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Created May 20, 2021
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The whitepaper format for zd3n puzzle
Bitcoin:APeer-to-PeerElectronicCashSystemSatoshiNakamotosatoshin@gmx.comwww.bitcoin.orgAbstract.Apurelypeer-to-peerversionofelectroniccashwouldallowonlinepaymentstobesentdirectlyfromonepartytoanotherwithoutgoingthroughafinancialinstitution.Digitalsignaturesprovidepartofthesolution,butthemainbenefitsarelostifatrustedthirdpartyisstillrequiredtopreventdouble-spending.Weproposeasolutiontothedouble-spendingproblemusingapeer-to-peernetwork.Thenetworktimestampstransactionsbyhashingthemintoanongoingchainofhash-basedproof-of-work,formingarecordthatcannotbechangedwithoutredoingtheproof-of-work.Thelongestchainnotonlyservesasproofofthesequenceofeventswitnessed,butproofthatitcamefromthelargestpoolofCPUpower.AslongasamajorityofCPUpoweriscontrolledbynodesthatarenotcooperatingtoattackthenetwork,they'llgeneratethelongestchainandoutpaceattackers.Thenetworkitselfrequiresminimalstructure.Messagesarebroadcastonabesteffortbasis,andnodescanleaveandrejointhenetworkatwill,acceptingthelongestproof-of-workchainasproofofwhathappenedwhiletheyweregone.1.IntroductionCommerceontheInternethascometorelyalmostexclusivelyonfinancialinstitutionsservingastrustedthirdpartiestoprocesselectronicpayments.Whilethesystemworkswellenoughformosttransactions,itstillsuffersfromtheinherentweaknessesofthetrustbasedmodel.Completelynon-reversibletransactionsarenotreallypossible,sincefinancialinstitutionscannotavoidmediatingdisputes.Thecostofmediationincreasestransactioncosts,limitingtheminimumpracticaltransactionsizeandcuttingoffthepossibilityforsmallcasualtransactions,andthereisabroadercostinthelossofabilitytomakenon-reversiblepaymentsfornon-reversibleservices.Withthepossibilityofreversal,theneedfortrustspreads.Merchantsmustbewaryoftheircustomers,hasslingthemformoreinformationthantheywouldotherwiseneed.Acertainpercentageoffraudisacceptedasunavoidable.Thesecostsandpaymentuncertaintiescanbeavoidedinpersonbyusingphysicalcurrency,butnomechanismexiststomakepaymentsoveracommunicationschannelwithoutatrustedparty.Whatisneededisanelectronicpaymentsystembasedoncryptographicproofinsteadoftrust,allowinganytwowillingpartiestotransactdirectlywitheachotherwithouttheneedforatrustedthirdparty.Transactionsthatarecomputationallyimpracticaltoreversewouldprotectsellersfromfraud,androutineescrowmechanismscouldeasilybeimplementedtoprotectbuyers.Inthispaper,weproposeasolutiontothedouble-spendingproblemusingapeer-to-peerdistributedtimestampservertogeneratecomputationalproofofthechronologicalorderoftransactions.ThesystemissecureaslongashonestnodescollectivelycontrolmoreCPUpowerthananycooperatinggroupofattackernodes.12.TransactionsWedefineanelectroniccoinasachainofdigitalsignatures.Eachownertransfersthecointothenextbydigitallysigningahashoftheprevioustransactionandthepublickeyofthenextownerandaddingthesetotheendofthecoin.Apayeecanverifythesignaturestoverifythechainofownership.Theproblemofcourseisthepayeecan'tverifythatoneoftheownersdidnotdouble-spendthecoin.Acommonsolutionistointroduceatrustedcentralauthority,ormint,thatcheckseverytransactionfordoublespending.Aftereachtransaction,thecoinmustbereturnedtotheminttoissueanewcoin,andonlycoinsissueddirectlyfromthemintaretrustednottobedouble-spent.Theproblemwiththissolutionisthatthefateoftheentiremoneysystemdependsonthecompanyrunningthemint,witheverytransactionhavingtogothroughthem,justlikeabank.Weneedawayforthepayeetoknowthatthepreviousownersdidnotsignanyearliertransactions.Forourpurposes,theearliesttransactionistheonethatcounts,sowedon'tcareaboutlaterattemptstodouble-spend.Theonlywaytoconfirmtheabsenceofatransactionistobeawareofalltransactions.Inthemintbasedmodel,themintwasawareofalltransactionsanddecidedwhicharrivedfirst.Toaccomplishthiswithoutatrustedparty,transactionsmustbepubliclyannounced[1],andweneedasystemforparticipantstoagreeonasinglehistoryoftheorderinwhichtheywerereceived.Thepayeeneedsproofthatatthetimeofeachtransaction,themajorityofnodesagreeditwasthefirstreceived.3.TimestampServerThesolutionweproposebeginswithatimestampserver.Atimestampserverworksbytakingahashofablockofitemstobetimestampedandwidelypublishingthehash,suchasinanewspaperorUsenetpost[2-5].Thetimestampprovesthatthedatamusthaveexistedatthetime,obviously,inordertogetintothehash.Eachtimestampincludestheprevioustimestampinitshash,formingachain,witheachadditionaltimestampreinforcingtheonesbeforeit.2BlockItemItem...HashBlockItemItem...HashTransactionOwner1'sPublicKeyOwner0'sSignatureHashTransactionOwner2'sPublicKeyOwner1'sSignatureHashVerifyTransactionOwner3'sPublicKeyOwner2'sSignatureHashVerifyOwner2'sPrivateKeyOwner1'sPrivateKeySignSignOwner3'sPrivateKey4.Proof-of-WorkToimplementadistributedtimestampserveronapeer-to-peerbasis,wewillneedtouseaproof-of-worksystemsimilartoAdamBack'sHashcash[6],ratherthannewspaperorUsenetposts.Theproof-of-workinvolvesscanningforavaluethatwhenhashed,suchaswithSHA-256,thehashbeginswithanumberofzerobits.Theaverageworkrequiredisexponentialinthenumberofzerobitsrequiredandcanbeverifiedbyexecutingasinglehash.Forourtimestampnetwork,weimplementtheproof-of-workbyincrementinganonceintheblockuntilavalueisfoundthatgivestheblock'shashtherequiredzerobits.OncetheCPUefforthasbeenexpendedtomakeitsatisfytheproof-of-work,theblockcannotbechangedwithoutredoingthework.Aslaterblocksarechainedafterit,theworktochangetheblockwouldincluderedoingalltheblocksafterit.Theproof-of-workalsosolvestheproblemofdeterminingrepresentationinmajoritydecisionmaking.Ifthemajoritywerebasedonone-IP-address-one-vote,itcouldbesubvertedbyanyoneabletoallocatemanyIPs.Proof-of-workisessentiallyone-CPU-one-vote.Themajoritydecisionisrepresentedbythelongestchain,whichhasthegreatestproof-of-workeffortinvestedinit.IfamajorityofCPUpoweriscontrolledbyhonestnodes,thehonestchainwillgrowthefastestandoutpaceanycompetingchains.Tomodifyapastblock,anattackerwouldhavetoredotheproof-of-workoftheblockandallblocksafteritandthencatchupwithandsurpasstheworkofthehonestnodes.Wewillshowlaterthattheprobabilityofaslowerattackercatchingupdiminishesexponentiallyassubsequentblocksareadded.Tocompensateforincreasinghardwarespeedandvaryinginterestinrunningnodesovertime,theproof-of-workdifficultyisdeterminedbyamovingaveragetargetinganaveragenumberofblocksperhour.Ifthey'regeneratedtoofast,thedifficultyincreases.5.NetworkThestepstorunthenetworkareasfollows:1)Newtransactionsarebroadcasttoallnodes.2)Eachnodecollectsnewtransactionsintoablock.3)Eachnodeworksonfindingadifficultproof-of-workforitsblock.4)Whenanodefindsaproof-of-work,itbroadcaststheblocktoallnodes.5)Nodesaccepttheblockonlyifalltransactionsinitarevalidandnotalreadyspent.6)Nodesexpresstheiracceptanceoftheblockbyworkingoncreatingthenextblockinthechain,usingthehashoftheacceptedblockastheprevioushash.Nodesalwaysconsiderthelongestchaintobethecorrectoneandwillkeepworkingonextendingit.Iftwonodesbroadcastdifferentversionsofthenextblocksimultaneously,somenodesmayreceiveoneortheotherfirst.Inthatcase,theyworkonthefirstonetheyreceived,butsavetheotherbranchincaseitbecomeslonger.Thetiewillbebrokenwhenthenextproof-of-workisfoundandonebranchbecomeslonger;thenodesthatwereworkingontheotherbranchwillthenswitchtothelongerone.3BlockPrevHashNonceTxTx...BlockPrevHashNonceTxTx...Newtransactionbroadcastsdonotnecessarilyneedtoreachallnodes.Aslongastheyreachmanynodes,theywillgetintoablockbeforelong.Blockbroadcastsarealsotolerantofdroppedmessages.Ifanodedoesnotreceiveablock,itwillrequestitwhenitreceivesthenextblockandrealizesitmissedone.6.IncentiveByconvention,thefirsttransactioninablockisaspecialtransactionthatstartsanewcoinownedbythecreatoroftheblock.Thisaddsanincentivefornodestosupportthenetwork,andprovidesawaytoinitiallydistributecoinsintocirculation,sincethereisnocentralauthoritytoissuethem.Thesteadyadditionofaconstantofamountofnewcoinsisanalogoustogoldminersexpendingresourcestoaddgoldtocirculation.Inourcase,itisCPUtimeandelectricitythatisexpended.Theincentivecanalsobefundedwithtransactionfees.Iftheoutputvalueofatransactionislessthanitsinputvalue,thedifferenceisatransactionfeethatisaddedtotheincentivevalueoftheblockcontainingthetransaction.Onceapredeterminednumberofcoinshaveenteredcirculation,theincentivecantransitionentirelytotransactionfeesandbecompletelyinflationfree.Theincentivemayhelpencouragenodestostayhonest.IfagreedyattackerisabletoassemblemoreCPUpowerthanallthehonestnodes,hewouldhavetochoosebetweenusingittodefraudpeoplebystealingbackhispayments,orusingittogeneratenewcoins.Heoughttofinditmoreprofitabletoplaybytherules,suchrulesthatfavourhimwithmorenewcoinsthaneveryoneelsecombined,thantounderminethesystemandthevalidityofhisownwealth.7.ReclaimingDiskSpaceOncethelatesttransactioninacoinisburiedunderenoughblocks,thespenttransactionsbeforeitcanbediscardedtosavediskspace.Tofacilitatethiswithoutbreakingtheblock'shash,transactionsarehashedinaMerkleTree[7][2][5],withonlytherootincludedintheblock'shash.Oldblockscanthenbecompactedbystubbingoffbranchesofthetree.Theinteriorhashesdonotneedtobestored.Ablockheaderwithnotransactionswouldbeabout80bytes.Ifwesupposeblocksaregeneratedevery10minutes,80bytes*6*24*365=4.2MBperyear.Withcomputersystemstypicallysellingwith2GBofRAMasof2008,andMoore'sLawpredictingcurrentgrowthof1.2GBperyear,storageshouldnotbeaproblemeveniftheblockheadersmustbekeptinmemory.4BlockBlockBlockHeader(BlockHash)PrevHashNonceHash01Hash0Hash1Hash2Hash3Hash23RootHashHash01Hash2Tx3Hash23BlockHeader(BlockHash)RootHashTransactionsHashedinaMerkleTreeAfterPruningTx0-2fromtheBlockPrevHashNonceHash3Tx0Tx1Tx2Tx38.SimplifiedPaymentVerificationItispossibletoverifypaymentswithoutrunningafullnetworknode.Auseronlyneedstokeepacopyoftheblockheadersofthelongestproof-of-workchain,whichhecangetbyqueryingnetworknodesuntilhe'sconvincedhehasthelongestchain,andobtaintheMerklebranchlinkingthetransactiontotheblockit'stimestampedin.Hecan'tcheckthetransactionforhimself,butbylinkingittoaplaceinthechain,hecanseethatanetworknodehasacceptedit,andblocksaddedafteritfurtherconfirmthenetworkhasacceptedit.Assuch,theverificationisreliableaslongashonestnodescontrolthenetwork,butismorevulnerableifthenetworkisoverpoweredbyanattacker.Whilenetworknodescanverifytransactionsforthemselves,thesimplifiedmethodcanbefooledbyanattacker'sfabricatedtransactionsforaslongastheattackercancontinuetooverpowerthenetwork.Onestrategytoprotectagainstthiswouldbetoacceptalertsfromnetworknodeswhentheydetectaninvalidblock,promptingtheuser'ssoftwaretodownloadthefullblockandalertedtransactionstoconfirmtheinconsistency.Businessesthatreceivefrequentpaymentswillprobablystillwanttoruntheirownnodesformoreindependentsecurityandquickerverification.9.CombiningandSplittingValueAlthoughitwouldbepossibletohandlecoinsindividually,itwouldbeunwieldytomakeaseparatetransactionforeverycentinatransfer.Toallowvaluetobesplitandcombined,transactionscontainmultipleinputsandoutputs.Normallytherewillbeeitherasingleinputfromalargerprevioustransactionormultipleinputscombiningsmalleramounts,andatmosttwooutputs:oneforthepayment,andonereturningthechange,ifany,backtothesender.Itshouldbenotedthatfan-out,whereatransactiondependsonseveraltransactions,andthosetransactionsdependonmanymore,isnotaproblemhere.Thereisnevertheneedtoextractacompletestandalonecopyofatransaction'shistory.5TransactionIn...InOut...Hash01Hash2Hash3Hash23BlockHeaderMerkleRootPrevHashNonceBlockHeaderMerkleRootPrevHashNonceBlockHeaderMerkleRootPrevHashNonceMerkleBranchforTx3LongestProof-of-WorkChainTx310.PrivacyThetraditionalbankingmodelachievesalevelofprivacybylimitingaccesstoinformationtothepartiesinvolvedandthetrustedthirdparty.Thenecessitytoannouncealltransactionspubliclyprecludesthismethod,butprivacycanstillbemaintainedbybreakingtheflowofinformationinanotherplace:bykeepingpublickeysanonymous.Thepubliccanseethatsomeoneissendinganamounttosomeoneelse,butwithoutinformationlinkingthetransactiontoanyone.Thisissimilartothelevelofinformationreleasedbystockexchanges,wherethetimeandsizeofindividualtrades,the"tape",ismadepublic,butwithouttellingwhothepartieswere.Asanadditionalfirewall,anewkeypairshouldbeusedforeachtransactiontokeepthemfrombeinglinkedtoacommonowner.Somelinkingisstillunavoidablewithmulti-inputtransactions,whichnecessarilyrevealthattheirinputswereownedbythesameowner.Theriskisthatiftheownerofakeyisrevealed,linkingcouldrevealothertransactionsthatbelongedtothesameowner.11.CalculationsWeconsiderthescenarioofanattackertryingtogenerateanalternatechainfasterthanthehonestchain.Evenifthisisaccomplished,itdoesnotthrowthesystemopentoarbitrarychanges,suchascreatingvalueoutofthinairortakingmoneythatneverbelongedtotheattacker.Nodesarenotgoingtoacceptaninvalidtransactionaspayment,andhonestnodeswillneveracceptablockcontainingthem.Anattackercanonlytrytochangeoneofhisowntransactionstotakebackmoneyherecentlyspent.TheracebetweenthehonestchainandanattackerchaincanbecharacterizedasaBinomialRandomWalk.Thesuccesseventisthehonestchainbeingextendedbyoneblock,increasingitsleadby+1,andthefailureeventistheattacker'schainbeingextendedbyoneblock,reducingthegapby-1.TheprobabilityofanattackercatchingupfromagivendeficitisanalogoustoaGambler'sRuinproblem.Supposeagamblerwithunlimitedcreditstartsatadeficitandplayspotentiallyaninfinitenumberoftrialstotrytoreachbreakeven.Wecancalculatetheprobabilityheeverreachesbreakeven,orthatanattackerevercatchesupwiththehonestchain,asfollows[8]:p=probabilityanhonestnodefindsthenextblockq=probabilitytheattackerfindsthenextblockqz=probabilitytheattackerwillevercatchupfromzblocksbehindqz={1ifp?q?q/p?zifp?q}6Identities
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