƙirƙira yanayin kai hari na asali: mai kai hari mai rabo q na jimlar hashrate na cibiyar sadarwa yana ƙoƙarin cin nasara akan sarkar gaskiya (mai hashrate p = 1 - q) bayan ya kasance a baya da tubalan z. Ana ƙirƙira tsarin a matsayin Binomin Tafiya Bazuwar. Yuwuwar mai kai hari ya taɓa kamawa daga rashi na tubalan z an samo shi kamar haka:

$P = \begin{cases} 1 & \text{idan } q \ge p \\ (q/p)^z & \text{idan } q < p \end{cases}$

Wannan sakamako mai kyau yana nuna cewa ga mai kai hari wanda ke da ƙasa da 50% na hashrate (q < 0.5), yuwuwar nasara tana raguwa da ƙima tare da adadin tabbatattun z.

4. Jira Don Tabbatarwa

Binciken ya koma ga hangen ɗan kasuwa: nawa ne tabbatattun (n) ya kamata mutum ya jira kafin ya ɗauki ma'amala a matsayin mai tsaro? Takardar ta ƙididdige yuwuwar cewa mai kai hari zai iya yin nasara har yanzu bayan ɗan kasuwa ya ga tabbatattun n. Wannan ya haɗa da ƙididdige yuwuwar cewa mai kai hari ya sami tubalan n+1 kafin cibiyar sadarwa ta gaskiya ta sami tubalan n, tare da la'akari da tseren da ke gudana. Sakamakon yuwuwar yana ba da tushe don shawararrun zurfin tabbatarwa.

5. Zane-zane da Bincike

Takardar ta gabatar da bincike na zane-zane wanda ke nuna yuwuwar cin nasarar cin zuba kudi sau biyu da adadin tabbatattun ɗan kasuwa (n) don nau'ikan hashrate na mai kai hari daban-daban (q). Muhimman fahimtoji da aka kwatanta sun haɗa da:

Don q=0.1 (hashrate 10%), yuwuwar nasara ta faɗi ƙasa da 0.1% bayan tabbatattun 5 kawai.
Don q=0.3, yana ɗaukar kusan tabbatattun 24 don cimma matakin tsaro iri ɗaya.
Yayin da q ya kusanci 0.5, tabbatattun da ake buƙata suna tashi sosai, suna nuna bakin kofa na "hare-haren 51%".

Waɗannan zane-zane suna da mahimmanci don tantance haɗari da kafa manufofin tabbatarwa masu amfani.

6. Tattalin Arzikin Cin Zuba Kudi Sau Biyu

Takardar ta gabatar da tsarin tattalin arziki, tana tsara harin a matsayin matsalar ɓarnatar da ɗan caca tare da matakan da suka bambanta. Kyautar mai kai hari ita ce ƙimar ma'amalar da yake nufin ya sake zuba kudi. Binciken ya yi la'akari da ƙimar da ake tsammani na harin ga mai kai hari, yana ƙaddara cewa sai dai idan ƙimar kayan da aka sace ya yi yawa sosai idan aka kwatanta da ladan tubalin, mai kai hari mai hankali tare da q < 0.5 zai ga haƙo ma'adinai da gaskiya ya fi riba fiye da ƙoƙarin sake zuba kudi. Wannan ya yi daidai da ƙa'idodin tsaro na wasan.

7. Ƙarshe

Binciken ya ba da ingantaccen tushe na lissafi don fahimtar haɗarin sake zuba kudi. Ya tabbatar da cewa ƙa'idar Bitcoin tana da ƙarfi sosai a kan sake zuba kudi ta hanyar masu kai hari waɗanda ke da ƙasa da 50% na hashrate na cibiyar sadarwa, muddin masu karɓa sun jira isassun adadin tabbatattun. Aikin yana ƙididdige cinikin tsaro tsakanin lokacin tabbatarwa da juriyar haɗari.

8. Fahimtar Asali & Hangen Masanin Bincike

Fahimtar Asali: Aikin Rosenfeld ba lissafi kawai ba ne; shine farkon ingantaccen tsarin farashin haɗari don matakin daidaitawa na Bitcoin. Ya canza ƙa'idar "sarkar mafi tsayi" ta Nakamoto mai ma'ana zuwa SLA (Yarjejeniyar Matakin Sabis) na tsaro mai ƙima, inda zurfin tabbatarwa n shine kuɗin da aka biya don takamaiman yuwuwar ƙarshe 1-P. Wannan shine ginshiƙin da duk manufofin tsaro na musayar crypto na zamani aka gina akan shi.

Kwararar Hankali: Hazaka tana cikin tsara harin a matsayin Binomin Tafiya Bazuwar—tsari na al'ada na stochastic. Ta hanyar ƙirƙira gano tubalin a matsayin tsarin Poisson, Rosenfeld ya rage tseren haƙo ma'adinai mai rikitarwa, mai kama da juna zuwa matsalar ɓarnatar da ɗan caca mai girma ɗaya wanda za a iya warwarewa. Tsalle daga Sashe na 3 (yuwuwar kamawa) zuwa Sashe na 4 (lokacin jiran ɗan kasuwa) yana da mahimmanci; yana haɗa iyawar mai kai hari zuwa manufar mai tsaro.

Ƙarfi & Kurakurai:
Ƙarfi: Sauƙin samfurin shine ƙarfinsa. Maganin rufaffiyar $P = (q/p)^z$ yana da ƙarfi kuma ana iya fassara shi cikin sauƙi. Binciken tattalin arziki a Sashe na 6 ya kasance a gaban zamansa, yana hasashen binciken wasan ka'idar blockchain na yau da kullun da ake gani a wurare kamar Taron ACM kan Ci gaban Fasahar Kuɗi (AFT).
Kurakurai Mai Mahimmanci: Samfurin yana ɗauka maƙiyi mai tsayayye tare da ƙayyadaddun q. Ya kasa yin la'akari da hashrate mai dabaru, mai canzawa—kamar mai kai hari yana hayar babban ƙarfin haƙo ma'adinai na gajimare a cikin ɗan gajeren lokaci mai niyya ("harin Goldfinger"), barazana da aka haskaka a cikin bincike na gaba kamar "Mining Pool" takarda ta Eyal da Sirer. Hakanan ya yi watsi da jinkirin cibiyar sadarwa da dabarun haƙo ma'adinai na son kai waɗanda zasu iya ƙara inganci q na mai kai hari.

Fahimtoji Masu Aiki: 1. Ga Musayar: Kada ku yi amfani da lambar tabbatarwa guda ɗaya. Yi amfani da dabarar Rosenfeld a hankali. Don ajiye $100, tabbatattun 3 na iya isa. Don cire $10 miliyan, kuna buƙatar dozin, ko mafi kyau, matsawa zuwa sarkar da aka haɓaka da kayan aikin ƙarshe. 2. Ga Masu Ƙirƙira Ƙa'idodi: Wannan takarda ita ce hujja ta al'ada don Shaida na Rike (PoS). Farashin tsaro mai ƙima ((q/p)^z) a cikin PoW yana da zalunci a tattalin arziki. Tsarin PoS kamar Casper na Ethereum, kamar yadda aka rubuta a cikin ƙayyadaddun bincikensa, yana neman maye gurbin wannan ƙarshen yuwuwar tare da ƙarshen sirri, mai yankewa, yana canza ƙididdigar harin gaba ɗaya. 3. Ga ƴan Kasuwa: Abin da ake karɓa na gaske shine cewa don ƙananan ƙima, biyan kuɗi nan take (kamar kofi), jiran kowane tabbatattun ba shi da amfani. Wannan gaskiyar tattalin arziki ta haifar da ci gaban tashoshin biyan kuɗi na kashe layi (Cibiyar Sadarwar Walƙiya), wanda ke kaucewa matsalar Rosenfeld gaba ɗaya ta hanyar motsa ma'amaloli daga matakin tushe.

9. Cikakkun Bayanai na Fasaha & Tsarin Lissafi

Samfurin asali yana ɗaukar gano tubalin a matsayin gwaje-gwaje masu zaman kansu. Bari p ya zama yuwuwar sarkar gaskiya ta sami tubalin na gaba, kuma q = 1-p ga mai kai hari. Yanayin tsarin shine rashi na mai kai hari z. Yuwuwar p_z cewa mai kai hari zai taɓa kaiwa daidaito daga rashi z ya gamsar da alaƙar maimaitawa da aka samo daga matsalar ɓarnatar da ɗan caca:

$p_z = q \cdot p_{z-1} + p \cdot p_{z+1}$

Tare da yanayin iyaka p_0 = 1 (daidaito nasara ne) da p_\infty = 0. Warware wannan yana haifar da madaidaicin madaidaicin magani $p_z = (q/p)^z$ don q < p.

Don yanayin ɗan kasuwa tare da tabbatattun n, yuwuwar mai kai hari ya yi nasara ita ce yuwuwar zai iya gina sarkar da ta fi tsayi fiye da sarkar gaskiya farawa daga tubalan n a baya. Ana ƙididdige wannan ta hanyar taƙaita duk yuwuwar yanayin jagora lokacin da ɗan kasuwa ya watsa ma'amalar.

10. Tsarin Bincike: Misalin Hali

Yanayi: Musayar cryptocurrency ta karɓi babban ajiya. Dole ne ta yanke shawarar nawa ne tabbatattun da za ta buƙaci kafin ta ƙididdige asusun mai amfani.

Ayyana Sigogi:
- Kiyasin rabon hashrate na mai kai hari: q = 0.2 (20%). Wannan na iya dogara ne akan bayanan tafkin haƙo ma'adinai na jama'a.
- Ƙimar cikin haɗari (adadin ajiya): V = $500,000.
- Juriya na haɗari na Musayar: Yuwuwar sake zuba kudi da aka yarda: $\epsilon = 0.001$ (0.1%).
Aiwatar da Samfurin Rosenfeld: Muna buƙatar nemo mafi ƙanƙanta n kamar yadda yuwuwar harin $P(n, q) \le \epsilon$. Yin amfani da dabarar $P \approx \sum_{k=0}^{\infty} \frac{\lambda^k e^{-\lambda}}{k!} \cdot (q/p)^{n+1-k}$ don $k \le n+1$ (inda $\lambda = n(q/p)$), ko tuntubi zane-zane/tebur da aka riga aka ƙididdige.
Ƙididdiga/Sakamako: Don q=0.2 da \epsilon=0.001, tabbatattun da ake buƙata n kusan 9 ne.
Yanke Shawara Kan Manufa: Musayar ta saita buƙatun tabbatarwa don wannan kadari zuwa tubalan 9. Don lokacin tubalin na mintuna 10, wannan yana nuna lokacin riƙe na mintuna 90 don ajiyar, yana daidaita tsaro da ƙwarewar mai amfani.

11. Aikace-aikacen Gaba & Hanyoyin Bincike

Manufofin Tabbatarwa Masu Ƙarfi: Haɗa bayanan hashrate na ainihin lokaci da ƙimar mempool don daidaita n a hankali, ƙirƙirar injin tabbatarwa "mai hankali ga haɗari".
Tsaro Tsakanin Sarkoki: Yin amfani da samfurin don tantance tsaron gadoji na blockchain da ma'amaloli tsakanin sarkoki, inda ƙimar tattalin arziki cikin haɗari na iya shimfiɗa sarkoki da yawa tare da ƙimar q daban-daban.
La'akari da Bayan-Quantum: Bincike kan yadda zuwan kwamfuta na quantum zai iya shafar farashin aiwatar da harin 51% (ta hanyar karya algorithms na haƙo ma'adinai) da sake daidaita sigar q a cikin samfuran tsaro.
Haɗawa tare da MEV (Ƙimar Cirewa Mafi Girma): Hare-haren sake zuba kudi na zamani sau da yawa sassa ne na dabarun MEV masu rikitarwa. Samfuran gaba dole ne su yi la'akari da ƙarin ribar da mai kai hari zai iya cirewa daga sake tsarawa ko tantance tubalan fiye da adadin sake zuba kudi kawai.

12. Nassoshi

Nakamoto, S. (2008). Bitcoin: Tsarin Kuɗin Lantarki na Peer-to-Peer.
Rosenfeld, M. (2014). Bincike Kan Cin Zuba Kudi Sau Biyu A Cikin Bitcoin Ta Hanyar Amfani Da Hashrate. arXiv:1402.2009.
Eyal, I., & Sirer, E. G. (2014). Mafi Rinjaye Bai Isa Ba: Haƙo Ma'adinan Bitcoin Yana Cikin Haɗari. Taron Ƙasa da Ƙasa kan Kuɗi na Sirri da Tsaron Bayanai.
Buterin, V., & Griffith, V. (2017). Casper the Friendly Finality Gadget. arXiv:1710.09437.
Gervais, A., Karame, G. O., Wüst, K., Glykantzis, V., Ritzdorf, H., & Capkun, S. (2016). Kan Tsaro da Aikin Proof of Work Blockchains. Taron ACM SIGSAC akan Tsaro da Sadarwar Kwamfuta.