Wannan takarda, "Aikin Tabbatar da Aiki tare da Iyakoki na Ainihi," ta magance babban iyaka a cikin yarjejeniyar blockchain: yanayin yuwuwar tsaro da kuma rashin tabbas a cikin tsarin Aikin Tabbatar da Aiki (PoW) na gargajiya kamar Bitcoin. Duk da cewa yarjejeniyar Nakamoto ta kawo juyin juya hali ga amincewar da ba ta da tsakiya, hujjojin tsarinta sun kasance mafi yawa na ƙwararru ko kuma ba su da tabbas, wanda ya bar masu amfani cikin shakku game da ainihin lokacin jira da ake buƙata don kammala ma'amala. Wannan rashin tabbas ana amfani da shi ta hanyar barazana kamar kashe kuɗi sau biyu da haƙar ma'adinai na son kai.
Marubutan, Patrik Keller da Rainer Böhme, sun ba da shawarar canji daga PoW na bi-da-bi (inda kowane toshe yana nuni da wani wasa mai wuyar gaske na baya) zuwa PoW na layi daya. Iyalin ka'idar su suna amfani da wasannin wuyar gaske $k$ masu zaman kansu a kowane toshe, wanda ke ba da damar ƙirƙira daga ƙasa zuwa sama daga ƙaramin ka'idar yarjejeniya mai ƙarfi. Babbar gudummawar ita ce samun iyakoki na ainihi, waɗanda ba su da iyaka don yuwuwar kasa a cikin hanyoyin sadarwa na maƙiyi masu aiki tare. Misalin da aka nuna tare da wasannin wuyar gaske $k=51$ ya sami yuwuwar kasa na $2.2 \cdot 10^{-4}$ don daidaito bayan toshe ɗaya, babban ci gaba akan ingantaccen PoW na bi-da-bi.
An gina ka'idar daga ka'idoji na farko, bisa ingantattun samfura daga wallafe-wallafen PoW na bi-da-bi amma sun bambanta a cikin injiniyoyin sa na asali.
Babban bambancin gine-gine ana ganinsa a cikin Hoto na 1 na takarda. PoW na Bi-da-Bi (Bitcoin) yana ƙirƙira sarkar layi daya inda hash ɗin kowane toshe shine mafita ga wasa mai wuyar gaske guda ɗaya wanda ke nuni zuwa toshe na baya. PoW na Layi Daya (Shawara) yana ƙirƙira toshe mai ɗauke da mafita ga wasannin wuyar gaske $k$ masu zaman kansu. Wannan tsari yana raba ƙimar damar yin yarjejeniya daga ƙimar ƙirƙirar toshe.
Tushen shine ka'idar yarjejeniya $A_k$ don sabon yanayi. Ƙwararrun nodes suna ƙoƙarin warware wasannin wuyar gaske $k$ masu zaman kansu a layi daya. An cimma yarjejeniya kan sabon yanayi bisa ga ƙofa na wasannin wuyar gaske da aka warware a cikin hanyar sadarwa. Daga nan sai a maimaita wannan ƙaramin ka'idar don samar da cikakkiyar ka'idar kwafin jiha, wanda ya gaji iyakokin kuskure na ainihi na matakin yarjejeniya.
Nazarin ya ɗauka cewa akwai hanyar sadarwa mai aiki tare tare da sanannen mafi munin jinkirin isar da saƙo $Δ$. Maƙiyin yana sarrafa wani ɓangare $β$ na jimlar ƙarfin lissafi. Samfurin yana la'akari da maƙiyin da zai iya karkata daga ka'idar da gaske amma an takura shi da rabonsa na lissafi da aikin tare na hanyar sadarwa.
Babbar gudummawar takarda tana cikin motsawa daga iyakokin tsaro na rashin iyaka zuwa na ainihi.
Marubutan sun ba da iyakoki na sama don mafi munin yuwuwar kasa (misali, keta daidaito). Yuwuwar cewa maharin zai iya yin sarkar caca ko kashe kuɗi sau biyu da nasara ana bayyana shi azaman aiki na maɓalli masu mahimmanci: adadin wasannin wuyar gaske a kowane toshe ($k$), ƙarfin dangi na maharin ($β$), jinkirin hanyar sadarwa ($Δ$), da ƙimar warware wasannin wuyar gaske na hanyar sadarwa mai gaskiya ($λ$). Iyaka yana ɗaukar siffa mai kama da iyakokin wutsiya a ka'idar yuwuwar, yana amfani da tsarin layi daya don ƙarfafa garanti sosai idan aka kwatanta da sarkar bi-da-bi.
Takardar tana ba da jagora mai amfani don zaɓar $k$ da tazarar toshe don rage yuwuwar kasa ga wani saiti na yanayin hanyar sadarwa ($Δ$, $β$). Wannan yana canza ƙirar ka'ida daga aikin ƙwararru zuwa matsalar ingantawa tare da maƙasudai masu ƙima.
Manufa: Daidaito bayan toshe 1 (saurin kammalawa).
Sigogi: $k=51$, $β=0.25$ (maharin 25%), $Δ=2s$.
Sakamako: Yuwuwar Kasa $≤ 2.2 \times 10^{-4}$.
Fassara: Maharin zai buƙaci ƙoƙarin dubban tubalan don nasara ɗaya ta haɗin kai.
An kimanta ginin da aka ba da shawara ta hanyar kwaikwayo da aka tsara don gwada ƙarfi. Kwaikwayon da gangan ya keta wasu ƙaƙƙarfan zato na ƙira (misali, cikakkiyar aiki tare) don tantance halayen ka'idar a cikin yanayin hanyar sadarwa mafi dacewa, "mai rikitarwa". Sakamakon ya nuna cewa ka'idar ta kasance mai ƙarfi ko da tare da ɓarna, yana nuna cewa iyakokin ka'idar sun kasance masu ra'ayin mazan jiya kuma ƙirar tana da juriya a aikace.
Babban kwatancen shine da ingantaccen saitin "Bitcoin mai sauri" (PoW na bi-da-bi tare da gajeriyar tazarar toshe) da ke nufin irin wannan jinkiri. Kamar yadda aka ambata daga Li et al. (AFT '21), irin wannan ka'idar bi-da-bi tana da yuwuwar kasa na ~9% a ƙarƙashin yanayi masu kama da ($β=0.25$, $Δ=2s$). Ka'idar PoW ta layi daya tana rage wannan da sama da oda biyu zuwa $2.2 \times 10^{-4}$, yana nuna mafi girman ikonta na samar da saurin kammalawa mai tsaro.
Hangar Mai Nazarin Masana'antu
Keller da Böhme ba kawai suna gyara Bitcoin ba; suna sake gina tushen aminci na blockchains na PoW da gaske. Fahimtar asali ita ce jinkirin tsaro (lokacin zuwa kammalawa) ba a haɗa shi da jinkirin samar da toshe ba. Ta hanyar sanya "aikin" a cikin toshe a layi daya, sun raba waɗannan masu canji biyu. Wannan ƙirar ce mafi zurfi fiye da ƙara girman toshe ko yawan maimaitawa kawai, saboda yana kai hari ga tushen kammalawa mai yuwuwa. Yana kama da motsawa daga na'ura mai aiki guda ɗaya, mai jinkiri, mai dogaro sosai zuwa jerin na'urori masu sauri, kaɗan kaɗan marasa dogaro, kuma ta amfani da hanyoyin zaɓe (ƙaramin ka'idar yarjejeniya $A_k$) don samun mafi girman dogaro da sauri—ra'ayi da ake gani a cikin tsarin lissafi masu juriya ga kuskure kamar RAID ko ƙungiyoyin Rashin Aiki na Byzantine (BFT), amma yanzu an yi amfani da su ga wasannin wuyar gaske na sirri.
Hankalin takarda yana da inganci daga ƙasa zuwa sama da tsaro na farko: 1) Gano Maɗaurin Rauni: Tsaron rashin iyaka bai isa ga kuɗin duniya na ainihi ba (yana ambaton aikin iyakoki na ainihi na Li et al. a matsayin mai haɓakawa). 2) Ware Maɗaukaki: Mayar da hankali kan ƙaramin ka'idar yarjejeniya, ba dukan sarkar ba. Wannan yana da wayo—yana rage rikitarwa. 3) Sake Injiniyan Maɗaukaki: Maye gurbin tseren wasa mai wuyar gaske guda ɗaya tare da yarjejeniyar ƙofa na wasannin wuyar gaske da yawa. 4) Ƙididdige Komai: Samun iyakoki na ainihi don wannan sabon maɗaukaki. 5) Haɗa Tsaro: Nuna cewa maimaita maɗaukakin tsaro yana haifar da sarkar tsaro. Wannan kwararar tana kama da ingantaccen injiniyan tsaro a wasu fagage, kamar tsarin tsaro mai tabbaci a cikin sirrin zamani (misali, aikin Shoup da Bellare-Rogaway akan hujjojin tsaro).
Ƙarfi: Iyakokin ainihi sun canza wasa don karɓar kamfani. CFOs yanzu suna iya duba tsaron blockchain kamar samfurin kuɗi. Lambobin aiki suna da jan hankali—yuwuwar kasa na $2.2 \times 10^{-4}$ vs. 9% ba ci gaba ne kawai ba; wani nau'in haɗari ne daban. Jagorar sigogi tana juya ƙirar ka'ida daga fasaha zuwa kimiyya.
Kurakurai & Gargaɗi: Zaton hanyar sadarwa mai aiki tare shine ƙashin dugadugansa. Duk da yake kwaikwayo sun nuna ƙarfi ga rashin aiki tare kaɗan, matsakaicin yanayi ya dogara da sanannen $Δ$. A duniyar gaske, jinkirin hanyar sadarwa yana canzawa kuma ana iya sarrafa su (misali, ta hanyar satar BGP). Ka'idar kuma tana ƙara rikitarwar sadarwa a kowane toshe da kashi $k$ (mafita don watsa shirye-shirye). Ga $k=51$, wannan ba ƙaramin abu bane. A ƙarshe, duk da yake yana rage kashe kuɗi sau biyu da kyau, nazarin da alama ya mai da hankali ne kan daidaito; wasu hare-haren kamar takunkumin ma'amala ko haƙar ma'adinai na son kai a cikin wannan samfurin na layi daya suna buƙatar zurfafa bincike.
Ga masu gine-ginen blockchain: Wannan takarda tana ba da tsarin gini don gina sarkoki na PoW masu tabbaci, masu saurin kammalawa don takamaiman aikace-aikace (misali, daidaita hukumomi, kadarorin wasa) inda za a iya iyakance yanayin hanyar sadarwa ko kuma a ba da wadatar su. Misalin $k=51$ shine farkon mataki, ba mafi kyawun duniya ba.
Ga masu zuba jari & masu nazari: Dubi kowane sarkar "PoW mai sauri" da ke da'awar saurin kammalawa tare da shakku sai dai idan ta ba da irin wannan iyakoki na ainihi. Wannan aikin ya kafa sabon ma'auni don da'awar tsaro.
Ga masu bincike: Babbar dama ita ce haɗa wannan hanya. Shin za mu iya haɗa iyakokin ainihi na PoW na layi daya tare da komawa zuwa yarjejeniyar jinkiri, mai tsaro ga rashin aiki tare (kamar sarkar PoW ta Chainweb ko yarjejeniyar Snowman) don magance katsewar hanyar sadarwa? Neman kammalawa mai ƙarfi, mai ƙima yanzu shine babban ƙalubale.
Nazarin tsaro ya dogara ne da ƙirar tsarin warware wasannin wuyar gaske na ƙwararrun nodes da maƙiyi a matsayin hanyoyin Poisson. Bari $λ$ ya zama jimlar ƙimar hash na hanyar sadarwa mai gaskiya, kuma $βλ$ ya zama ƙimar maƙiyi ($0 < β < 0.5$). A cikin ka'idar layi daya tare da wasannin wuyar gaske $k$, ƙimar hanyar sadarwa mai gaskiya don warware kowane wasa mai wuyar gaske ita ce $λ/k$.
Jigon iyaka ya ƙunshi lissafin yuwuwar cewa maƙiyin zai iya warware isassun wasannin wuyar gaske a asirce don ƙirƙirar sarkar gasa wanda zai zarce girman sarkar mai gaskiya a cikin wani taga na lokaci, wanda aiki ne na jinkirin hanyar sadarwa $Δ$. Tsarin layi daya yana ba da damar amfani da iyakokin nau'in Chernoff don rarraba binomial/Poisson don takura wannan yuwuwar da kyau. Yuwuwar kasa $ε$ don daidaito bayan toshe ɗaya an iyakance shi da magana kamar haka: $$ε \leq f(k, β, λΔ)$$ inda $f$ aiki ne wanda ke raguwa da ƙarfi ko sama da ƙarfi tare da $k$ don ƙayyadaddun $β$ da $λΔ$, yana bayyana babban ci gaba akan PoW na bi-da-bi.
Hali: Sarkar blockchain na ƙungiya don daidaita tsakanin bankuna tana buƙatar kammalar ma'amala a cikin mintuna 15 tare da yuwuwar gazawar tsaro kasa da $10^{-6}$ a kowane daidaitawa. Hanyar sadarwa tana da wadataccen wadata tare da matsakaicin aunannun jinkiri $Δ = 1.5$ seconds. Mahalarta sun kiyasta cewa maharin mai yuwuwa zai iya sarrafa har zuwa 30% na ƙarfin lissafi ($β=0.3$).
Aikace-aikacen Tsarin:
Aikace-aikace Nan da Nan: Ka'idar ta dace daidai don sarkoki na blockchain masu sarrafawa inda aikin tare na hanyar sadarwa zato ne mai ma'ana. Wannan ya haɗa da sarkoki masu zaman kansu/ƙungiya don daidaita kuɗi, asalin sarkar wadata, da bin diddigin kadarorin kamfani. Ikon sa na samar da saurin kammalawa mai ƙima babbar fa'ida ce akan PoW na gargajiya ko ma wasu tsarin Tabbatar da Hannun Jari da ke fuskantar hare-haren dogon zango.
Hanyoyin Bincike na Gaba: