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ʻO ka papahana kaʻana like huna a Shamir

E noʻonoʻo i kahi hiʻohiʻona kahi e pono ai ʻoe e hoʻopaʻa i kahi waihona waihona. Manaʻo ʻia ʻaʻole hiki ke loaʻa me ke kī ʻole, i hāʻawi ʻia iā ʻoe i ka lā mua o ka hana. ʻO kāu pahuhopu ka mālama pono ʻana i ke kī.

E ʻōlelo mākou e hoʻoholo ʻoe e mālama i ke kī me ʻoe i nā manawa a pau, e hāʻawi ana i ke komo i ka waihona e like me ka mea e pono ai. Akā e ʻike koke ʻoe ʻaʻole maikaʻi ka hoʻonā ʻana i ka hoʻomaʻamaʻa ʻana, no ka mea, koi ʻia kou noho kino i kēlā me kēia manawa e wehe ai ʻoe i ka waihona. Pehea ka hoʻomaha i hoʻohiki ʻia ai ʻoe? Eia kekahi, ʻoi aku ka weliweli o ka nīnau: pehea inā e nalowale kāu kī hoʻokahi?

Me kāu hoʻomaha hoʻomaha, hoʻoholo ʻoe e hana i kope o ke kī a hāʻawi iā ia i kekahi limahana. Eia naʻe, maopopo iā ʻoe ʻaʻole kūpono kēia. Ma ka pālua ʻana i ka helu o nā kī, e pāpālua pū ʻoe i nā manawa o ka ʻaihue kī.

I ka minamina, luku ʻoe i ka lua a hoʻoholo e hoʻokaʻawale i ke kī kumu i ka hapalua. I kēia manawa, manaʻo paha ʻelua mau kānaka hilinaʻi me nā ʻāpana kī e hele kino e hōʻiliʻili i ke kī a wehe i ka waihona. ʻO ia hoʻi, pono ka ʻaihue e ʻaihue i ʻelua ʻāpana, ʻoi aku ka paʻakikī o ka ʻaihue i hoʻokahi kī. Eia naʻe, ʻike koke ʻoe ʻaʻole ʻoi aku ka maikaʻi o kēia hoʻolālā ma mua o ke kī hoʻokahi wale nō, no ka mea inā nalowale kekahi i ka hapalua kī, ʻaʻole hiki ke hoʻihoʻi ʻia ke kī piha.

Hiki ke hoʻoponopono ʻia ka pilikia me nā kī a me nā kī hou, akā e koi koke kēia ala he nui nā kī a me nā laka. Hoʻoholo ʻoe ʻo ka hoʻolālā kūpono ke kaʻana like ʻana i ke kī i ʻole e hilinaʻi ka palekana i kahi kanaka hoʻokahi. Manaʻo ʻoe e loaʻa kekahi paepae no ka helu o nā ʻāpana a inā e nalowale kekahi ʻāpana (a i ʻole inā hele ke kanaka i ka hoʻomaha), hoʻomau ke kī holoʻokoʻa.

Pehea e kaʻana like i kahi huna

Ua noʻonoʻo ʻia kēia ʻano hoʻolālā hoʻokele koʻikoʻi e Adi Shamir i ka makahiki 1979 i kāna paʻi ʻana i kāna hana "Pehea e kaʻana like ai i kahi mea huna". Ua wehewehe pōkole ka ʻatikala i ka mea i kapa ʻia ʻO ka papahana kaʻana like huna a Shamir paena no ka hoʻokaʻawale ʻana i kahi waiwai huna (e like me ke kī cryptographic) i loko ʻO ka papahana kaʻana like huna a Shamir ʻāpana. A laila, i ka manawa a i ka manawa wale nō ʻO ka papahana kaʻana like huna a Shamir mai ʻO ka papahana kaʻana like huna a Shamir ua hui ʻia nā ʻāpana, hiki iā ʻoe ke hoʻihoʻi maʻalahi i ka mea huna ʻO ka papahana kaʻana like huna a Shamir.

Mai kahi manaʻo palekana, ʻo kahi waiwai koʻikoʻi o kēia hoʻolālā ʻaʻole pono e ʻike ka mea hoʻouka i kekahi mea ke ʻole ʻo ia ma ka liʻiliʻi. ʻO ka papahana kaʻana like huna a Shamir ʻāpana. ʻOiai ke alo ʻO ka papahana kaʻana like huna a Shamir ʻAʻole pono nā ʻāpana e hāʻawi i kekahi ʻike. Kapa mākou i kēia waiwai palekana semantic.

Huina polinomial

Shamir paepae paepae ʻO ka papahana kaʻana like huna a Shamir kūkulu ʻia a puni ka manaʻo polynomial interpolation. Inā ʻaʻole ʻoe i kamaʻāina i kēia manaʻo, he maʻalahi loa ia. ʻOiaʻiʻo, inā ua kahakiʻi ʻoe i nā kiko ma ka pakuhi a laila hoʻopili iā lākou me nā laina a i ʻole nā ​​pihi, ua hoʻohana mua ʻoe!

ʻO ka papahana kaʻana like huna a Shamir
Ma o nā helu ʻelua hiki iā ʻoe ke huki i ka helu palena ʻole o nā polynomial o ke degere 2. No ke koho ʻana i hoʻokahi wale nō mai ia mau mea, pono ʻoe i kahi helu ʻekolu. Kiʻi: ʻO Wikipedia

E noʻonoʻo i kahi polynomial me ke degere hoʻokahi, ʻO ka papahana kaʻana like huna a Shamir. Inā makemake ʻoe e hoʻolālā i kēia hana ma ka pakuhi, ʻehia mau helu āu e pono ai? ʻAe, ʻike mākou he hana laina kēia e hana i kahi laina a no laila pono ʻelua mau helu. A laila, e noʻonoʻo i kahi hana polynomial me ke degere ʻelua, ʻO ka papahana kaʻana like huna a Shamir. He hana quadratic kēia, no laila, pono ʻekolu mau kiko no ka hoʻolālā ʻana i ka pakuhi. Pehea e pili ana i ka polynomial me ka degere ekolu? ʻEhā mau helu. A pela aku a pela aku.

ʻO ka mea maikaʻi loa e pili ana i kēia waiwai, ʻo ia ka mea i hāʻawi ʻia i ke degere o ka hana polynomial a ma ka liʻiliʻi loa ʻO ka papahana kaʻana like huna a Shamir nā helu, hiki iā mākou ke loaʻa nā helu hou no kēia hana polynomial. Kāhea mākou i ka extrapolation o kēia mau helu hou polynomial interpolation.

Ka hana huna

Ua ʻike mua paha ʻoe ʻo kēia kahi e pāʻani ai ka hana akamai a Shamir. E ʻōlelo kāua i kā mākou mea huna ʻO ka papahana kaʻana like huna a Shamir Ua ʻO ka papahana kaʻana like huna a Shamir. Hiki iā mākou ke huli ʻO ka papahana kaʻana like huna a Shamir i kahi kiko ma ka pakuhi ʻO ka papahana kaʻana like huna a Shamir a hiki mai me ka hana polynomial me ke degere ʻO ka papahana kaʻana like huna a Shamir, ka mea e māʻona ai i kēia manaʻo. E hoʻomanaʻo mākou iā ʻoe ʻO ka papahana kaʻana like huna a Shamir ʻo ko mākou paepae o nā ʻāpana i koi ʻia, no laila inā mākou e hoʻonoho i ka paepae i ʻekolu mau ʻāpana, pono mākou e koho i kahi hana polynomial me ke degere ʻelua.

E loaʻa i kā mākou polynomial ke ʻano ʻO ka papahana kaʻana like huna a Shamirkahi ʻO ka papahana kaʻana like huna a Shamir и ʻO ka papahana kaʻana like huna a Shamir — nā huina maikaʻi i koho wale ʻia. Ke kūkulu nei mākou i kahi polynomial me ke degere ʻO ka papahana kaʻana like huna a Shamir, kahi o ke koena kuokoa ʻO ka papahana kaʻana like huna a Shamir - ʻO kā mākou mea huna kēia ʻO ka papahana kaʻana like huna a Shamir, a no kēlā me kēia o nā mea ma hope ʻO ka papahana kaʻana like huna a Shamir hua'ōlelo aia kahi helu helu maikaʻi i wae ʻia. Inā hoʻi mākou i ka laʻana kumu a manaʻo i kēlā ʻO ka papahana kaʻana like huna a Shamir, a laila loaʻa iā mākou ka hana ʻO ka papahana kaʻana like huna a Shamir.

I kēia manawa hiki iā mākou ke hana i nā ʻāpana ma ka hoʻopili ʻana ʻO ka papahana kaʻana like huna a Shamir huinahelu kū hoʻokahi i ʻO ka papahana kaʻana like huna a Shamirkahi ʻO ka papahana kaʻana like huna a Shamir (no ka mea, ʻo kā mākou mea huna). Ma kēia hiʻohiʻona, makemake mākou e puʻunaue i ʻehā mau ʻāpana me ka paepae o ʻekolu, no laila ke hoʻohua nei mākou i nā helu. ʻO ka papahana kaʻana like huna a Shamir a e hoʻouna i hoʻokahi helu i kēlā me kēia o nā kānaka hilinaʻi ʻehā, nā mea mālama i ke kī. Hoʻomaopopo pū mākou i nā kānaka i kēlā ʻO ka papahana kaʻana like huna a Shamir, no ka mea, ua manaʻo ʻia kēia i ka ʻike lehulehu a pono no ka hoʻihoʻi ʻana ʻO ka papahana kaʻana like huna a Shamir.

Hoʻihoʻi hou i ka mea huna

Ua kūkākūkā mua mākou i ka manaʻo o ka interpolation polynomial a me ke ʻano o ke kumu o ka paepae paepae o Shamir ʻO ka papahana kaʻana like huna a Shamir. Ke makemake kekahi ʻekolu o nā kahu ʻehā e hoʻihoʻi ʻO ka papahana kaʻana like huna a Shamir, pono lākou e interpolate ʻO ka papahana kaʻana like huna a Shamir me kona mau kiko ponoi. No ka hana ʻana i kēia, hiki iā lākou ke hoʻoholo i kā lākou mau helu ʻO ka papahana kaʻana like huna a Shamir a e helu i ka polynomial interpolation Lagrange me ka hoʻohana ʻana i ke kumu hoʻohālike. Inā ʻoi aku ka maopopo o ka polokalamu iā ʻoe ma mua o ka makemakika, a laila ʻo ka pi ka mea hoʻohana for, ka mea e hoʻonui i nā hopena a pau, a ʻo ka sigma for, e hoʻohui i nā mea a pau.

ʻO ka papahana kaʻana like huna a Shamir

ʻO ka papahana kaʻana like huna a Shamir

ma ʻO ka papahana kaʻana like huna a Shamir hiki iā mākou ke hoʻoponopono e like me kēia a hoʻihoʻi i kā mākou hana polynomial mua:

ʻO ka papahana kaʻana like huna a Shamir

No ka mea, ʻike mākou i kēlā ʻO ka papahana kaʻana like huna a Shamir, ho'ōla ʻO ka papahana kaʻana like huna a Shamir hana maʻalahi:

ʻO ka papahana kaʻana like huna a Shamir

Ke hoʻohana nei i ka helu helu integer palekana

ʻOiai ua hoʻokō pono mākou i ka manaʻo kumu o Shamir ʻO ka papahana kaʻana like huna a Shamir, waiho ʻia mākou me kahi pilikia i mālama ʻole ʻia a hiki i kēia manawa. Hoʻohana kā mākou hana polynomial i ka helu helu integer palekana. E hoʻomanaʻo, no kēlā me kēia helu hou i loaʻa i ka mea hoʻouka kaua ma ka pakuhi o kā mākou hana, ʻoi aku ka liʻiliʻi o nā mea hiki ke loaʻa nā wahi ʻē aʻe. Hiki iā ʻoe ke ʻike i kēia me kou mau maka ponoʻī ke hoʻolālā ʻoe i ka helu mahuahua o nā helu no kahi hana polynomial me ka hoʻohana ʻana i ka helu helu helu. He kūʻē kēia i kā mākou pahuhopu palekana i ʻōlelo ʻia, no ka mea, ʻaʻole ʻike ka mea hoʻouka a hiki i ka liʻiliʻi loa ʻO ka papahana kaʻana like huna a Shamir nā ʻāpana.

No ka hōʻike ʻana i ka nāwaliwali o ka pōʻai helu helu integer, e noʻonoʻo i kahi hiʻohiʻona i loaʻa ai i ka mea hoʻouka ʻelua mau helu. ʻO ka papahana kaʻana like huna a Shamir a ʻike i ka ʻike lehulehu kēlā ʻO ka papahana kaʻana like huna a Shamir. Mai kēia ʻike hiki iā ia ke hoʻoholo ʻO ka papahana kaʻana like huna a Shamir, like me ʻelua, a hoʻopili i nā waiwai i ʻike ʻia i loko o ke ʻano ʻO ka papahana kaʻana like huna a Shamir и ʻO ka papahana kaʻana like huna a Shamir.

ʻO ka papahana kaʻana like huna a Shamir

Hiki i ka mea hoʻouka ke loaʻa ʻO ka papahana kaʻana like huna a Shamir, helu ana ʻO ka papahana kaʻana like huna a Shamir:

ʻO ka papahana kaʻana like huna a Shamir

No ka mea, ua wehewehe mākou ʻO ka papahana kaʻana like huna a Shamir ma ke ʻano he mau helu maikaʻi i koho ʻole ʻia, aia ka helu palena o ka hiki ʻO ka papahana kaʻana like huna a Shamir. Ke hoʻohana nei i kēia ʻike, hiki i ka mea hoʻouka ke hoʻoholo ʻO ka papahana kaʻana like huna a Shamir, no ka mea, ʻoi aku ka nui ma mua o 5 e hana ʻO ka papahana kaʻana like huna a Shamir ʻinoʻino. He ʻoiaʻiʻo kēia ʻoiai ua hoʻoholo mākou ʻO ka papahana kaʻana like huna a Shamir

Hiki i ka mea hoʻouka ke helu i nā waiwai kūpono ʻO ka papahana kaʻana like huna a Shamirpani ana ʻO ka papahana kaʻana like huna a Shamir в ʻO ka papahana kaʻana like huna a Shamir:

ʻO ka papahana kaʻana like huna a Shamir

Me nā koho palena no ʻO ka papahana kaʻana like huna a Shamir akaka ka maʻalahi o ke koho a nānā i nā waiwai ʻO ka papahana kaʻana like huna a Shamir. ʻElima wale nō nā koho ma aneʻi.

Hoʻoholo i ka pilikia me ka helu helu integer palekana

No ka hoʻopau ʻana i kēia nāwaliwali, manaʻo ʻo Shamir e hoʻohana i ka helu helu modular, e hoʻololi ʻO ka papahana kaʻana like huna a Shamir maluna o ʻO ka papahana kaʻana like huna a Shamirkahi ʻO ka papahana kaʻana like huna a Shamir и ʻO ka papahana kaʻana like huna a Shamir - ka hoʻonohonoho o nā helu prima a pau.

E hoʻomanaʻo koke kākou i ka hana ʻana o ka helu helu modular. ʻO ka uaki me nā lima he manaʻo kamaʻāina. Hoʻohana ʻo ia i kahi wati ʻO ka papahana kaʻana like huna a Shamir. I ka hala ʻana o ka lima hola i ka ʻumikūmālua, ua hoʻi hou i ka lima. ʻO kahi waiwai hoihoi o kēia ʻōnaehana ʻo ia ma ka nānā wale ʻana i ka uaki, ʻaʻole hiki iā mākou ke unuhi i ka nui o nā kipi i hana ʻia e ka lima hola. Eia nō naʻe, inā ʻike mākou ua hala ka lima hola i ʻehā mau manawa, hiki iā mākou ke hoʻoholo piha i ka helu o nā hola i hala me ka hoʻohana ʻana i kahi ʻano maʻalahi. ʻO ka papahana kaʻana like huna a Shamirkahi ʻO ka papahana kaʻana like huna a Shamir ʻo ko mākou māhele (eia ʻO ka papahana kaʻana like huna a Shamir), ʻO ka papahana kaʻana like huna a Shamir ʻo ia ka coefficient (ehia mau manawa e komo ai ka mea puʻunaue i ka helu kumu me ke koena ʻole, maanei ʻO ka papahana kaʻana like huna a Shamir), aii ʻO ka papahana kaʻana like huna a Shamir ʻO ke koena, ka mea maʻamau e hoʻihoʻi i kahi kelepona operator modulo (eia ʻO ka papahana kaʻana like huna a Shamir). ʻO ka ʻike ʻana i kēia mau waiwai āpau e ʻae iā mākou e hoʻoponopono i ka hoohalike no ʻO ka papahana kaʻana like huna a Shamir, akā inā haʻalele mākou i ka coefficient, ʻaʻole hiki iā mākou ke hoʻihoʻi i ka waiwai kumu.

Hiki iā mākou ke hōʻike pehea e hoʻomaikaʻi ai kēia i ka palekana o kā mākou papahana ma o ka hoʻohana ʻana i ka papahana i kā mākou hiʻohiʻona mua a me ka hoʻohana ʻana ʻO ka papahana kaʻana like huna a Shamir. ʻO kā mākou hana polynomial hou ʻO ka papahana kaʻana like huna a Shamir, a me na helu hou ʻO ka papahana kaʻana like huna a Shamir. I kēia manawa hiki i nā mea mālama kī ke hoʻohana hou i ka interpolation polynomial e kūkulu hou i kā mākou hana, ʻo kēia wale nō ka hoʻohui ʻana a me ka hoʻonui ʻana i nā hana me ka modulo reduction. ʻO ka papahana kaʻana like huna a Shamir (ea ʻO ka papahana kaʻana like huna a Shamir).

Ke hoʻohana nei i kēia hiʻohiʻona hou, e manaʻo mākou ua aʻo ka mea hoʻouka i ʻelua o kēia mau mea hou, ʻO ka papahana kaʻana like huna a Shamir, a me ka ʻike lehulehu ʻO ka papahana kaʻana like huna a Shamir. I kēia manawa, hoʻopuka ka mea hoʻouka, ma muli o nā ʻike āpau i loaʻa iā ia, i nā hana aʻe, kahi ʻO ka papahana kaʻana like huna a Shamir ʻo ia ka hoʻonohonoho o nā huina maikaʻi a pau, a ʻO ka papahana kaʻana like huna a Shamir hōʻike i ke koena modulus ʻO ka papahana kaʻana like huna a Shamir.

ʻO ka papahana kaʻana like huna a Shamir

I kēia manawa, ʻike hou kā mākou mea hoʻouka ʻO ka papahana kaʻana like huna a Shamir, helu ana ʻO ka papahana kaʻana like huna a Shamir:

ʻO ka papahana kaʻana like huna a Shamir

A laila hoʻāʻo hou ʻo ia ʻO ka papahana kaʻana like huna a Shamirpani ana ʻO ka papahana kaʻana like huna a Shamir в ʻO ka papahana kaʻana like huna a Shamir:

ʻO ka papahana kaʻana like huna a Shamir

I kēia manawa he pilikia koʻikoʻi kāna. Nalo nā kumu waiwai ʻO ka papahana kaʻana like huna a Shamir, ʻO ka papahana kaʻana like huna a Shamir и ʻO ka papahana kaʻana like huna a Shamir. No ka mea he helu pau ʻole o nā hui ʻana o kēia mau ʻano, ʻaʻole hiki iā ia ke loaʻa i nā ʻike hou aʻe.

Nā Manaʻo Palekana

Hōʻike ka papahana kaʻana like huna a Shamir palekana mai ka manaʻo o ka manaʻo ʻike. ʻO ia ke ʻano o ka makemakika ke kū kūʻē i ka mea hoʻouka me ka mana helu palena ʻole. Eia nō naʻe, loaʻa i ke kaapuni kekahi mau pilikia i ʻike ʻia.

No ka laʻana, ʻaʻole hana ka hoʻolālā a Shamir nā ʻāpana e nānā ʻia, ʻo ia hoʻi, hiki i nā kānaka ke hōʻike manuahi i nā ʻāpana hoʻopunipuni a keʻakeʻa i ka hoʻihoʻi ʻana i ka mea huna pololei. Hiki i ka mea mālama ʻāpana ʻino me ka ʻike kūpono ke hana i kahi ʻāpana ʻē aʻe ma o ka hoʻololi ʻana ʻO ka papahana kaʻana like huna a Shamir ma kou manao iho. Hoʻopau ʻia kēia pilikia me ka hoʻohana ʻana nā papahana kaʻana like huna, e like me ka papahana a Feldman.

ʻO kekahi pilikia ʻo ia ka lōʻihi o kekahi ʻāpana like me ka lōʻihi o ka mea huna e pili ana, no laila ua maʻalahi ka lōʻihi o ka mea huna. Hiki ke hoʻoponopono ʻia kēia pilikia me nā mea liʻiliʻi hoʻopaʻa lole mea huna me nā helu ʻokoʻa a hiki i ka lōʻihi paʻa.

ʻO ka mea hope loa, he mea nui e hoʻomaopopo i hiki i kā mākou hopohopo palekana ke hoʻonui aku ma mua o ka hoʻolālā ponoʻī. No nā noi cryptographic honua maoli, loaʻa pinepine ka hoʻoweliweli o ka hoʻouka ʻaoʻao ʻaoʻao kahi e hoʻāʻo ai ka mea hoʻouka e unuhi i ka ʻike pono mai ka manawa hoʻokō noi, ka hoʻopaʻa ʻana, nā ulia, etc. Inā he mea hopohopo kēia, pono e noʻonoʻo pono i ka wā o ka hoʻomohala ʻana i ka hoʻohana ʻana i nā mea pale e like me nā hana a me nā nānā manawa mau, pale ʻana i ka hoʻomanaʻo ʻana i ka disk, a me kekahi mau manaʻo ʻē aʻe ma waho o ke kiko o kēia ʻatikala.

Hōʻike

maluna o kēiaʻaoʻao Aia kahi hōʻike pānaʻi o ke kaʻana like huna a Shamir. Hōʻike ma muli o ka waihona ssss-js, ʻo ia iho kahi awa JavaScript o ka papahana kaulana manawa. E hoʻomaopopo i ka helu ʻana i nā waiwai nui ʻO ka papahana kaʻana like huna a Shamir, ʻO ka papahana kaʻana like huna a Shamir и ʻO ka papahana kaʻana like huna a Shamir lawe paha i kahi manawa.

Source: www.habr.com

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