ื“ื™ ืคึผืึธืกื˜-ืงื•ื•ืึทื ื˜ื•ื ืงืจื™ืคึผื˜ืึธื’ืจืึทืคื™ืง ืึทืœื’ืขืจื™ื“ืึทื SIKE, ืื•ื™ืกื’ืขืงืœื™ื‘ืŸ ื“ื•ืจืš NIST, ืื™ื– ื ื™ืฉื˜ ืคึผืจืึธื˜ืขืงื˜ืขื“ ืคื•ืŸ ื›ืึทืงื™ื ื’ ืื•ื™ืฃ ืึท ืจืขื’ื•ืœืขืจ ืงืึธืžืคึผื™ื•ื˜ืขืจ

ืจืขืกืขืึทืจื˜ืฉืขืจืก ืคื•ืŸ ื“ื™ ืงืึทื˜ื”ืึธืœื™ืง ืื•ื ื™ื•ื•ืขืจืกื™ื˜ืขื˜ ืคื•ืŸ ืœืขื•ื•ื•ืขืŸ ื”ืึธื‘ืŸ ื“ืขื•ื•ืขืœืึธืคึผืขื“ ืึท ืžืขื˜ืึธื“ ืคื•ืŸ ืึทื˜ืึทืงื™ื ื’ ื“ื™ ืฉืœื™ืกืœ ืขื ืงืึทืคึผืกื•ืœืึทื˜ื™ืึธืŸ ืžืขืงืึทื ื™ื–ืึทื SIKE (ืกื•ืคึผืขืจืกื™ื ื’ื•ืœืึทืจ ื™ืกืึธื’ื ื™ ืงื™ื™ ืขื ืงืึทืคึผืกื•ืœืึทื˜ื™ืึธืŸ), ื•ื•ืึธืก ืื™ื– ื’ืขื•ื•ืขืŸ ืึทืจื™ื™ึทื ื’ืขืจืขื›ื ื˜ ืื™ืŸ ื“ื™ ืœืขืฆื˜ ืคื•ืŸ ื“ื™ ืคึผืึธืกื˜-ืงื•ื•ืึทื ื˜ื•ื ืงืจื™ืคึผื˜ืึธืกื™ืกื˜ืขืžืก ืคืึทืจืžืขืกื˜ ื’ืขื”ืืœื˜ืŸ ื“ื•ืจืš ื“ื™ ื™ื•. ืขืก. ื ืึทืฉืึทื ืึทืœ ืื™ื ืกื˜ื™ื˜ื•ื˜ ืคื•ืŸ ืกื˜ืึทื ื“ืึทืจื“ืก ืื•ืŸ ื˜ืขื›ื ืึธืœืึธื’ื™ืข (SIKE). ืื™ื– ืึทืจื™ื™ึทื ื’ืขืจืขื›ื ื˜ ืื•ืŸ ืึท ื ื•ืžืขืจ ืคื•ืŸ ื ืึธืš ืึทืœื’ืขืจื™ื“ืึทืžื– ื•ื•ืึธืก ื“ื•ืจื›ื’ืขื’ืื ื’ืขืŸ ื“ื™ ื”ื•ื™ืคึผื˜ ืกืขืœืขืงืฆื™ืข ืกื˜ืึทื’ืขืก, ืึธื‘ืขืจ ื’ืขืฉื™ืงื˜ ืคึฟืึทืจ ืจืขื•ื•ื™ื–ื™ืข ืฆื• ืขืœื™ืžื™ื ื™ืจืŸ ื‘ืึทืžืขืจืงื•ื ื’ืขืŸ ืื™ื™ื“ืขืจ ื–ื™ื™ ื˜ืจืึทื ืกืคืขืจื“ ืฆื• ื“ืขืจ ืงืึทื˜ืขื’ืึธืจื™ืข ืคื•ืŸ โ€‹โ€‹ืจืขืงืึทืžืขื ื“ื™ื“). ื“ื™ ืคืืจื’ืขืœื™ื™ื’ื˜ ื‘ืึทืคืึทืœืŸ ืื•ืคึฟืŸ ืึทืœืึทื•ื–, ืื•ื™ืฃ ืึท ืจืขื’ื•ืœืขืจ ืคึผืขืจื–ืขื ืœืขืš ืงืึธืžืคึผื™ื•ื˜ืขืจ, ืฆื• ืฆื•ืจื™ืงืงืจื™ื’ืŸ ื“ื™ ื•ื•ืขืจื˜ ืคื•ืŸ ื“ื™ ืฉืœื™ืกืœ ื’ืขื ื™ืฆื˜ ืคึฟืึทืจ ืขื ืงืจื™ืคึผืฉืึทืŸ ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ื“ื™ SIDH (Supersingular Isogeny Diffie-Hellman) ืคึผืจืึธื˜ืึธืงืึธืœ ื’ืขื ื™ืฆื˜ ืื™ืŸ SIKE.

ื ืคืึทืจื˜ื™ืง ื™ืžืคึผืœืึทืžืขื ื˜ื™ื™ืฉืึทืŸ ืคื•ืŸ ื“ื™ SIKE ื›ืึทืงื™ื ื’ ืื•ืคึฟืŸ ืื™ื– ืืจื•ื™ืก ื•ื•ื™ ืึท ืฉืจื™ืคื˜ ืคึฟืึทืจ ื“ื™ ืžืึทื’ืžืึท ืึทืœื’ืขื‘ืจืึทื™ืง ืกื™ืกื˜ืขื. ืฆื• ืฆื•ืจื™ืงืงืจื™ื’ืŸ ื“ื™ ืคึผืจื™ื•ื•ืึทื˜ ืฉืœื™ืกืœ ื’ืขื ื™ืฆื˜ ืฆื• ืขื ืงืจื™ืคึผื˜ ื–ื™ื›ืขืจ ื ืขืฅ ืกืขืฉืึทื ื–, ื ื™ืฆืŸ ื“ื™ SIKEp434 (ืžื“ืจื’ื” 1) ืคึผืึทืจืึทืžืขื˜ืขืจ ืฉื˜ืขืœืŸ ืื•ื™ืฃ ืึท ืื™ื™ืŸ-ื”ืึทืจืฅ ืกื™ืกื˜ืขื, ืขืก ื’ืขื ื•ืžืขืŸ 62 ืžื™ื ื•ื˜, SIKEp503 (ืžื“ืจื’ื” 2) - 2 ืฉืขื” 19 ืžื™ื ื•ื˜, SIKEp610 (ืžื“ืจื’ื” 3) - 8 ืฉืขื” 15 ืžื™ื ื•ื˜, SIKEp751 (ืžื“ืจื’ื” 5) - 20 ืฉืขื” 37 ืžื™ื ื•ื˜. ืขืก ื”ืึธื˜ ื’ืขื“ื•ื™ืขืจื˜ ืจื™ืกืคึผืขืงื˜ื™ื•ื•ืœื™ 182 ืื•ืŸ 217 ืžื™ื ื•ื˜ ืฆื• ืกืึธืœื•ื•ืข ื“ื™ ืคืึทืจืžืขืกื˜ ื˜ืึทืกืงืก $ IKEp4 ืื•ืŸ $ IKEp6 ื“ืขื•ื•ืขืœืึธืคึผืขื“ ื“ื•ืจืš ืžื™ื™ืงืจืึธืกืึธืคึฟื˜.

ื“ื™ SIKE ืึทืœื’ืขืจื™ื“ืึทื ืื™ื– ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ื“ื™ ื ื•ืฆืŸ ืคื•ืŸ ืกื•ืคึผืขืจืกื™ื ื’ื•ืœืึทืจ ื™ืกืึธื’ืขื ื™ (ืกื™ืจืงืœื™ื ื’ ืื™ืŸ ืึท ืกื•ืคึผืขืจืกื™ื ื’ื•ืœืึทืจ ื™ืกืึธื’ืขื ื™ืข ื’ืจืึทืคื™ืง) ืื•ืŸ ืื™ื– ื’ืขื•ื•ืขืŸ ื‘ืื˜ืจืื›ื˜ ื“ื•ืจืš NIST ื•ื•ื™ ืึท ืงืึทื ื“ื™ื“ืึทื˜ ืคึฟืึทืจ ืกื˜ืึทื ื“ืขืจื“ื™ื–ื™ื™ืฉืึทืŸ, ื•ื•ื™ื™ึทืœ ืขืก ืื™ื– ื’ืขื•ื•ืขืŸ ืึทื ื“ืขืจืฉ ืคื•ืŸ ืื ื“ืขืจืข ืงืึทื ื“ืึทื“ื™ื™ืฅ ืื™ืŸ ื–ื™ื™ืŸ ืงืœืขื ืกื˜ืขืจ ืฉืœื™ืกืœ ื’ืจื™ื™ืก ืื•ืŸ ืฉื˜ื™ืฆืŸ ืคึฟืึทืจ ื’ืื ืฅ ืคืึธืจื•ื™ืก ื‘ืขืกืึธื“ื™ืงื™ื™ึทื˜ (ืงืึธืžืคึผืจืึทืžื™ื™ื–ื™ื ื’ ืื™ื™ื ืขืจ) ืคื•ืŸ ื“ื™ ืœืึทื ื’-ื˜ืขืจืžื™ืŸ ืฉืœื™ืกืœืขืŸ ื˜ื•ื˜ ื ื™ืฉื˜ ืœืึธื–ืŸ ื“ืขืงืจื™ืคึผื˜ื™ืึธืŸ ืคื•ืŸ ืึท ืคืจื™ืขืจ ื™ื ื˜ืขืจืกืขืคึผื˜ืึทื“ ืกืขืกื™ืข). SIDH ืื™ื– ืึทืŸ ืึทื ืึทืœืึธื’ ืคื•ืŸ ื“ื™ Diffie-Hellman ืคึผืจืึธื˜ืึธืงืึธืœ ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ืกืขืจืงืœื™ื ื’ ืื™ืŸ ืึท ืกื•ืคึผืขืจืกื™ื ื’ื•ืœืึทืจ ื™ืกืึธื’ืขื ื™ืง ื’ืจืึทืคื™ืง.

ื“ื™ ืืจื•ื™ืก SIKE ืงืจืึทืงื™ื ื’ ืื•ืคึฟืŸ ืื™ื– ื‘ืื–ื™ืจื˜ ืื•ื™ืฃ ื“ื™ 2016 ืคืืจื’ืขืœื™ื™ื’ื˜ ืึทื“ืึทืคึผื˜ื™ื•ื• ื’ืคึผืกื˜ (Galbraith-Petit-Shani-Ti) ื‘ืึทืคืึทืœืŸ ืื•ื™ืฃ ืกื•ืคึผืขืจืกื™ื ื’ื•ืœืึทืจ ื™ืกืึธื’ืขื ื™ืง ืฉืœื™ืกืœ ืขื ืงืึทืคึผืกื•ืœืึทื˜ื™ืึธืŸ ืžืขืงืึทื ื™ื–ืึทืžื– ืื•ืŸ ืขืงืกืคึผืœื•ื™ืฅ ื“ื™ ืขืงื–ื™ืกื˜ืขื ืฅ ืคื•ืŸ ืึท ืงืœื™ื™ืŸ ื ื™ื˜-ืกืงืึทืœืึทืจ ืขื ื“ืึธืžืึธืจืคื™ืกื ืื™ืŸ ื“ื™ ืึธื ื”ื™ื™ื‘ ืคื•ืŸ ื“ื™ ื•ื™ืกื‘ื™ื™ื’, ื’ืขืฉื˜ื™ืฆื˜ ื“ื•ืจืš ื ืึธืš. ืื™ื ืคึฟืึธืจืžืึทืฆื™ืข ื•ื•ืขื’ืŸ ื“ื™ ื˜ืึธืจืกื™ืึธืŸ ืคื•ื ื˜ ื˜ืจืึทื ืกืžื™ื˜ื˜ืขื“ ื“ื•ืจืš ืึทื’ืขื ืฅ ื™ื ื˜ืขืจืึทืงื˜ื™ื ื’ ืื™ืŸ ื“ืขื ืคึผืจืึธื˜ืึธืงืึธืœ.

ืžืงื•ืจ: opennet.ru

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