第8回 CrypGeek勉強会

第8回 CrypGeek勉強会の資料です。

Transcript

1. ୈ8ճCrypGeek ษڧձ - ྔࢠ৘ใՊֶ - Tokyo Institute of Technology OHKAWA TAKEHIKO
2. ྔࢠ৘ใՊֶͱ͸? ྔࢠ৘ใՊֶ<> D D ྔࢠίϯϐϡʔλ ྔࢠ҉߸ ྔࢠ
   ςϨϙʔςʔγϣϯ
3. ͳͥྔࢠ৘ใՊֶ͕Ξπ͍ͷ͔? • ૉҼ਺෼ղ͕ૣ͘ղ͚Δɺ҉߸ղಡ • ૊߹ͤ࠷దԽ໰୊͕ૣ͘ղ͚Δ • ػցֶश΁ͷԠ༻ • ྔࢠίϯϐϡʔλͷ঎ۀԽ(D-Wave) • Google, IBM౳ͷاۀͷࢀೖ • ෺ྲྀɺҩྍɺ੡ༀɺۚ༥෼໺΁ͷԠ༻
4. ྔࢠྗֶͱ͸? 
   χϡʔτϯྗֶ ཻࢠ 
   ి࣓ؾֶ ೾ d
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sha1_base64="NEQuolWvNLQXm2O28snoUJqORI0=">AAACnHichVFdKwRRGH6Mr7W+FjdKSTaitL0jRa4UFyTla5dCmhlnOe3szDQzu2HzB9y4RK6IC/kRkht+gKT8Abmk3Ljw7uyUEN5pznnOc97nPc/bqzum9HyihzKlvKKyqjpSE62tq29ojDU1pzw75xoiadim7S7qmidMaYmkL31TLDqu0LK6KRb0zGjxfiEvXE/a1ry/5YiVrLZuybQ0NJ+pZM9mn9O7GotTgoLo+AnUEMQRxrQdu8Iy1mDDQA5ZCFjwGZvQ4PG3BBUEh7kVFJhzGcngXmAHUdbmOEtwhsZshtd1Pi2FrMXnYk0vUBv8ism/y8oOdNEdndML3dAFPdH7r7UKQY2ily3e9ZJWOKuNu61zb/+qsrz72PhU/enZRxpDgVfJ3p2AKXZhlPT57f2XueHZrkI3ndAz+z+mB7rmDqz8q3E2I2aP/vCjs5dS34/0zupbuqRTumdFlIemfh/RT5DqT6iUUGcG4iMT4fgiaEMnenhGgxjBOKaR5Dcl9nCAQ6VdGVMmlalSqlIWalrwJZTUB6T8mN4=</latexit> <latexit sha1_base64="NEQuolWvNLQXm2O28snoUJqORI0=">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</latexit> ૬ۭؒͷ࠲ඪ | i <latexit 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sha1_base64="El24i3QUOaiT2xpIda8rk3+OJug=">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</latexit> <latexit sha1_base64="El24i3QUOaiT2xpIda8rk3+OJug=">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</latexit> ෆ֬ఆੑݪཧ
5. 1 0 લఏ஌ࣝ1:ॏͶ߹Θͤ(Superposition) ೋॏεϦοτͷ࣮ݧ ɹిࢠॐ͔ΒిࢠΛ1ݸͣͭൃࣹͯ͠ɺ޲͜͏ଆͷ2ຊͷεϦοτΛ௨աͤ͞ Δɻ͢ΔͱεΫϦʔϯ൘ʹ͸ిࢠʹΑΔײޫͰ೾ͷׯবࣶ͕ඳ͔ΕΔ[2]ɻ
6. લఏ஌ࣝ1:ॏͶ߹Θͤ(Superposition) ྔࢠϏοτ(qubit)[3] ɹݹయϏοτ͸0͔1͔ͷͲͪΒ͔ͷঢ়ଶ͔͠ͱΔ͜ͱ͕Ͱ͖ͳ͍͕ɺྔࢠϏοτ͸ɺ0ͱ1͚ͩͰͳ͘0 ͱ1ͷঢ়ଶͷྔࢠྗֶతॏͶ߹Θͤঢ়ଶ΋ͱΔ͜ͱ͕Ͱ͖Δɻϒϥ-έοτه๏Ͱ͸ɺ1ྔࢠϏοτ͸ɺ ҎԼͷΑ͏ʹදݱ͞ΕΔɻ͜͜Ͱɺα, β͸ ؔ܎Λຬͨ͢ෳૉ਺Ͱ͋Δɻ͜ΕΛ؍ଌͨ͠ ࡍʹɺঢ়ଶ ΛಘΔ֬཰ ͸Ͱ͋Γɺ ঢ়ଶΛಘΔ֬཰͸ Ͱ͋Δɻಉ͡ه๏ͰݹయϏοτΛදݱ ͢Δͱɺ͸ɺͲͪΒ͔͕0Ͱɺ΋͏Ұํ͕1Ͱ͋Δɻ | i = ↵|0i + |1i <latexit sha1_base64="9jP9x7tmaODV5eFzfcNHTnvdEV8=">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</latexit> <latexit sha1_base64="9jP9x7tmaODV5eFzfcNHTnvdEV8=">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</latexit> <latexit sha1_base64="9jP9x7tmaODV5eFzfcNHTnvdEV8=">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</latexit> <latexit sha1_base64="9jP9x7tmaODV5eFzfcNHTnvdEV8=">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</latexit>
7. લఏ஌ࣝ1:ॏͶ߹Θͤ(Superposition) ྔࢠϏοτ(qubit) ɹྔࢠϏοτ͸ݹయϏοτͱ͸ҧ͍ɺ͔͔͚ͩͰ͸ͳ͘ɺͦͷlதؒతzͳঢ়ଶ΋औΔ͜ͱ͕Ͱ͖Δɻ ͳͲͷ஋ΛͱΔΘ͚Ͱ͸ͳ͍ɻ
   ͨͩ͠ɺॏͳΓ߹ͬͨঢ়ଶ͕อͨΕΔͷ͸ɺ୭΋؍ଌ͍ͯ͠ͳ͍ঢ়ଶʹݶΓɺͦΕΛ؍ଌ͢Δͱ͋Δ֬཰ Ͱcʼʹɺ·ͨผͷ֬཰ͰcʼʹͳΔɻ
   ɹݹయϏοτ͸ɺྫ͑͹ɺͭฒ΂ͨʻʼ΍ʻʼͱ͍ͬͨݸʑͷ৘ใΛݸผʹ͔͠ѻ͑ͳ͍͕ɺ ྔࢠϏοτͰ͸ɺcʼ͔Βcʼ·Ͱɺͭͷશͯͷঢ়ଶΛಉ࣌ʹѻ͑ΔɻݸྔࢠϏοτΛฒ΂Ε ͹ɺѻ͑Δঢ়ଶ͸ஹʹ΋ͳΓɺ͜ͷஹݸͷঢ়ଶʹରͯ͋͠ΔॲཧΛߦ͏ͱஹݸͷॏͶ߹Θͬͨ͞શͯ ͷঢ়ଶʹରͯ͠ฒྻతʹͦͷॲཧ͕ߦΘΕΔɻ
   ɹ΋ͪΖΜɺஹݸͷঢ়ଶͰಉ࣌ʹॲཧ͕ߦ͑ͨͱͯ͠΋ɺҰ౓ଌఆ͢Ε͹ɺͦͷதͷͲΕ͔ͭͷঢ়ଶ ͕֬཰తʹબ୒͞Εͯ͠·͏ɻͦΕͰ͸ҙຯ͕ͳ͍ͷͰɺ࠷ऴతʹɺཉ͍͠౴ͷঢ়ଶ͚ͩΛऔΓग़ͨ͢Ί ʹɺཉ͍͠౴͕ଌఆʹΑΓબ୒͞ΕΔ֬཰ΛߴΊΔ͜ͱ͕ඞཁ͕͋Δɻ͜ͷΑ͏ʹɺྔࢠܭࢉͰ͸ଌఆ͕ ܾఆతͳҙຯΛ࣋ͪɺଌఆͱ͍͏ॲཧʹࢸΔ·Ͱʹ͍͔ʹͯ͠ॏͶ߹Θͤঢ়ଶΛޮ཰Α͘ॲཧ͢Δ͔Λߟ ͑Δͷ͕ྔࢠΞϧΰϦζϜͷݚڀͰ͋Δɻ
8. લఏ஌ࣝ2: ྔࢠ΋ͭΕ(quantum entanglement) ɹҰํͷిࢠͷεϐϯঢ়ଶΛ؍ଌͨ͠ॠؒʹɺ΋͏Ұํͷిࢠͷεϐϯঢ়ଶ ͕ܾ·Δɻ ͜ΕʹΑΓɺ཭Εͨ৔ॴʹྔࢠঢ়ଶΛసૹ͢Δ͜ͱ͕Ͱ͖Δͱݴ ΘΕ͍ͯΔɻ(ྔࢠςϨϙʔςʔγϣϯ) 1 0 ? ?
9. લఏ஌ࣝ3: ྔࢠτϯωϧޮՌ ɹݹయྗֶతʹ͸৐Γӽ͑ΒΕͳ͍͸ͣͷϙςϯγϟϧোนΛཻࢠ͕͔͋ͨ ΋োนʹ͍͋ͨτϯωϧΛൈ͚͔ͨͷΑ͏ʹ௨ա͢Δ͜ͱ[4]ɻ
10. લఏ஌ࣝ4: ޫࢠͷภۃ ɹޫͷ࠷খ୯Ґ͸ޫࢠͰ͋Γɺޫࢠ͸ۭؒΛৼಈ͠ͳ͕ΒਐΉɻਐߦํ޲ͱ ৼಈͷ֯౓Λภۃͱ͍͏ɻภۃͷঢ়ଶΛ஌ΔͨΊʹ͸ɺภޫϑΟϧλͱ͍͏ εϦοτΛ࢖ͬͯ؍ଌ͢Δɻ
 ɹ

11. લఏ஌ࣝ4: ޫࢠͷภۃ ɹޫࢠͷภۃͷੑ࣭Λར༻ͯ͠ɺϏοτͱภۃΛ࣋ͭޫࢠΛ૬ޓʹม׵͢Δ ϧʔϧΛఆٛͰ͖Δ[8]ɻภۃεΩʔϜͱ͸ɺภޫϑΟϧλΛ૊Έ߹Θͤͨ΋ ͷͰ͋Δɻ
12. ྔࢠ҉߸
13. ྔࢠ҉߸? • ૉҼ਺෼ղͷࠔ೉ੑΛར༻ͯ͠ެ։伴҉߸(RSAํࣜ౳)ͷ҆શ͕୲อ͞Εͯ ͍ΔͷͰɺྔࢠίϯϐϡʔλʹΑͬͯૉҼ਺෼ղ͕ഁΒΕͯ͠·͏ͱةݥͰ ͋Δɻ
 → ྔࢠίϯϐϡʔλΛར༻ͨ͠ૉҼ਺෼ղͷΞϧΰϦζϜͷ঺հ • ྔࢠίϯϐϡʔλ͕࣮༻Խͨ͠ੈքͰ৽͍͠ྔࢠ଱ੑͷ͋Δ҉߸Λߟ͑Δඞ ཁ͕͋Δɻ
 → ྔࢠڞ௨伴҉߸ͱͦͷ伴഑ૹΞϧΰϦζϜͷ঺հ
14. ૉҼ਺෼ղ͕ղ͚Ε͹RSA͕ղ͚Δ!? • ެ։伴 e,Nɺൿີ伴 d, ϝοηʔδ m, ॺ໊ σ ͱ͢Δͱɹɹɹɹɹɹɹɹ Ͱ͋Δ Α͏ͳॺ໊͕ੜ੒͞ΕΔɻ(N͸ೋͭͷେ͖ͳૉ਺ p,q Λ͔͚ͨ΋ͷ N = p×q) • ݕূ͸ެ։伴ʹΑͬͯߦΘΕΔɻɹɹɹɹɹɹɹɹ Λຬͨ͢d,eͷଘࡏ͸ΦΠ ϥʔͷఆཧʹΑͬͯอূ͞ΕΔɻ • ΦΠϥʔͷఆཧ ਖ਼੔਺ a, m ͕ޓ͍ʹૉͰ͋Δͱ͖ɼҎԼ͕੒Γཱͭɻ ΦΠϥʔؔ਺ φ(m)͸ʮm ΑΓখ͍͞ਖ਼ͷ੔਺ͷ͏ͪɼmͱޓ͍ʹૉͳ਺ͷݸ਺ʯ = md modN <latexit sha1_base64="AcHk7/bnIdLA2hT6le1A2wlhQqw=">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</latexit> <latexit sha1_base64="AcHk7/bnIdLA2hT6le1A2wlhQqw=">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</latexit> <latexit sha1_base64="AcHk7/bnIdLA2hT6le1A2wlhQqw=">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</latexit> <latexit 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sha1_base64="tP4Md2HraJwE80lHzwl4Myu6fiQ=">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</latexit>
15. ૉҼ਺෼ղ͕ղ͚Ε͹RSA͕ղ͚Δ!? : ΦΠϥʔؔ਺ φ(m)͸ʮm ΑΓখ͍͞ਖ਼ͷ੔਺ͷ͏ͪɼmͱޓ͍ʹૉͳ਺ͷݸ਺ʯ • m͕ૉ਺pͷ࣌ɺm ΑΓখ͍͞ਖ਼ͷ੔਺ͷ͏ͪɼmͱޓ͍ʹૉͳ਺͸1, 2, ... p-1ͳͷͰɺφ(m) = p-1 ɻ • m͕N=p×q (ૉ਺p,q) ͷ࣌ɺm ΑΓখ͍͞ਖ਼ͷ੔਺ͷ͏ͪɼmͱޓ͍ʹૉͳ਺͸ 1, 2, ... p-1 ͱ 1, 2, ... q- 1 ͷ೚ҙͷ૊ΈͷੵͰ͋ΔͷͰɺφ(m) = (p - 1)(q - 1) ɻ • ͜ΕΑΓɺൿີ伴d͕ٻΊΒΕΔ[8]ɻ
 ެ։伴 e,Nɺॺ໊ σ ͸ط஌Ͱɺࠓɺ߹੒਺NͷૉҼ਺p, q͕ٻ·ͬͨ࣌ɺp, qΑΓφ(m)͕Θ͔ΔɻΦΠ ϥʔͷఆཧΑΓɺφ(m) = d+e-1ͱͳΔd, eͷଘࡏ͕ࣔ͞Εɺॺ໊ΛݕূͰ͖Δൿີ伴d͕ٻΊΒΕΔɻ • ެ։伴҉߸(RSA҉߸)ͷ҆શੑ͸ૉҼ਺෼ղͷࠔ೉ੑʹ݁ͼͭ͘ɻ
 a'(m) ⌘ 1 (mod m) <latexit sha1_base64="tP4Md2HraJwE80lHzwl4Myu6fiQ=">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</latexit> <latexit sha1_base64="tP4Md2HraJwE80lHzwl4Myu6fiQ=">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</latexit> <latexit sha1_base64="tP4Md2HraJwE80lHzwl4Myu6fiQ=">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</latexit> <latexit sha1_base64="tP4Md2HraJwE80lHzwl4Myu6fiQ=">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</latexit>
16. ShorͷૉҼ਺෼ղΞϧΰϦζϜ 1. ޓ͍ʹૉͳ਺̣,̰Λݟ͚ͭΔɻ
 ̣ͱ̰ͷ࠷େެ໿਺ gcd(N,a) ΛϢʔΫϦουͷޓআ๏Ͱܭࢉ͢Δɻ͜Ε͕̍Ͱͳ͔ͬͨ ΒҼ਺͕ݟ͔ͭͬͨ͜ͱʹͳΔɻgcd(N,a) ͕̍ͳΒ̣ͱ̰͸ޓ͍ʹૉͰ͋Δ͔Β࣍ͷε ςοϓʹਐΉɻ 2. Ґ਺́Λݟ͚ͭΔɻ
 ̣ͱ̰͕ޓ͍ʹૉͰ͋Δͱ͖ɺɹɹɹɹɹɹ Ͱ͋ΔΑ͏ͳ࠷খͳ́ΛҐ਺ʢOrder)ͱ ݺͿɻ̣ͱ̰͕ޓ͍ʹૉͰ͋Δͱ͖ɼNΑΓখ͍͞Ґ਺͕́ඞͣଘࡏ͢Δɻ(ϑΣϧϚʔ ͷখఆཧ [5]) ap 1 ⌘ 1 mod p <latexit sha1_base64="wv3hAjKr1ljg18MqtZ36AwC+Hrw=">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</latexit> <latexit sha1_base64="wv3hAjKr1ljg18MqtZ36AwC+Hrw=">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</latexit> <latexit sha1_base64="wv3hAjKr1ljg18MqtZ36AwC+Hrw=">AAACuXichVE9TxtBEH1c+HAcAk7SINFYWKA0sebSJHIapDRJZz4MSByx9o4Fb7gv7taWyMltivyBFFSgpIighRYhGvgBKELKH4goQUpDwfh8UpQgYE63+/btvNk3Gjt0VayJznqMB719/QO5h/lHg4+HhgtPns7FQTNyZM0J3CBasEUsXeXLmlbalQthJIVnu3LeXnvbuZ9vyShWgT+rN0K55IlVX60oR2im6oWi+JCEL8y2JdebqlU0rYrlCd2IvMQLlttWJawXSlSmNIo3gZmBErKoBoVDWFhGAAdNeJDwoRm7EIj5W4QJQsjcEhLmIkYqvZdoI8/aJmdJzhDMrvG6yqfFjPX53KkZp2qHX3H5j1hZxDid0g+6oGPaod90dWutJK3R8bLBu93VyrA+/GVk5s+9Ko93jcZf1Z2eNVbwOvWq2HuYMp0unK6+9enrxUxlejyZoG06Z/9bdEZH3IHfunS+T8npzTv82Oyl2/cvumL1CR3QN/rJijwPzfx/RDfB3MuySWVzikqT77Px5TCKMTznGb3CJN6hihq/+Rm72MO+8cYQRsP42E01ejLNM/wTRnwNbsakyQ==</latexit> <latexit sha1_base64="wv3hAjKr1ljg18MqtZ36AwC+Hrw=">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</latexit> ar ⌘ 1 mod p <latexit sha1_base64="ygMi2FtcJGMW2Ft6kTPY2HjfA5o=">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</latexit> <latexit sha1_base64="ygMi2FtcJGMW2Ft6kTPY2HjfA5o=">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</latexit> <latexit sha1_base64="ygMi2FtcJGMW2Ft6kTPY2HjfA5o=">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</latexit> <latexit sha1_base64="ygMi2FtcJGMW2Ft6kTPY2HjfA5o=">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</latexit>
17. ShorͷૉҼ਺෼ղΞϧΰϦζϜ 3. r ͕ۮ਺ͷͱ͖
 ࣜมܗͯ͠ɺɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ ΛಘΔͷͰɺ ɹɹɹɹɹɹɹɹɹ Ͱͳ͍͔͗Γ࠷େެ໿਺ ɹɹɹɹɹɹɹɹ·ͨ͸ ʊʊʊʊʊʊ_____͕Ҽ਺Λ༩͑Δɻ 4. ͕́ح਺·ͨ͸ɹɹɹɹɹɹɹɹɹ ͷͱ͖ɻ
 ผͷ̰ΛબΜͰɼ͕́ۮ਺Ͱ͋Γɼɹɹɹɹɹɹɹɹɹ Ͱͳ͍Α͏ͳ਺̰Λ ಘΔ·Ͱ̰Λม͑ͯ΍Ε͹Α͍ɻେࡶ೺ʹ͸ɼ֬཰50%Ҏ্Ͱ๬·͍̰͠Λ ಘΔ͜ͱ͕Ͱ͖ΔͷͰɼ͜ͷࢼߦ͸͙͢ʹऴΘΔɻ (ar/2 + 1)(ar/2 1) = integer ⇥ N <latexit sha1_base64="D0gZXTq800vFIH+UjCX3sSFHlvI=">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</latexit> <latexit 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sha1_base64="D0gZXTq800vFIH+UjCX3sSFHlvI=">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</latexit> <latexit sha1_base64="D0gZXTq800vFIH+UjCX3sSFHlvI=">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</latexit> ar/2 ± 1 ⌘ 0 mod N <latexit 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sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit> <latexit 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sha1_base64="bSyAKivgGBRfDjhK080124Z0m/Q=">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</latexit> <latexit sha1_base64="bSyAKivgGBRfDjhK080124Z0m/Q=">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</latexit> <latexit sha1_base64="bSyAKivgGBRfDjhK080124Z0m/Q=">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</latexit> ar/2 ± 1 ⌘ 0 mod N <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit> <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit> <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit> <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">AAACwHichVE9SxxRFD2Oxuia6KqNkGZwMUm1ubNNZCvRRhvxI6uCY5aZ8bn7cL525u2CDvsHBGsLKyUpQsq0CRLSxB8gIvgHQkoDaSxyd3YgJBJzh3nvvPPuue9crh26MlZEVz1ab9+D/ocDg7mhR4+HR/KjY2tx0IwcUXECN4g2bCsWrvRFRUnlio0wEpZnu2Ld3p3r3K+3RBTLwH+l9kKx5Vk1X+5Ix1JMVfPPrNdJ9KLU1s3Q0w3dFI2mbOlklk3PUvXIS7xgu22WF6v5AhUpDf0uMDJQQBZLQf4zTGwjgIMmPAj4UIxdWIj524QBQsjcFhLmIkYyvRdoI8faJmcJzrCY3eW1xqfNjPX53KkZp2qHX3H5j1ipY4ou6B3d0Fd6T9/o9p+1krRGx8se73ZXK8LqyMHE6s//qjzeFeq/Vfd6VtjBdOpVsvcwZTpdOF19a//oZrW8MpU8pVP6zv5P6Iq+cAd+64fzdlmsHN/jx2Yv3b6v6ZbV53RGb+iSFTkemvH3iO6CtVLRoKKxTIWZhWx8A3iCSTznGb3EDOaxhAq/eYgP+IhP2qxW1wKt0U3VejLNOP4Ibf8XbL2muw==</latexit> ar/2 ± 1 ⌘ 0 mod N <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit> <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit> <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit> <latexit sha1_base64="X7ukdjyqGNxZdp6H/mxqOcUHXJY=">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</latexit>
18. ShorͷૉҼ਺෼ղΞϧΰϦζϜ ̣Λͱ͠ɼૉҼ਺෼ղ͍ͨ͠ͱ͢Δɻ̰ͱͯ͠ΛͱΔͱɼ
    ̐ Q
    NPE
    Λ̿Λ͔̍Β࢝Ίͯܭࢉ ͢Δ<>ɻ
    
    NPE
    
    
    
    
    NPE
    
    
    
    
    
    NPE
    
    
    
    NPE
    
    
    
    Y
    
    
    
    NPE
    
    
    
    
    
    NPE
    
    
    
    NPE
    
    
    
    Y
    
    
    NPE
    
    
    
    
    NPE
    
    
    
    NPE
    
    
    
    Y
    
    
    NPE
    
    
    
    
    NPE
    
    
    
    NPE
    
    
    
    Y
    
    
    
    NPE
    
    
    
    
    NPE
    
    
    
    NPE
    
    
    
    Y
    
    
    
    NPE
    
    
    
    
    ͱͳΓɼ͜ͷ͋ͱ͸
    
    
    
    
    ʜͱଓ͘͜ͱʹͳΔɻ͕̿ɼɼɼʜͷͱ͖ʹ̐Q
    NPE
    ͕̍ʹͳΔ͜ͱ͕෼͔Δɻैͬͯ࠷খͷ̿͸Ͱ͋Γɼۮ਺Ͱ͋Δ͜ͱ͔Βɼ͜Ε͕Ґ਺Ͱ͋Δɻ
    ͜ͷͱ͖ɼ࠷େެ໿਺͸ϢʔΫϦουͷޓআ๏Ͱܭࢉͯ͠ɼ
    HDE BS
    
    
    / HDE 
    
    
     HDE 
     ɼ͔ͭ
    HDE BS
    
    
    / HDE 
    ʵ
    
     HDE 
     
    ͱͳ̣ͬͯʹ̏̑ͷૉҼ਺ͱͯ̑͠ͱ̓ΛಘΔ͜ͱ͕Ͱ͖ͨɻ
19. ShorͷૉҼ਺෼ղΞϧΰϦζϜ • ShorͷૉҼ਺෼ղͷΞϧΰϦζϜ͸ɺେ͖ͳ߹੒਺ʹରͯ͠΋ޮ཰తʹૉҼ ਺ΛܭࢉͰ͖Δ͜ͱ͕஌ΒΕ͍ͯΔɻ • ϢʔάϦουޓআ๏͸ݹయతίϯϐϡʔλͰޮ཰తʹܭࢉͰ͖ΔͷͰɺҐ਺r Λߴ଎ʹٻΊΔ͜ͱ͕՝୊Ͱ͋Δɻ • ͜ͷ཭ࢄతͳύλʔϯͷपظੑΛٻΊΔͨΊʹɺ཭ࢄϑʔϦΤม׵Λྔࢠί ϯϐϡʔλͰ࣮૷ͯ͠ɺૉҼ਺෼ղΛߴ଎ʹٻΊΒΕΔ[8]ɻ
20. ྔࢠڞ௨伴҉߸[8] ϥϯμϜʹภۃεΩʔϜΛੜ੒͠ɺରԠද͔ΒฏจmΛ҉߸Խ͢Δɻ෮߸ͷ ࡍ΋ಉ༷ʹରԠදΛར༻͢Δɻ
21. ྔࢠ҉߸ͷ҆શੑ[8] • ߈ܸऀ͸keyͷภۃεΩʔϜͷϦετΛ஌Βͳ͍ͨΊɺࣗΒݕग़ثΛར༻ ͯ͠ภۃΛௐ΂Δඞཁ͕͋Δɻ(ͨͩ͠ɺ؍ଌޙʹঢ়ଶ͕มԽ͢ΔͨΊɺ߈ ܸऀ͸Ұ౓͔͠؍ଌͷνϟϯε͕ͳ͍͜ͱʹ஫ҙɻ) ޡͬͨݕग़ثΛར༻͢Δͱɺ ͷ֬཰ͰޡΔ
22. ྔࢠ҉߸ͷ՝୊[8] • ྔࢠ௨৴Ͱ͸ޫࢠΛૹΔͨΊɺޫϑΝΠόʔ͕ඞཁʹͳΔɻ • ౪ௌΛड͚ͨͱ͖ʹྔࢠ৘ใ͕มԽ͢ΔͨΊʹ͸ɺඍऑͳޫͰ௨৴͠ͳ͚ Ε͹ͳΒͳ͍ɻ • ҉߸ͷૹड৴ʹ͸ݕग़ث͕ඞཁʹͳΔɻ • ૹड৴ऀͷؒͰൿີ伴Λڞ༗͓ͯ͘͠ඞཁ͕͋Δɻ
 →ྔࢠ伴഑ૹϓϩτίϧͷ׆༻
23. ྔࢠ伴഑ૹϓϩτίϧ[8]
24. ྔࢠ伴഑ૹϓϩτίϧ[8] 4FOEFS 3FDFJWFS ˣ&ODSZQU
25. ྔࢠ伴഑ૹϓϩτίϧ[8] 4FOEFS 3FDFJWFS ˣ&ODSZQU
26. ྔࢠ伴഑ૹϓϩτίϧ[8] 4FOEFS 3FDFJWFS ˣ&ODSZQU
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28. ྔࢠ伴഑ૹϓϩτίϧ[8] 4FOEFS 3FDFJWFS ˣ&ODSZQU
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    SBOEPN@LFZ LFZ ੺ͷ෦෼͸LFZͱSBOEPN@LFZͷภۃεΩʔ Ϝ͕౳͍͠ͷͰਖ਼͘͠%FDPEFग़དྷͯΔ͸ͣɻ
29. ྔࢠ伴഑ૹϓϩτίϧ[8] 4FOEFS 3FDFJWFS ˣ&ODSZQU
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    SBOEPN@LFZ LFZ ੺ͷ෦෼͸LFZͱSBOEPN@LFZͷภۃεΩʔ Ϝ͕౳͍͠ͷͰਖ਼͘͠%FDPEFग़དྷͯΔ͸ͣɻ ϥϯμϜʹ੺৭ͷத͔ΒϏοτΛબͿɻ྆ ऀ͸ͦͷϏοτʹ͍ͭͯ֬ೝ͢Δɻ
30. ྔࢠ伴഑ૹϓϩτίϧ[8] 4FOEFS 3FDFJWFS ˣ&ODSZQU
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31. ྔࢠ伴഑ૹϓϩτίϧ[8] 4FOEFS 3FDFJWFS ˣ&ODSZQU
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32. ྔࢠ伴഑ૹϓϩτίϧͷ҆શੑ[8] • 伴ͷൿಗੑ
 ߈ܸऀ͸࠷ऴతʹڞ௨伴ʹ࢖͏ϏοτҐஔ(྘Ґஔ)͸ಛఆͰ͖Δ͕ɺภۃ ͷঢ়ଶͦΕࣗମΛڞ༗ͨ͠Θ͚Ͱ͸ͳ͍ͷͰɺ伴ͦͷ΋ͷ͸Θ͔Βͳ͍ɻ ͜ͷ࣌ɺภۃͷ؍ଌ͕ඞཁʹͳΔ͕ɺ1/2Ͱݕग़ثΛؒҧ͑ͯɺ׬શʹڞ ௨伴ΛಛఆͰ͖ͳ͍ɻ • ౪ௌݕ஌
 ྆ऀ͕ϏοτͷมԽ͕ͳ͍͔νΣοΫ͢Δࡍ(੨৭ͷ࿮ͷϏοτΛௐ΂Δͱ ͖)ɺԾʹ߈ܸऀ͕ޡͬͨݕग़ثͰ੨৭ͷ࿮ͷϏοτΛ౪ௌͨ͠ͱ͖ɺ1/2 Ͱਖ਼͍݁͠Ռ͕ฦͬͯ͘Δ͕ɺϏοτͷ਺Λ૿΍͢͜ͱͰશͯҰக͢Δ֬ ཰Λ͔ͳΓ཈͑Δ͜ͱ͕Ͱ͖Δɻ

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