Bitcoin: Tsamaiso ea Chelete ea Marang rang e Sebetsang Pakeng tsa Batho ka Bobona.”

E ngotsoe ke Satoshi Nakamoto 31 Mphalane 2008

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Abstract

Bitcoin ke mofuta oa chelete e sa bonahaleng, empa e sebetsang ka marang-rang, oo batho ba ka o sebelisang ho lefa kapa ho amohela tefo ka kotloloho ho tloha ho motho e mong ho ea ho e mong — ntle le banka kapa mokhatlo oa dichelete bohareng. Ha motho a romela Bitcoin, sistimi e sebelisa matshwao a dijithale ho netefatsa hore ke eena ka ’nete ea romellang. Ho na le tsela e ikhetang e bitsoang Pontsho ea mosebetsi, e fanang ka tsela ea ho netefatsa hore phetiso e 'ngoe le e'ngoe e nepile. 'me ha ho motho ea ka qhekellang ka ho sebedisa chelete e le'ngoe habedi. Ho e-na le hore banka e netefatse ditšebedisano, Bitcoin e sebedisa marang-rang a batho ba hokahaneng. Batho bana bohle ba nang le khomphutha e hokahaneng marang-rang a Bitcoin ba thusa ho boloka direkoto tsa ditshebelisano. Ketane eo e telele e bontša hore litšebelisano tsohle li etsahetse hantle, ’me hore batho ba sebelisitseng matla a lik’homphieutha ba entse mosebetsi o nepahetseng. Ha feela batho ba bangata ba sebelisang marang-rang ana ba sa batle ho a senya, ketane ena e lula e le matla ’me e sireletsehile. Sistimi ena ha e hloke sebopeho se rarahaneng — melaetsa e romelloa ho mang kapa mang ea hokahaneng, ’me motho a ka kena kapa a tsoa neng kapa neng. Ha a khutla, o fumana ketane e telele ka ho fetisisa, e bontšang hore na se etsahetseng ha a ne a le sieo.

Selelekela

Khoebo ea inthaneteng e se e itshetlehile haholo ka mekhatlo ea lichelete e sebetsang e le batho ba boraro ba tšeptjoang ho tsamaisa litefo tsa marang rang. Le hoja tsamaiso ena e sebetsa hantle maemong a mangata, e ntse e e-na le bofokoli bo tlisoang ke hore e ipapisitse le tshepo. Ho ke ke ha khoneha ho etsa litshebelisano tse ke keng tsa khutliswa ka botlalo, hobane mekhatlo ea lichelete e tlameha ho kenella ha ho ka hlaha likhohlano. Ho kenella hona ho eketsa litshenyehelo, ho etsa hore litshebelisano tse nyenyane li be thata kapa li se ke tsa khoneha, ’me ho senya monyetla oa hore ho ka etsoa litefo tse nyane kapa tse bonolo. Hape, ho lahleheloa ke bokhoni ba ho etsa litefo tse ke keng tsa khutliswa bakeng sa lits'ebeletso tse ke keng tsa fetoloa ho hlahisa litshenyehelo tse pharaletseng. Ha litefo li ka khutlisoa, tlhoko ea tshepo e eketseha. Barekisi ba tlameha ho ba hlokolosi ka bareki ba bona, ’me hangata ba ba kopa tlhahisoleseling e ngata ho feta kamoo ho hlokahalang. Le ha ho le joalo, palo e itseng ea bomenemene e nkoa e le ntho e ke keng ea qojoa. Litshenyehelo tsena le ho se tsitse ha litefo li ka qojoa ha batho ba sebelisana ka chelete ea 'nete, empa ha ho na mokhoa o lumellang hore litefo li etsoe ka marang-rang ntle le motho oa boraro ea tsheptjoang.

Seo se hlokahalang ke tsamaiso ea tefo ea elektroniki e thehiloeng bopaking ba mahlale a lekunutu (cryptographic proof), eseng tshepo. Tsamaiso ena e tla dumella batho ba babeli ba ikemetseng ho etsa tefo ka kotloloho pakeng tsa bona, ntle le ho sebelisa motho oa boraro ea tshepahalang. Litefo tse ke keng tsa khutlisoa habonolo ka khomputara li tla sireletsa barekisi khahlanong le boshodu. Ka nako e tshwanang, ho ka sebedisoa mokhoa o tloaelehileng oa escrow ho sireletsa bareki, ho etsa bonnete ba hore tefo e etsoa ka mokhoa o sireletsehileng le o hlakileng. Ka pampiri ena, re fana ka tharollo bakeng sa bothata ba ho sebedisa chelete habedi, ka ho sebedisa seva sa nako se ajoang pakeng tsa batho (peer-to-peer distributed timestamp server). Sena se thusa ho etsa bopaki ba khomputara bo bontshang tatellano e nepahetseng ea litefo ka nako. Tsamaiso ena e bolokehile ha feela likhomphutha tse tšepahalang li sebedisa matla a mangata a CPU ho feta sehlopha leha e le sefe sa likhomphutha tse kopaneng tse lekang ho e hlasela.

litshebelisano

Re hlalosa chelete ea elektroniki e le ketane ea Tshoaetso tsa dijithale. Mong’a chelete o fetisetsa chelete ho ea mong’a e latelang ka tshoaetso ea dijithale hash ea tšebelisano e fetileng hammoho le senotlolo sa sechaba (public key) sa emong’a mocha, ebe o li kenya qetellong ea ketane ea chelete. Motho ea amohelang tefo (payee) a ka netefatsa lipontšo tsena tsa dijithale ho tiisa hore ketane ea beng ba chelete e nepahetse ebile e tsamaile ka tatellano e nepahetseng.

Bothata, ehlile, ke hore motho ea amohelang tefo ha a khone ho netefatsa hore mong’a chelete eo ha aa ka a sebelisa chelete eo habeli. Tharollo e tloaelehileng ke ho kenya mokhatlo o bohareng o tshepahalang, kapa sebaka se bitsoang mint, se hlahlobang litshebelisano tsohle ho bona hore ha ho na chelete e sebelisoang habeli. Ka mor’a tshebelisano e ’ngoe le e ’ngoe, chelete e tlameha ho khutlisetsoa ho mint hore ho hlahisoe chelete e ncha, ’me feela chelete e tsoang ka kotloloho ho mint e nkoa e le e tshepahalang hore ha e sebelisoe habeli. Bothata ba tharollo ena ke hore tsamaiso eohle ea chelete e itshetlehile ka khampani e tsamaisang mint eo, kaha litshebelisano tsohle li tlameha ho feta ho bona — joalo ka ha ho sebetsa banka.

Re hloka mokhoa oo motho ea amohelang tefo a ka netefatsang hore beng ba pele ha baa ka ba saena litshebelisano tse ling pele. Tabeng ena, tshebelisano ea pele ke eona e nkoang e le ea bohlokoa, kahoo ha re tsotelle boiteko ba morao ba ho sebelisa chelete habeli (double-spend). Tsela feela ea ho tiisa hore ha ho na tshebelisano e ’ngoe e patiloeng ke ho tseba ka litshebelisano tsohle. Mokhoeng oa khale oa mint, sebaka seo se ne se tseba ka litshebelisano tsohle ’me se etsa qeto ea hore na ke efe e fihlileng pele. Ho etsa sena ntle le motho oa boraro ea tshepahalang, litshebelisano li tlameha ho phatlalatsoa hore bohle ba li bone, ’me ho hlokahala tsamaiso e lumellang barupeluoa ho lumellana ka histori e le ’ngoe ea hore na litshebelisano li amohetsoe ka tatellano efe. Motho ea amohelang tefo o hloka bopaki ba hore ka nako eo tšebelisano e etsahalang, boholo ba nodes (likhomphutha tse hokahaneng marang-rang) bo ne bo lumellana hore ke eona e fihlileng pele.

Seva ea setempe sa nako

Tharollo eo re e sisinyang e qala ka seva sa nako (timestamp server). Seva sa nako se sebetsa ka ho nka hash ea blokhi ea lintho tse tla fuoa nako ea tsona (timestamp) le ho phatlalatsa hash eo haholo, joalo ka ka koranta kapa poso ho Usenet[2-5]. Nako e bontša hore data e tlameha ebe e e ntse e le teng ka nako eo, ho hlakile, e le hore e ka kenella ho hash. Nako e ’ngoe le e ’ngoe e kenyelletsa nako e fetileng ho hash ea eona, e theha ketane, moo nako e ’ngoe le e ’ngoe e ekelitsoeng e matlafatsang tseo tse fetileng.

Bopaki ba Mosebetsi

Ho sebelisa seva sa nako se arolelletsoeng ka mokhoa oa peer-to-peer, re tla sebelisa tsamaiso ea bopaki-ba-mosebetsi (proof-of-work) e tshoanang le Hashcash ea Adam Back[6], eseng ka koranta kapa liposo tsa Usenet. Tsamaiso ena e sebetsa ka ho batla palo e khethiloeng eo, ha e hash-oa (joalo ka SHA-256), hash e qalang ka li-zero bits tse itseng. Boholo ba mosebetsi o hlokahalang bo eketseha ka palo ea li-zero bits, ’me ho netefatsa hore mosebetsi o entsoe u ka etsa hash e le ’ngoe feela.

Bakeng sa marang-rang a rona a nako, re kenya tshebetsong bopaki-ba-mosebetsi (proof-of-work) ka ho eketsa nonce ka blokeng ho fihlela ho fumanoa boleng bo fanang ka li-zero bits tse hlokahalang ho hash ea blokeng. Ha CPU e se e entse mosebetsi oo ho fihlela e khotsofatsa bopaki-ba-mosebetsi, blokeng ha e sa ka ea fetoloa ntle le ho pheta mosebetsi oo. Ha li-block tse latelang li hokeloa ka mor’a eona, mosebetsi oa ho fetola blokeng o tla kenyelletsa ho pheta mosebetsi oa li-block tsohle tse latelang ka mor’a eona.

Bopaki-ba-mosebetsi bo thusa ho rarolla bothata ba ho tseba ke mang ea nang le boemeli bo boholo ha liqeto li etsoa. Haeba boemeli bo ne bo itshetlehile ka IP e le ’ngoe – votu e le ’ngoe, mang kapa mang ea ka abelang li-IP tse ngata a ka fetoha molao. Bopaki-ba-mosebetsi bo sebetsa joaloka CPU e le ’ngoe – votu e le ’ngoe. Ketane e telele ka ho fetisisa e bontsha qeto ea boholo-holo hobane e na le mosebetsi o moholo ka ho fetisisa oa bopaki-ba-mosebetsi. Haeba boholo-holo ba matla a CPU bo laoloa ke li-node tse tshepahalang, ketane e tshepahalang e hōla kapele ’me e feta liketane tse ling tsohle. Ha mohanyetsi a batla ho fetola blokeng ea khale, o tla tlameha ho pheta mosebetsi oa blokeng eo le oa li-block tsohle tse latelang, ebe a tlisa mosebetsi oa li-node tse tshepahalang. Ha li-block tse ling li ntse li eketsoa, monyetla oa hore mohanyetsi a fihle ka morao o fokotseha haholo.

Ho leka ho leka-lekanya lebelo le eketsehang la lisebelisoa le thahasello e fapaneng ea ho tsamaisa li-node ka nako, bothata ba bopaki-ba-mosebetsi bo khethoa ka karolelano e tsamaeang, e shebiloeng ho fumana palo e tloaelehileng ea li-block ka hora. Ha li hlahisoa ka potlako haholo, bothata bo eketseha.

Marang-rang

Mekhoa ea ho tsamaisa marang-rang e latelang ke ena:

1. Litshebelisano tse ncha li phatlalatsoa ho li-node tsohle.
2. Node e ’ngoe le e ’ngoe e bokella litshebelisano tse ncha ka har’a blokeng.
3. Node e ’ngoe le e ’ngoe e sebetsa ho fumana bopaki-ba-mosebetsi bo thata bakeng sa blokeng ea eona.
4. Ha node e fumana bopaki-ba-mosebetsi, e phatlalatsa blokeng ho li-node tsohle.
5. Li-node li amohela blokeng feela haeba litshebelisano tsohle ka har’a eona li nepahetse ’me li sa sebelisoe pele.
6. Li-node li bontsha hore li amohetse blokeng ka ho sebetsa ho etsa blokeng e latelang ketaneng, li sebelisa hash ea blokeng e amohetsoeng e le hash ea pele.

Li-node kamehla li nka ketane e telele ka ho fetisisa e le ’nete. Ha li-node tse peli li phatlalatsa li-block tse fapaneng ka nako e le ’ngoe, tse ling li ka amohela e ’ngoe pele. Li sebetsa ho blokeng eo li e amohetseng qalong, empa li boloka e ’ngoe ka morao haeba e ka hōla ho feta. Ha bopaki-ba-mosebetsi bo latelang bo fumanoa, lekala le leng le hōla ho feta, ’me li-node tsohle li fetela ho lekala le lelelele, li tsoelapele ho haha ketane e kholo.

Litshebelisano tse ncha ha lia tlameha ho fihla ho li-node tsohle hang-hang. Ha feela li fihla ho li-node tse ngata, li tla kena ka har’a blokeng haufinyane. Ho phatlalatsa li-block ho boetse ho mamella melaetsa e lahlehileng. Haeba node e sa amohele blokeng, e tla e kopa ha e amohela blokeng e latelang ’me e hlokomela hore e ile ea fosa blokeng e ’ngoe.

khothatso

Ka tloaelo, tshebelisano ea pele ka har’a blokeng ke tshebelisano e ikhethang e qalang chelete e ncha e seng ea motho ea e entseng. Sena se fa li-node khothatso ea ho tshehetsa marang-rang, ’me se fana ka tsela ea ho abela chelete pele e kenella tshebedisong, kaha ha ho na puso e kholo e e hlahisang. Ho eketsoa ha chelete e ncha ka mokhoa o tsitsitseng ho tshwana le ho kuta khauta moo balemi ba khauta ba sebelisang lisebelisoa ho eketsa khauta tshebedisong. Tabeng ea rona, ke nako ea CPU le motlakase o sebelisoang.

Khothatso e ka fuoa chelete hape ka litefiso tsa litshebelisano. Ha boleng ba tsoelo-pele ea tshebelisano bo le tlase ho boleng ba eona bo kenang, phapang eo ke tefiso ea tshebelisano e eketsoang khothatsong ea blokeng e nang le tshebelisano eo. Ha palo e itseng ea li-coin e se e kenile tshebedisong, khothatso e ka fetoha ka botlalo hore e be litefiso tsa litshebelisano feela ’me e se na tshusumetso ea ho eketsa chelete.

Khothatso e ka thusa ho khothaletsa li-node ho lula li tshepahala. Haeba mohanyetsi ea hlohlorang a khona ho bokella matla a CPU a fetang a li-node tsohle tse tshepahalang, o tla tlameha ho khetha pakeng tsa ho sebelisa matla ao ho utsisa batho ka ho khutlisa litefo tsa hae, kapa ho a sebelisa ho hlahisa li-coin tse ncha. Ho molemo ho hae ho bapala ka melao, hobane melao e mo fa li-coin tse ncha tse ngata ho feta tseo bohle ba li kopantseng, ho feta ho senya tsamaiso le ho lahleheloa ke chelete ea hae.

Ho fumana sebaka se setseng ho disk

Hang ha tshebelisano ea morao-rao ka har’a chelete e se e koahetsoe ke li-block tse ngata, litshebelisano tse sebelisitsoeng pele li ka lahleloa ho boloka sebaka sa disk. Ho etsa sena ntle le ho senya hash ea blokeng, litshebelisano li hash-oa ka har’a Merkle Tree [7][2][5], ’me feela motso o kenngoa ho hash ea blokeng. Li-block tse khale li ka fokotsoa ka ho khaola makala a sefate. Li-hash tse ka hare ha lia hlokahala hore li bolokehe.

Hore blokeng e be le hlooho feela ntle le litshebelisano, e ka ba ka boholo ba 80 bytes. Haeba re nahana hore li-block li hlahisoa nako e ’ngoe le e ’ngoe metsotso e 10, 80 bytes * 6 * 24 * 365 = 4.2MB ka selemo. Ka sistimi tsa khomphutha tse tloaelehileng tse rekisoang ka 2GB RAM ho tloha ka 2008, le Molao oa Moore o hakanya kholo ea 1.2GB ka selemo, polokelo ha e lokela ho ba bothata leha hlooho tsa li-block li bolokoa ka memori.

Netefatso e Nolofalitsoeng ea Tefo

Ho ka khoneha ho netefatsa litefo ntle le ho tsamaisa node e felletseng ea marang-rang. Mo sebelisa feela o hloka ho boloka kopi ea hlooho tsa li-block tsa ketane e telele ka ho fetisisa ea bopaki-ba-mosebetsi, eo a ka e fumanang ka ho botsa li-node tsa marang-rang ho fihlela a kholisehile hore o na le ketane e telele. O boetse o fumana lekala la Merkle le hokahanyang tshebelisano le blokeng eo e fanoeng ka nako. Ha a khone ho hlahloba tshebelisano ka boeena, empa ka ho e hokahanya le sebaka ka har’a ketane, o bona hore node ea marang-rang e e amohetse, ’me li-block tse latelang li netefatsa hore marang-rang a e amohetse.

Ka hona, ho netefatsa litefo ho tshepahala haeba li-node tse tshepahalang li laola marang-rang, empa ho ka ba bonolo ho kenngoa kotsi haeba mohanyetsi a matla ho feta marang-rang. Ha li-node tsa marang-rang li ka hlahloba litshebelisano ka bo tsona, mokhoa o bonolo o ka hlokomolisoa ke litshebelisano tse entsoeng ke mohanyetsi ho fihlela a sa ntse a matla ho feta marang-rang. Leano le le leng la ho itšireletsa ke ho amohela tsebiso ho li-node tsa marang-rang ha li bona blokeng e fosahetseng, e lebisang software ea mosebelisi ho jarolla blokeng e felletseng le litshebelisano tse tsebisitsoeng ho netefatsa hore ho na le phoso. Likhoebo tse amohelang litefo khafetsa li tla ntse li batla ho tsamaisa li-node tsa tsona bakeng sa polokeho e ikemetseng le netefatso e potlakileng.

Ho Kopanya le ho Arola Boleng

Le hoja ho ka khoneha ho sebetsana le li-coin ka ’ngoe, ho ne ho tla ba bothata ho etsa tshebelisano e ikemetseng bakeng sa sente e ’ngoe le e ’ngoe ea phetisetso. Ho lumella boleng ho aroloa le ho kopanngoa, litshebelisano li na le mehloli le liphello tse ngata. Ka tloaelo, ho tla ba le mohloli o le mong ho tsoa tshebelisanong e kholo e fetileng, kapa mehloli e mengata e kopanyang litefiso tse nyane, ’me hangata ho tla ba le liphello tse peli feela: e le ’ngoe bakeng sa tefo, le e ’ngoe e khutlisang chelete e setseng, haeba e le teng, ho romelli.

Ho lokela ho hlokomeloa hore “fan-out,” moo tshebelisano e itshetlehileng ka litshebelisano tse ngata, ’me litshebelisano tseo li itshetlehileng ka tse ling tse ngata haholo, ha se bothata mona. Ha ho na tlhoko ea ho fumana kopi e felletseng ea nalane ea tshebelisano ka bo eona.

Lekunutu

Mokhoa oa banka oa setso o boloka leeme ka ho lekanya boitsebiso feela ho batho ba amehang le motho oa boraro ea tshepahalang. Ho tlaleha litshebelisano tsohle ka ho phatlalatsa ho thibela mokhoa ona, empa boitsebiso bo ka bolokoa ka ho thibela phallo ea tlhaiso-leseling sebakeng se seng: ka ho boloka linotlolo tsa sechaba li sa tsejoe. Batho ba ka bona hore motho o romela chelete ho motho e mong, empa ntle le tlhaiso-leseling e hokahanyang tshebelisano le mang kapa mang. Sena se tshwana le boitsebiso bo hlahisoang ke li-stock exchange, moo nako le boholo ba khoebo e ’ngoe le e ’ngoe, e bitsoang “tape”, e phatlalatsoang, empa ntle le ho bua hore ke mang batho ba amehang.

E le sesebelisoa se eketsehileng sa tshireletso, setlhopha se secha sa linotlolo se lokela ho sebelisoa ho tshebelisano e ’ngoe le e ’ngoe ho thibela hore li hokahanye le mong’a tsona ea tshwanang. Leha ho le joalo, ho ka ’na ha hlahella ho hokahana ka litshebelisano tse nang le mehloli e mengata, hobane ho bontsha hore mehloli eohle e ne e le ea mong’a e le ’ngoe. Kotsi ke hore haeba mong’a senotlolo a senoloa, ho hokahana ho ka bontsha litshebelisano tse ling tse neng li le tsa mong’a o tshwanang.

Lipalo

Re nahana ka boemo boo mohanyetsi a lekang ho hlahisa ketane e fapaneng kapele ho feta ketane e tshepahalang. Le hoja sena se ka khoneha, ha se folele tsamaiso hore e lumelle liphetoho tse sa laoleheng, joalo ka ho hlahisa chelete e sa teng kapa ho nka chelete e seng ea mohanyetsi. Li-node ha li tla amohela tshebelisano e fosahetseng e le tefo, ’me li-node tse tshepahalang ha li tla amohela blokeng e nang le tsona. Mohanyetsi a ka leka feela ho fetola e ’ngoe ea litshebelisano tsa hae ho khutlisa chelete eo a e sebelisitseng morao tjena.

Mokete pakeng tsa ketane e tshpahalang le ketane ea mohanyetsi o ka hlalosoa e le Binomial Random Walk. Tshebeliso e atlehileng ke ha ketane e tshepahalang e atolosoa ka blokeng e le ’ngoe, e eketsang phapang ka +1, ’me tshebeliso e hlolehileng ke ha ketane ea mohanyetsi e atolosoa ka blokeng e le ’ngoe, e fokotsang phapang ka -1.

Monyetla oa mohanyetsi oa ho fihlela ketane e tshepahalang ha a qala a le ka morao o tshwana le bothata ba “Gambler's Ruin”. Nahana ka sebapali sa lipapali se nang le mokoloto o sa lekanyetsoang se qalang se le ka morao ’me se bapala liteko tse sa lekanyetsoang ho leka ho fihlela tekano. Re ka bala monyetla oa hore a ka fihlela tekano, kapa hore mohanyetsi a ka lula a latela ketane e tshepahalang, ka tsela e latelang[8]:

$$\begin{array}{rcl}p& =& \text{ probability an honest node finds the next block}\\ q& =& \text{ probability the attacker finds the next block}\\ q_z& =& \text{ probability the attacker will ever catch up from }z\text{ blocks behind}\end{array}$$$$q_z=\left\{\begin{array}{cc}1& \mathit{\text{if}}p\le q\\ (q/p{)}^z& \mathit{\text{if}}p>q\end{array}\right\}$$

Ho latela maikutlo a rona a joalo

$p>q$

, Monyetla oa mohanyetsi o theoha ka potlako ha palo ea li-block tseo a tlamehang ho li latela e ntse e eketseha. Ka maemo a khahlano le eena, haeba a sa atlehe ho tsamaea ka lehlohonolo qalong, menyetla ea hae e tla fokola haholo ha a ntse a qeta ho siea ka morao.

Joale re nahana hore na moamoheli oa tshebelisano e ncha o lokela ho emela nako e kae pele a kholiseha hore mo romellang ha a ka fetola tshebelisano. Re nka hore mo romellang ke mohanyetsi ea batlang ho etsa moamoheli a nahane hore o se a lefa, ebe ka mora nako a fetola tshebelisano hore a khutlisetse chelete ho eena. Moamoheli o tla tsebisoa ha sena se etsahala, empa mo romellang o tshepa hore ho tla se be teng nako e nepahetseng.

Moamoheli o hlahisa setlhopha se secha sa linotlolo ’me a fa a mo romellang senotlolo sa sechaba hanyane pele a saena. Sena se thibela mo romellang ho lokisetsa ketane ea li-block pele ka ho sebetsa ho eona ka mokhoa o tsoelang pele ho fihlela a le lehlohonolo a feta pele, ebe a phetha tshebelisano ka nako eo. Hang ha tshebelisano e romelloa, mo romellang ea sa tshepahaleng o qala ho sebetsa ka botsebi ho ketane e tshwanang e nang le mofuta o fapaneng oa tshebelisano ea hae.

Moamoheli o emela ho fihlela tshebelisano e se e kentsoe ka har’a blokeng ’me li-block tse z li hokahantsoe kamora eona. Ha a tsebe hantle hore na mohanyetsi o fihletse kae, empa haeba re nka hore li-block tse tshepahalang li nkile nako e tloaelehileng ka blokeng, tsoelo-pele e ka bang teng ea mohanyetsi e tla latela phallo ea Poisson ka boleng bo lebeletsoeng:

$$\lambda =z\frac{q}{p}$$

Ho fumana monyetla oa hore mohanyetsi a ka ntse a fihla hona joale, re eketsa khatello ea Poisson bakeng sa boholo bo fapaneng ba tsoelo-pele eo a ka e entseng ka monyetla oa hore a ka fihla ho tloha moo:

$$\sum _{k=0}^{\mathrm{\infty }}\frac{{\lambda }^k{e}^{-\lambda }}{k!}\cdot \left\{\begin{array}{cc}(q/p{)}^{(z-k)}& \mathit{\text{if}}k\le z\\ 1& \mathit{\text{if}}k>z\end{array}\right\}$$

Ho hlophisa hape ho qoba ho bokella karolo e sa feleng ea phallo ea monyetla…

$$1-\sum _{k=0}^z\frac{{\lambda }^k{e}^{-\lambda }}{k!}\left(1-(q/p{)}^{(z-k)}\right)$$

E fetolela ho khoutu ea C..

#include 
double AttackerSuccessProbability(double q, int z)
{
	double p = 1.0 - q;
	double lambda = z * (q / p);
	double sum = 1.0;
	int i, k;
	for (k = 0; k <= z; k++)
	{
		double poisson = exp(-lambda);
		for (i = 1; i <= k; i++)
			poisson *= lambda / i;
		sum -= poisson * (1 - pow(q / p, z - k));
	}
	return sum;
}

Ha re sebelisa liphetho tse ling, re ka bona monyetla o theoha haholo ka z.

q=0.1
z=0    P=1.0000000
z=1    P=0.2045873
z=2    P=0.0509779
z=3    P=0.0131722
z=4    P=0.0034552
z=5    P=0.0009137
z=6    P=0.0002428
z=7    P=0.0000647
z=8    P=0.0000173
z=9    P=0.0000046
z=10   P=0.0000012

q=0.3
z=0    P=1.0000000
z=5    P=0.1773523
z=10   P=0.0416605
z=15   P=0.0101008
z=20   P=0.0024804
z=25   P=0.0006132
z=30   P=0.0001522
z=35   P=0.0000379
z=40   P=0.0000095
z=45   P=0.0000024
z=50   P=0.0000006

Ho rarolla P ka tlase ho 0.1%.

P < 0.001
q=0.10   z=5
q=0.15   z=8
q=0.20   z=11
q=0.25   z=15
q=0.30   z=24
q=0.35   z=41
q=0.40   z=89
q=0.45   z=340

Qetello

Re hlahisitse tsamaiso ea litshebelisano tsa elektroniki ntle le ho itshetleha ka tshepo. Re qala ka moelelo oa setso oa li-coin tse entsoeng ka li-signature tsa dijithale, tse fanang ka taolo e matla ea boemo, empa ha e phetheloe ntle le tsela ea ho thibela ho sebelisa chelete ka makhetlo a mabeli. Ho rarolla sena, re hlahisitse marang-rang a peer-to-peer a sebelisang bopaki-ba-mosebetsi ho ngola nalane ea litshebelisano e phatlalalitsoeng, eo mohanyetsi a sa khoneng ho e fetola kapele haeba li-node tse tshepahalang li laola karolo e kholo ea matla a CPU. Marang-rang a matla ka mokhoa oa ona o bonolo, oo o se nang sebopeho. Li-node li sebetsa ka nako e le ’ngoe ntle le tsamaiso e ngata. Ha li hloke ho tsejoa, hobane melaetsa ha e tsamaisoe sebakeng se itseng feela ’me e hloka feela ho afuoa ka boiteko bo botle. Li-node li ka tlohela ’me tsa khutlela marang-rang ha li batla, li amohela ketane ea bopaki-ba-mosebetsi e le bopaki ba se etsahalang ha li ne li le sieo. Li lōtleloa ka matla a tsona a CPU, li bontša hore li amohetse li-block tse nepahetseng ka ho sebetsa ho li atolosa, ’me li hana li-block tse fosahetseng ka ho hana ho li sebetsa. Melao le khothatso e hlokahalang e ka phethahala ka tsamaiso ena ea tumellano.

litshupiso

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