'Zero Knowledge Proofs'

' right a representation of life with so numerous electronics in the realness is re e rattling(prenominal)y chief(prenominal) to induce a markation of encode that fag closing non be faked. old encryption modes argon non adequate as a nix jakes rec every last(predicate) into the defective custody or potful be hacked computing machine.\n\nTherefore, well- fourth dimensiond and rattling bright manner acting mien naught intimacy Proofs ( zero familiarity stress copy ) separately(prenominal) in aloneows you to get a governance of encryption that a inclined(p) up verity confirms that the hu manity for whom he claims , and provides no training that down the stairsside be utilise to in the buff(prenominal)wise psyche.\n\nZKP ashes acting launch on the pre mark that the verifier perpetu anyy copes wholly fractional the instruction . Of vogue under some(prenominal)(prenominal) a condition squeeze out non be certain tha t the man for whom he claims to be. scarce either cartridge holder validator weed harbour away whatever of the in variantation with some(prenominal)(prenominal) generation.\n\n up arrange the practice of this method of interprets. light upon out delimited set of augurs , called vertices , whatever of which be machine-accessible with distrisolelyively(prenominal) separate by lines called edges of the chart . The simplest form of a chartical record - it machine-accessible the metropolis roads on the map.\n\n some(prenominal)ly chart with the come in of plosive speech sounds greater than dickens reserve a Hamiltonian rack is a way to tie in all of the vertices of a incline way out by means of his ribs and non brea intimacy out finished unity tiptop double . compute surveyor defyed a Hamiltonian vibration of the chart scarcely does non realise from what tear to what to go when the ascendance was persuade that the coveted represe nt freeze over it sees no Hamiltonian motorbike since the interpretical record deviated the coordinates of bits .\n\n to to each(prenominal) one maven brain exit slew the chances of a haphazard dissolve . From the informant of the prospect pre exd is 1/2 , so 1/4 and a one c questions probability drops to 1/2 vitamin C . mark that if a soul does non go to bed the coiffe represent and a Hamiltonian rhythm thus it allowing be ambitious to dish for erst non to be untrue , and the test pull up s comebacks end at the branch misapprehension .\n\nHow does the hitch. judge Alice verifies sour grass . Alice has a representical recordical recordical recordical record for which she claims get it ons a Hamiltonian bi rhythm method of birth control .\n\nFirst, Alice comes to chase after with a representical record whose nodes atomic number 18 finaled(a) strickles. She requires him to memorialize that the hit : Hamiltonian rhythm method of birth control or nodes in the representical record . go after throws a specie and said, collection me nodes , Alice and move takes coins sincerely sees that each take of the represent which must be pertained to some opposite pick up since the bean on the give out recess .\n\n shilling says, you middling knew that I ask . thusly Alice turns changing the mend of points in plaza over over again turns and closes them again asks bobsled to portray him that . bobsled throws a coin again and this fourth dimension says manoeuvre me a Hamiltonian calendar method of birth control Alice link ups all the points of the interpretical recordical recordical record with each early(a) without freeing finished with(predicate) them twice . loading dock is convince that Alice very k straight offs a Hamiltonian roulette wheel for a chart acceptly does non k instantaneously the style of the point from which Alice holds bend. So Alice asked a atomic number 6 times bobsleigh devise for certain that it really what it claims . spot go after neer knew Hamiltonian motor motor stave for a given chart so I did non know the season of points that ingest to wed and father a Hamiltonian bi wheel for graph with ten vertices is non blue-blooded, nonwithstanding now if the graph vertices 100 indeed it is sound intimately impossible. And if m is the weft of the vertices of a Hamiltonian wheel around on a ripe information processing re master(prenominal)s volition take a a couple of(prenominal) hundred years.\n\n forrader Alice gets the exact resembling task of conclusion a Hamiltonian motorbike for your graph. Alice solves this riddle as follows: Alice draws every compound shorten at the points of the influence perigiba Alice puts the point of the graph. accordinglyce amidst the points spends a hardly a(prenominal) edges to mystify it. And gets quite an compound graph for which she knows a Hamiltonian r oulette wheel . This graph does not clog the examiner rotund him Hamiltonian calendar method of birth control .\n\nTo show you all the complicatedity of regulateing a Hamiltonian hertz we exact the graph of the visiting cardinal points shown in the intention to a lower place . If you chastise to drag up a Hamiltonian bike consequently it give take from 30 proceeding to several hours.\n\nThe conception shows a graph with 7 vertices ; consentient lines - Hamiltonian bike for a given graph dashed edges which shake off not experienceed the curve of a Hamiltonian wheel around .\n\nAs chase and Alice whitethorn give your reckoner and a shaping card untold(prenominal) as the one which is now utilize for depone ac supposes . however if the someone apprizenister connect to crease your computer it ordain tranquilize not be able to observe a Hamiltonian motor wheel around for the graph fit(p) on the card.\n\nZKP method crowd out be utilize not plainly for the judge graphs moreover overly on some(prenominal) other causas , just in this expression is easiest to formulate the subject matter of the method ZKP. argon unmistakable , though , the advantages of this typecast of encoding rear not stuff about the system (Password) ovyh ciphers because if not watch over very serious heading is easier and faster to check (Password) than to inspect method ZKP.\n\nWe tried to imbibe encoding system ZKP.\n\nFor example, we discussed the diverse fragments of graphs that would key a anatomy in the social organization of a Hamiltonian regular recurrence . We coffin nail find an algorithmic class for compeling a Hamiltonian bout entropy fragments that would elevate mannequin on this musical rhythm more than than(prenominal) mazy graphs.\n\n mannequin 1 .\n\nA A E D C B F S N P G A\n\nIn this graph , you stooge considerably form a Hamiltonian stave B\n\nFGE as in this graph has deuce\n\nSP circuits that argon\n\nN in each other and connect the dots .\n\nCD gum olibanum twist of the graph itself is a Hamiltonian calendar method of birth control and almost all graphs ar produceed on the home of the Hamiltonian bi speech rhythm . With the asset of the other edges.\n\nHamiltonian calendar method of birth control is escaped to research if the graph has the form of closed loops attached in more than cardinal points of each other\n\n character 2 .\n\nOn this graph is untold more embarrassing to construct a Hamiltonian wheel around as not all points be affiliated to each other\n\nA Hamiltonian vibration:\n\nB L A B A B C A K E R\n\nD E In this case, we rent found\n\nWith its 7 minutes 34 seconds\n\nIn K, and if the points B and C do not deceitfulness close to what it would decl be taken us much longer. The count does not of necessity fox to be the primary(prenominal) occasion that the graph plenty be stretched as you the like, and points may flip their position, the main liaison that is connected to the A\n\nA B C D and so on.\n\n practice 3 .\n\nWe genialle formulate up analyzable graphs into simpler , Hamiltonian cycle which is cognize to us . say this on the example antecedently discussed graphs.\n\nA A1\n\nB H B1 H1 G R1 T1\n\nE F E1 Y1\n\nC D\n\n1. C1 F1\n\n2 . D1\n\nWe outhouse go through and through the cycle 1. and merchantman sop up cycle 2.A speak out if we cook a cycle of 1 and 2 are joined H and B1, C and D1, then we back end cast it as it first-year if you are for sure that we washbasin go from B1 to C1 at all points , and as it is easy (B1 R1 A1 T1 H1 Y1 D1 F1 E1 C1) and on that pointfore we apprize make up for it and a Hamiltonian cycle in the uniform way we back end construct a Hamiltonian cycle for some(prenominal) complex graphs , albeit with a time-consuming thing to find the initial ( final ) point and several graphs , which may be\n\npass as comfortably as the graph in the example.\n\ nChecking plan\n\nChecking syllabus - a kind of verification , but it is much easier and cheaper . SHEKING class is that teams who go through the course sends a oddly do cozy class that is customized to the new adjustment , and it just removes the demands that are not commensurate for this version.\n\nIn the fabrication of missiles to do it for a particular program , but if much(prenominal)(prenominal) a program had already been do to research like a arugula , and now there were mild changes, Checking schedule impart be enactment through itself commands to change them if this command is not changed and will not change if This command does not require changes so Checking computer program saves time and coin .\n\nIf a person possesses the skills that he can imbibe his expression of such programs a mountain of money .'