Game da (Rashin) Tsaro na Blockchains na Dogon-Sarkar da ke Dogara akan Shaidar Sarari (PoSpace)

Table of Contents

1. Gabatarwa

Wannan aikin ya gabatar da sakamako na asali na rashin yiwuwar gina blockchains na dogon-sarkar masu tsaro waɗanda suka dogara kacokan akan Shaidar Sarari (PoSpace) a ƙarƙashin yanayin samuwa mai canzawa. Ya ƙididdige raunin ta hanyar ƙa'ida, yana nuna cewa maƙiyi koyaushe zai iya ƙirƙirar reshe mai nasara mai tsayin da aka iyakance, wanda ke buƙatar ƙarin zato na sirri kamar Ayyukan Jinkiri da za a iya Tabbatarwa (VDFs) don tsaro.

2. Bayanan Baya & Bayyana Matsala

2.1. Yarjejeniyar Nakamoto & Shaidar Aiki (PoW)

Tsaron Bitcoin ya dogara ne akan Shaidar Aiki (PoW) da dokar dogon-sarkar. Yana ba da garantin tsaro idan mutane masu gaskiya sun mallaki mafi yawan ƙarfin hashing, ko da a ƙarƙashin jimlar ƙarfi mai canzawa ("canjin albarkatu").

2.2. Shaidar Sarari (PoSpace) a matsayin Madadin Mai Dorewa

An gabatar da PoSpace a matsayin madadin mai dorewa ga PoW, inda masu haƙa ma'adinai ke ba da sararin ajiya maimakon lissafi. Duk da haka, tsaronsa a cikin yanayin da ba a ba da izini ba kuma mai canzawa, matsala ce da ba a warware ba.

2.3. Kalubalen Tsaro: Samuwa Mai Canzawa (Dynamic Availability)

Babban kalubalen shine "samuwa mai canzawa": sararin gaskiya na iya canzawa (matsakaicin $1 \pm \varepsilon$ a kowane block), kuma maƙiyan na iya "sake tsara" sararinsu (sake amfani da shi don ƙalubale da yawa) tare da farashin lokaci daidai da block $\rho$.

3. Tsarin Tsaro na Ƙa'ida & Sakamakon Rashin Yiwuwa

3.1. Ma'anar Wasa & Ƙarfin Maƙiyi

Wasan tsaro ya ɗauka cewa mutane masu gaskiya sun mallaki sarari $\phi > 1$ sau da yawa fiye da maƙiyi a kowane lokaci. Maƙiyin na iya:

• Canza sararin gaskiya da matsakaicin $1 \pm \varepsilon$ a kowane block.
• Sake tsara sarari tare da farashin lokaci na block $\rho$.

3.2. Ka'idar Ƙananan Iyaka (Lower Bound Theorem)

Ka'ida (Ƙananan Iyaka): Don kowace dokar zaɓin sarkar, a cikin wannan wasan, maƙiyi zai iya ƙirƙirar reshe mai tsayi $L$ wanda za a karɓa, inda:

$L \leq \phi^2 \cdot \rho / \varepsilon$

Wannan sakamako ne na rashin yiwuwa: ba za a iya ba da garantin tsaro daga reshe gajarta fiye da wannan iyaka ba.

3.3. Babban Iyaka (Mai Ban Mamaki) & Dokar Daidaitawa

Ka'ida (Babban Iyaka): Akwai (doka mai zaɓin sarkar da ba ta dace ba sosai) wacce ke buƙatar maƙiyi ya ƙirƙiri reshe mai tsayi aƙalla:

$L \geq \phi \cdot \rho / \varepsilon$

Wannan yana nuna ƙananan iyaka ya cika har zuwa matsakaicin $\phi$.

4. Cikakkun Bayanai na Fasaha & Tsarin Lissafi

Rashin yiwuwar ya samo asali ne daga ikon maƙiyin yin amfani da rashin daidaituwa tsakanin lokaci da sarari. Yayin da sararin gaskiya ke daure har tsawon lokacin ƙalubale, maƙiyin, ta hanyar tattara adadin sarari da aka ƙayyade da sake tsarawa, zai iya kwaikwayi ƙarin sarari na "kama-da-kai" a tsawon lokaci. Babban rashin daidaito da ke haifar da iyaka yana da alaƙa da ingantaccen albarkatun sarari-lokaci na maƙiyi $A_{eff}$, albarkatun sarari-lokaci na gaskiya $H_{eff}$, da tsayin reshe $L$:

$A_{eff} \approx \frac{L}{\rho} \cdot A \quad \text{da} \quad H_{eff} \approx \phi \cdot A \cdot \frac{L}{\varepsilon^{-1}}$

Yin amfani da waɗannan a ƙarƙashin ƙayyadaddun wasan yana kaiwa ga ƙarshen iyaka $L \approx \phi^2 \rho / \varepsilon$.

5. Sakamako & Tasiri

5.1. Babban Iyakar Tsaro

5.2. Bukatar Ƙarin Fasaloli (Misali, VDFs)

Sakamakon ya tabbatar da cewa PoSpace kadai bai isa ba. Ƙa'idodi kamar Chia daidai sun haɗa Ayyukan Jinkiri da za a iya Tabbatarwa (VDFs) don ƙara jinkiri na lokaci wanda ba za a iya aiwatarwa tare ba tsakanin block, yana rage hanyar harin sake tsarawa. Wannan yana tabbatar da zaɓin gine-ginen Chia daga mahangar ka'ida.

5.3. Nazarin Harka: Cibiyar Sadarwar Chia

Chia tana amfani da PoSpace + VDFs ("Shaidar Lokaci"). VDF ɗin yana tabbatar da mafi ƙarancin lokacin agogo tsakanin block, yana sa sigar $\rho$ ta zama babba sosai ga maƙiyin da ke ƙoƙarin ƙirƙirar madadin sarkar, ta haka yana ɗaga iyakar tsayin reshe a aikace zuwa matakan da ba za a iya aiwatarwa ba.

6. Tsarin Bincike & Misalin Harka

Tsarin don Kimanta Ƙa'idodin Dogon-Sarkar na PoX:

1. Gano Albarkatu: Ayyana ƙarancin albarkatu (Sarari, Lokaci, Lissafi).
2. Samfurin Canzawa: Ƙirƙirar samfurin canjin albarkatun gaskiya ($\varepsilon$) da sarrafa albarkatun maƙiyi (misali, farashin sake tsarawa $\rho$).
3. Binciken Hanyar Hari: Gano yadda maƙiyi zai iya canza wani albarkatu zuwa wani (sarari zuwa lokaci ta hanyar sake tsarawa).
4. Samun Iyaka: Ƙirƙirar rashin daidaito tsakanin samfurin albarkatu-lokaci na maƙiyi da na gaskiya don tsayin reshe $L$.
5. Binciken Gibin Fasaloli: Ƙayyade ko iyakar tana da tsaro a aikace. Idan ba haka ba, gano ƙarin fasalolin da ake buƙata (VDF, PoW, hannun jari).

Misalin Aikace-aikace: Kimanta sarkar "Shaidar Ajiya" na hasashe. Ƙayyade saurin sake sanya ajiya ($\rho$) da saurin canjin hannun jari ($\varepsilon$). Tsarin zai nuna saurin kamuwa da irin wannan harin "sake sanyawa" sai dai idan an ƙara makullin lokaci (VDF) ko tsarin yanke hukunci.

7. Ayyuka na Gaba & Hanyoyin Bincike

• Samfuran Yarjejeniya na Haɗakaɗɗu: Ƙirƙirar ƙa'idodin PoSpace+PoS ko PoSpace+PoW na haɗakaɗɗu don cimma tsaro ba tare da wuce gona da iri ba.
• Ƙirƙirar VDFs Ƙarfafaɗɗu: Bincike a cikin ƙirƙirar VDFs masu inganci ko rarraba don rage wuce gona da iri na ƙara garantin lokaci.
• Tabbatarwa ta Ƙa'ida: Yin amfani da wannan samfurin ga sauran tsarin "shaida-na-X" (Shaidar Aiki Mai Amfani, Shaidar Aikin Jiki) don hana lahani na tsaro.
• La'akari da Bayan Quantum: Bincika ƙirƙirar da ke dogara akan PoSpace waɗanda suka kasance masu tsaro a zamanin lissafi bayan quantum, inda VDFs da ke dogara akan murabba'i na jeri na iya zama masu rauni.

8. Nassoshi

1. Nakamoto, S. (2008). Bitcoin: Tsarin Kuɗin Lantarki na Tsakanin Mutane.
2. Dziembowski, S., Faust, S., Kolmogorov, V., & Pietrzak, K. (2015). Shaidar Sarari. CRYPTO 2015.
3. Cohen, B., & Pietrzak, K. (2018). Cibiyar Sadarwar Blockchain na Chia. https://www.chia.net/assets/ChiaGreenPaper.pdf
4. Boneh, D., Bonneau, J., Bünz, B., & Fisch, B. (2018). Ayyukan Jinkiri da za a iya Tabbatarwa. CRYPTO 2018.
5. Garay, J., Kiayias, A., & Leonardos, N. (2015). Ƙa'idar Gindi na Bitcoin: Bincike da Aikace-aikace. EUROCRYPT 2015.
6. Pass, R., & Shi, E. (2017). FruitChains: Blockchain Mai Adalci. PODC 2017.

9. Binciken Kwararru & Sharhi Mai Muhimmanci

Babban Fahimta

Wannan takarda ta gabatar da harbi mai kyau da lalata ga mafarkin "Bitcoin kore" wanda aka gina shi kacokan akan Shaidar Sarari (PoSpace). Ba hari ne kawai akan wata ƙa'ida ta musamman ba; hujja ce ta asali game da alaƙar tsakanin sarari, lokaci, da tsaro a cikin yarjejeniyar da ba ta da cibiya. Babban fahimtar shine cewa sarari, ba kamar lissafi a cikin PoW ba, ba a "kone" shi a asalinsa. Maƙiyin na iya sake yin amfani da shi. Wannan ikon sake yin amfani, a ƙarƙashin shiga cikin aiki mai canzawa, yana haifar da madauki na ciniki na mutuwa wanda kowace dokar dogon-sarkar ba za ta iya karewa da shi ba. Ta bayyana a ƙa'ida dalilin da yasa ayyuka kamar Chia dole su haɗa Aiki na Jinkiri da za a iya Tabbatarwa (VDF) - ba zaɓi ne na ingantawa ba amma larura ta ka'ida.

Matsalar Hankali

Hankalin marubutan ba shi da lahani kuma yana bin tsarin hujjar rashin yiwuwa na gargajiya: 1) Ayyana samfurin maƙiyi na gaske ($\phi$, $\varepsilon$, $\rho$) wanda ya ɗauki ƙayyadaddun duniya na ajiya (lokacin sake tsarawa) da canjin cibiyar sadarwa. 2) Nuna cewa a cikin wannan samfurin, don kowace dokar da za a iya tunani don zaɓar tsakanin sarkoki, maƙiyin da ke da ƙarancin sarari koyaushe zai iya wuce mutane masu gaskiya a kan reshe mai tsayi isa, amma an iyakance. 3) Iyakar $L \leq \phi^2 \rho / \varepsilon$ ita ce bindigar hayaƙi. Tana ƙididdige rashin tsaro. Bayanan da ke biye da nuna babban iyaka mai kusan daidaitawa tare da doka "mai ban mamaki" shine ƙusa na ƙarshe, yana tabbatar da cewa iyaka ya cika kuma raunin yana cikin albarkatu, ba ƙirar doka ba.

Ƙarfi & Kurakurai

Ƙarfi: Sigogin samfurin ($\rho$ don sake tsarawa, $\varepsilon$ don canzawa) an zaɓe su da wayo, suna ɗaukar mahimman ilimin kimiyyar lissafi na matsalar. Sakamakon yana da tsabta, gabaɗaya, kuma nan da nan za a iya aiwatarwa. Yana ɗaga tattaunawar daga "shin wannan ƙa'idar tana da tsaro?" zuwa "menene mafi ƙarancin ƙarin zato da ake buƙata don tsaro?".

Kurakurai/Iyakoki: Samfurin yana ɗauka cewa mafi rinjaye na gaskiya mara aiki wanda baya daidaita dabarunsa bisa ga gano reshe - zato na yau da kullun amma wani lokaci yana iyakancewa a cikin binciken dogon-sarkar. Mafi mahimmanci, yayin da yake tabbatar da wajibcin ƙarin fasaloli kamar VDF, bai ƙididdige sigogin wadatar na wannan VDF ba (nawa ne jinkiri ya isa?). Wannan yana barin gibi tsakanin ka'ida da aiki. Ƙari ga haka, dokar zaɓin sarkar "mai ban mamaki" wacce ta kusan dace da iyaka abin sha'awa ne na sirri amma ba ta da amfani a aikace, yana nuna zurfin matsalar.

Fahimta Mai Aiki

Ga masu ƙirƙirar ƙa'ida: Daina ƙoƙarin gina ƙa'idodin dogon-sarkar na PoSpace mai tsabta. Wannan takarda ita ce sanarwar dakatar da ku ta ƙa'ida. Hanyar da za a iya aiwatarwa ita ce ta hanyar haɗakaɗɗu kawai.

1. Jinkiri na Wajibi (Hanyar VDF): Bi jagorar Chia. Haɗa VDF don sanya $\rho$ ya zama babba sosai ga maharin, yana tura iyakar tsayin reshe fiye da yadda za a iya aiwatarwa. Bincike ya kamata ya mayar da hankali kan sanya VDFs su zama masu inganci da rarraba.
2. Bincika Tsarin da ba na Dogon-Sarkar ba: Yi la'akari da madadin iyalai na yarjejeniya kamar Shaidar Hannun Jari (PoS) tare da kayan aikin ƙarshe (misali, Casper FFG) ko ƙa'idodin BFT na kwamiti. Waɗannan na iya haɗa PoSpace daban-daban, yana yuwuwar guje wa wannan hanyar hari gaba ɗaya. Aikin da Gidauniyar Ethereum ta yi akan haɗa VDFs tare da PoS don bazuwar (RANDAO+VDF) yana nuna fa'idodin waɗannan fasalolin.
3. Ƙaƙƙarfan Sigogi: Idan kuna gina haɗakaɗɗu, yi amfani da tsarin wannan takarda. A bayyane yake ƙirƙirar samfurin cinikin sarari-lokaci na maƙiyinku, ayyana $\varepsilon$ na cibiyar sadarwar ku, kuma yi amfani da iyakar da aka samo don gwada ƙirar ku. Wannan ba ilimi kawai bane; shi ne tsarin tsaron ku.

A ƙarshe, Baig da Pietrzak ba kawai sun warware matsala da ba a buɗe ba; sun zana layi ja mai haske a cikin yashi na ka'idar yarjejeniya. Sun motsa fagen daga injiniyanci mai bege zuwa ilimin kimiyyar lissafi mai ƙarfi, suna ayyana abin da ba zai yiwu ba kuma ta haka suna haskaka hanyar kunkuntar zuwa ga abin da zai yiwu. Wannan aiki ne na asali wanda zai ceci ayyuka masu yawa na gaba daga gine-ginen ƙarshen matattu.