Ngaba uyintombazana kanobhala owafumana iindaba ezibi. Kukho abantu abali-16 abakumgangatho ophezulu kuhulumeni onokuthumela kubo umyalezo, kwaye ufuna ukukhetha abahlanu kubo, kunye nabathathu kubo ubuncinane xa kuvulwa umyalezo. Ngokomzekelo - awufuni umongameli azi, kodwa ufuna inkokeli yomkhosi, kunye nabalawuli abane babalawuli belungelo lokuvula umyalezo. Ngokubethela okuqhelekileyo, ungathumela umyalezo kumntu ngamnye ngokwahlukeneyo, kodwa awunakunyanzeliswa ukuba kubekho imfuneko yenani labantu ababandakanyekayo ekuvuleni umyalezo. Ingcamango yokubethela kwemida kukuba uneqela labantu abali-N abazi intaba yabo yombini ibhalwe kwibhock enye. Nabani na angakhetha abali-L kubo kwaye enze itsimbi yokubethela esebenzisa izitshixo zabo zombini ezivela kwi-block. Emva koko bangabeka umda we-T kwaye babethele umyalezo othunyelwa kubamkeli be-L. Umyamkeli ngamnye wenze ukubuyiselwa kwesiqingatha. Eli candelo linokuba nzima kakhulu - okanye unyanzelekile ukuba ibe lula kakhulu - kuxhomekeke kwindlela isicelo esenziwa ngayo. Ngokomzekelo, ungayenza ukuba ukubuyiselwa kwenkonzo kwenzeke kwikhompyuter enye, kwaye bonke abantu abayinxalenye ye-quorum bangenise i-pass phrase yabo kweso sixhobo. Okanye ungaba nokubuyiselwa kwenkonzo yomntu ngamnye kuthunyelwe kumntu omnye kuluhlu odlula ngayo ukuze ibuyiselwe ngokupheleleyo. Nje ukuba inani leemfuneko zabantu zenze inxalenye yazo, inyathelo lokugqibela lokubuyiselwa komyalezo lingenzeka. I-matematika engasemva kokubethela kwemida inzima kakhulu. Ngeminye imininingwane,   Ndiyibuyekeze ngekhodi, kunye nenkcazo ye-  . Okunomdla kukuphuculwa kwemida yokubethela. Ngelixa ukuqonda i-matematika kunceda, ukuqonda ukusetyenziswa okunokwenzeka yingxaki enomdla ngakumbi. jonga i-NIST. matematika kunye nekhodi apha Kulo algorithm, u-N ungamandla ka-2. Oku akubalulekanga kuba ungaba nenani labasebenzisi abangamanga. Kodwa kuchaphumela ubungakanani bebhloko yedatha yombini. Inani labantu umyalezo ubhalwe kubo, "L" kwingcaciso engentla, lingaphantsi okanye lilingana no-N. Ngoko, kwenzeka ntoni kwimida? Ukuba L = N, ngoko bonke abantu kuluhlu bangaba yi-"decryptor". Ukuba T = 1, ufumana inkqubo yokuhambisa. Umyalezo omnye obhalwe uthunyelwa kuye wonke umntu, kwaye umntu ngamnye ungawubuyisela ngokwakhe. Ukuba i-matematika yenze umsebenzi, u-T kufuneka abe ngaphantsi okanye alingane no-L. Unganyanzelisa bonke abantu kuluhlu ukuba bathathe inxaxheba ekubuyiseleni ngokumisela u-T = L. Kumzekelo wenkokeli, ungathumela umyalezo kubantu abahlanu emva koko uthi bonke aba bahlanu kufuneka babekho ukuze bavule umyalezo kuba utshokolethi kufuneka usasazwe. I-algorithm ipheleleyo ichazwe kusetyenziswa amanyathelo asixhenxe. Inyathelo lokuqala yi-"setup," echaza inqanaba lokhuseleko kunye nenani elipheleleyo labasebenzisi u-N onokuthi uphathwe ngalo. Ukuba, kwixesha elizayo, ufuna ukongeza abasebenzisi abaninzi, uqala apha nge-2N ukuze wenze into eyaziwa ngokuba yi-"Common Reference String." I-CRS yibhock ye-vector kunye ne-matrix enobungakanani obuxhomekeke ku-N. Ngokwakhiwa kwe-CRS, umntu ngamnye wenza itsimbi yangasese, eguqulelwa itsimbi yombini. Ndiyayithanda ingcamango yokuba izitshixo ezingasese azigcinwa; zihlala zibuyiselwa ngehashi ye-pass phrase. Ngokubuyekezwa kwe-algorithm kunye ne-elliptic curves, oku kulula. Itsimbi epheleleyo yombini yomsebenzisi ngamnye iquka amanqaku ama-4N, ngoko ke inkulu kakhulu kune-algorithm yesitshixo yombini esemgangathweni. Ukukhetha ukuba ngubani ofumana umyalezo kubizwa ngokuba yinyathelo le-"preprocess". Umthumeli ukhetha abamkeli be-L, kwaye i-algorithm idibanisa izitshixo zabo zombini kwitsimbi yokubethela kunye ne-vector ebizwa ngokuba yi-aggregation key. Itsimbi yokubethela ixhomekeke kubasebenzisi kuluhlu lwe-L. I-aggregation key yidibaniselwano yezitshixo ezingekho ku-L kunye nezitshixo eziku-L. Ezi zitshixo zimbini ngoku zingasetyenziswa kwinyathelo elilandelayo. Inyathelo lokubethela lisebenzisa iinamba ezininzi ezingajongwayo zidibene ne-CRS kunye netsimbi yokubethela ukufihla umyalezo. Umyalezo luhlobo lwenombolo, kodwa nawuphi na umtya ungaguqulelwa kwinombolo esebenzayo ngokulula ngenxa yokuba iinamba zinkulu kakhulu. Umzekelo wenkqubo endiyibhalileyo unayo inombolo eyi-byte eyi-520. Emva kokucinga ngendlela endiyibhalileyo ngayo inkqubo, ndaqonda ukuba ndingasebenzisa ixabiso elifanayo lokufihla kwiiseti ezininzi zeebhloko ze-byte ezingama-520. Ke ngoko, akukho mda wokwenyani kubungakanani bomyalezo omnye onokufihla. Kodwa kunokuba lula ukusebenzisa ii-byte ezingama-520 njengesitshixo se-algorithm ye-symmetric. Nje ukuba bonke bafumene umyalezo obhalwe, ngamnye wabo usebenzisa itsimbi yabo engabonakaliyo ukwenza itsimbi yombini yenye ixesha. Ngamnye kubo ukhetha inombolo engajongwayo ukudibanisa kunye nedatha ye-CRS kunye netsimbi yabo yombini. Kwi-algorithm, oku kubizwa ngokuba yi-"partial decryption", kodwa ngokwenyani yidibaniselwano yemiphumela eyaziwayo kunye nenombolo engajongwayo ukufihla itsimbi yabo engabonakaliyo. I-aggregator yazo zonke iimvume zokubuyiselwa kwenkonzo zokubuyiselwa kwenkonzo zenze inyathelo le-"partial verify" kusetyenziswa itsimbi yombini yomsebenzisi ngamnye kunye nedatha ye-CRS. Oku akubalulekanga ngokwenene, kodwa akukho nto imbi ukujonga izinto xa unako. Ngokubhekiselele kwinkqubo yokwenziwa, kukuqinisekiswa kokhuseleko okubalulekileyo. Xa abasebenzisi abaneleyo badibene iimvume zabo zokubuyiselwa kwenkonzo, umyalezo ungavulwa. Le yindawo apho i-matematika yenza nzima kakhulu. Zonke iinamba ezingajongwayo ziyahlula, zonke izitshixo zombini zidibana, kwaye i-inverse matrix isusa iseti yeenziba ezingafihliweyo kwi-CRS. Ukuba uyayithanda i-matematika, iyonqabile. I-matematika isekelwe ekubhanqeni kwezantsi nge-elliptic curves. Ngoku, akukho algorithm eyaziwayo enokuthi ibuyisele ngasemva i-matematika (ebizwa ngokuba yingxaki ye-elliptic curve logarithm). Iialgoritma ziphumelele zokuba zingasebenza kwikhompyuter ye-quantum kunye ne-2^32 yee-Toffoli gates. Nje ukuba enye i-Toffoli gate yenziwe, umthetho kaMoore weekhompyutha ze-quantum ungakhula. Ukuba ixesha lokubini liyiminyaka emibini, ngoko kukho iminyaka engama-32 ngaphambi kokuba i-128-bit secure elliptic curves ziqhekekile. Ukuba ufuna ukufihla izinto iminyaka engama-50, ngoko mhlawumbi ufuna ukuxhalabela iikhompyutha ze-quantum eziqhekeza umyalezo wakho emva kweminyaka engama-40. Kodwa kuba iwashi ayiqalanga, kunokwenzeka ukuba iminyaka engama-60 ngaphambi kokuba nabani na aqhekeke i-elliptic curve algorithm yanamhlanje. Kubantu abaninzi, ukubethela kwemida kukhuselekile ngokupheleleyo kwaye kuya kuba njalo iminyaka engaphezu kwama-30. Ngokukodwa ukuba ufuna ukufihla izinto iminyaka embalwa. Ndinethemba ukuba kukho iindlela ezininzi zokubethela kwemida endingazicingelanga. Ngoko, jonga kwaye ubone ukuba ungayenza njani.

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