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勉強会7.pdf
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titech.crypto
June 10, 2018
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勉強会7.pdf
titech.crypto
June 10, 2018
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Transcript
౦େϒϩοΫνΣʔϯݚڀձ $SZQHFFL ษڧձ 4DIOPSSॺ໊ͰͷίϯύΫτ͔ͭߴͳ ϚϧνγάωνϟΛ࣮ݱ͢ΔΈ !NBOFLJOFLP@TPM
#JUDPJO4DSJQU w νϡʔϦϯάෆશͳTUBDL CBTFEݴޠͰɺ#JUDPJOͷ USBOTBDUJPOݕূʹ༻͞ΕΔ w TUBDLঢ়ʹੵΈॏͳͬͨσʔλ ߏͱɺσʔλߏΛૢ࡞͢Δ TDSJQUͰߏ͞ΕΔ w
جຊૢ࡞ TDSJQUͷΛTUBDLʹอଘɺ ຢԋࢉΛ࣮ߦ͢Δ ࣮ߦΧʔιϧΛҰͭࠨ ͷૢ࡞Δ ਤҾ༻.BTUFSJOH#JUDPJOQ 'JH
w 6OMPDLJOH4DSJQU w ॺ໊ऀ͕ॴ༗͢Δ6590Λࢧ͍ʹ༻͢ΔͨΊͷॺ໊ͱɺࣗ ͷެ։伴ΛؚΉ w 5SBOTBDUJPOͷJOQVUʹهࡌ͞ΕΔ w -PDLJOH4DSJQU w
ࢧઌͷΞΧϯτͷެ։伴ʢͷϋογϡʣͱԋࢉࢠΛؚΉ w 5SBOTBDUJPOͷPVUQVUʹهࡌ͞ΕΔ w ݕূʹ6OMPDLJOH4DSJQU -PDLJOH4DSJQU͕༻͞ΕΔ ͭͷ#JUDPJO4DSJQU TJH1VC, 6OMPDLJOH 4DSJQU %61)"4)1VC,)BTI&26"-7&3*':$)&$,4*( -PDLJOH4DSJQU
5SBOTBDUJPOͷݕূ4DSJQUͷݕূ TJH1VC, 6OMPDLJOH 4DSJQU %61)"4)1VC,)BTI&26"-7&3*':$)&$,4*( -PDLJOH4DSJQU 0VUQVU *OQVU 5SBOTBDUJPO ݕূ
:FT /P ϒϩοΫνΣʔϯʹهɺDPOpSNBUJPO غ٫
4DSJQUͷݕূྲྀΕᶃ ਤҾ༻.BTUFSJOH#JUDPJOQ 'JH
4DSJQUͷݕূྲྀΕᶄ ਤҾ༻.BTUFSJOH#JUDPJOQ 'JH
#JUDPJOUSBOTBDUJPOͷछྨ w #JUDPJOͰͷUSBOTBDUJPOͷछྨओʹ̏ͭɻઌఔѻͬͨͷɺ ݱߦͰओྲྀͳ11,)ํࣜɻ w 1BZUP1VCMJD,FZ 11, w ެ։伴ࣗମΛݕূʹ༻͢ΔɻैདྷΘΕ͍͕ͯͨɺ
USBOTBDUJPO༰ྔ͕େ͖͍ͨΊ11,)ʹସ͞Ε͍ͯΔɻ w 1BZUP1VCMJD,FZ)BTI 11,) w ެ։伴 CZUF ͷϋογϡʢCZUFʣΛ༻͍Δ͜ͱͰ USBOTBDUJPO༰ྔΛ͍͑ͯΔɻ w 1BZUP4DSJQU)BTI 14) w ࢧ͍࣌ͷ-PDLJOHTDSJQUΛҰ෦VOMPDLJOHଆʹճ͢͜ͱ ͰɺϚϧνγάࢧ͍ऀͷίετΛ͑Δɻʢ͑ͨίε τड͚ख͕কདྷෛ୲͢ΔΈʣ ৄࡉ.BTUFSJOH#JUDPJOQΛࢀর
#JUDPJO4DSJQUͰͷϚϧνγά w #JUDPJOͰNPGOϚϧνγάωνϟʢOਓͷ͏ͪNਓ͕ ॺ໊͢Ε༗ޮʣ͕࣮͞Ε͍ͯΔɻ w -PDLJOHTDSJQU w 6OMPDLJOHTDSJQU 01@4JH4JHʜ N1,1,ʜ1,OO01@$)&$,.6-5*4*(
01@$)&$,.6-5*4*(NதͷOݸͷ伴ʹରԠͨ͠ॺ໊͕͋Δ͔Λ֬ೝ͢Δૢ࡞ ͜͜ͰNݸͷத͔ΒҙͷOݸͷॺ໊͕ඞཁ Ϛϧνγάॺ໊ऀͷશͯͷެ։伴͕ඞཁ
#JUDPJOTDSJQUϚϧνγάͷαΠζ 01@4JH4JHʜ N1,1,ʜ1,OO01@$)&$,.6-5*4*( TJH1VC, 6OMPDLJOH 4DSJQU %61)"4)1VC,)BTI&26"-7&3*':$)&$,4*( -PDLJOH4DSJQU w γϯάϧγάωνϟ
w Ϛϧνγάωνϟ ݱߦͷ#JUDPJOͰ&$%4"ॺ໊Λ༻͓ͯ͠Γɺ NPGOํࣜͰNݸͷެ։伴ͱOݸͷ ॺ໊͚ͩTDSJQUαΠζ͕૿େʂ
4DIOPSSॺ໊ͷಛ w طଘͷ#JUDPJO &UIFSFVNʹ࣮͞Ε͍ͯΔପԁۂઢॺ໊ΞϧΰϦ ζϜʢ&$%4"ʣΑΓσʔλྔ͕খ͘͞ɺݕূ͕ߴͳॺ໊Λ࣮ݱ Մೳ w γϯάϧγάωνϟͱಉ༷ͷσʔλαΠζͰɺηΩϡϦςΠత ੑ˞ΛอͪͭͭɺΑΓϓϥΠόγʔΛอޢͨ͠Ϛϧνγάωνϟ Λ࣮Ͱ͖Δ
˞࣮ͷํ๏ʹΑͬͯɺࢄରʢ%-ʣʹΑΔ҆શੑΛΫϦΞ͢ΔͷͱɺΑΓ҆શཁٻ͕ߴ͍ϫϯ ϞΞࢄରʢ0.%-ʣΛΫϦΞ͢Δͷ͕͋Δɻৄࡉޙड़ɻ ˞4IOPSSॺ໊ࣗମʹ͍ͭͯલճʢ$SZQHFFLษڧձʣΛࢀর 5PEBZ`TUPQJD 4DIOPSSॺ໊ʹΑΔσʔλྔ͕খ͘͞ɺ ߴͳσδλϧॺ໊ͷΈͷղઆ
4DIOPSSॺ໊ʹΑΔσʔλݮ w 4DIOPSSॺ໊͕ϒϩοΫνΣʔϯͷσʔλྔΛݮ͢Δํ๏Ҏ Լͷͭʹ͚ͯߟ͑ΒΕΔ &$%4"ॺ໊ൺͰॺ໊͋ͨΓͷσʔλαΠζ͕খ͍͞ &$%4" 4JHdCZUFT 4DIOPSS4JHdCZUFTʣ
伴ूʹΑΔγϯάϧγάಉͷαΠζͷϚϧνγάͷ࣮ݱˠ #JUPDJO5YPVUQVUͷσʔλݮɺݕূ༻ॺ໊ͷݮ ҟͳΔϝοηʔδʹର͢Δॺ໊ूˠෳJOQVUΛ࣋ͭ5Yͷॺ໊ Λݮ #1"4& #MPDLDIBJO1SPUPDPM"OBMZTJTBOE4FDVSJUZ&OHJOFFSJOH ʹͯ 1JFUFS8VJMMFࢯ͜ͷ伴ूํ๏ʹΑͬͯ#JUDPJO5Yͷଞͷ෦Λͦͷ··Ͱ ͷσʔλݮ͕Մೳͩͱ༧ଌ
4DIOPSSॺ໊ͷදݱ w ຊষͰѻ͏4DIOPSSॺ໊ͷܗࣜ ॺ໊ 3 T S( ) 9
3 N Y ݕূT(3 ) 9 3 N 9 ˞લճͷࢿྉʢ҉߸ֶͷશͯ४ڌʣͷܗࣜͱ4DIOPSSॺ໊ͷܗ͕ࣜҟͳ͍ͬͯΔɻ͜ͷҧ͍ʹ͍ͭͯௐࠪ ͕ͨ͠ɺ૬ޓͷมํ๏ͳͲݟͨΒͳ͔ͬͨɻཁௐࠪɻࠓճ͜ͷܗࣜͰΛਐΊΔɻ Sॺ໊ऀʹΑͬͯબ͞ΕͨϥϯμϜϊϯε Yൿີ伴 9ެ։伴
࣍ ࠓճNPGNϚϧνγάωνϟͷͭͷख๏Λհ ୯७ͳϚϧνγάʢ/BJWF4DIOPSSNVMUJTJHʣ w 伴ूʹΑΔίϯύΫτͳ4DIOPSSॺ໊ܗࣜͷϚϧνγάɻ ୠ͠3PHVF,FZ߈ܸʹΑΔ੬ऑੑ͋Γɻ #FMMBSF/FWFOϚϧνγά w
3PHVF,FZ߈ܸੑΛ֬อ͍ͯ͠Δ͕ɺ伴ू͕Ͱ͖ͣɺ 4DIOPSSॺ໊ͷܗ͔ࣜΒͯ͠͠·͏ɻ .V4JHϚϧνγά w 3PHVF,FZ߈ܸੑΛ֬อͭͭ͠ɺ伴ूɺ4DIOPSSॺ໊ ܗࣜʹ४ڌɻ
୯७ͳϚϧνγάωνϟ࣮ J൪ͷਓʢJOʣࣗͷϥ ϯμϜϊϯεSJΛܾΊͯɺޓ͍ʹ3JSJ( ͱެ։伴9JΛڞ༗͢Δ ڞ༗ใ͔ΒOݸͷެ։伴9JͷͰ͋Δ 9 3JͷͰ͋Δ3Λܭࢉ͢Δ ͦΕͧΕͷॺ໊ऀ TJSJ )
9 3 N YJΛܭࢉ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূT(3 ) 9 3 N 9 ڞ༗ใ SSS 33 3 3 99 9 9 3J 9J ڞ༗ใͷ࡞ɾڞ༗
୯७ͳϚϧνγάωνϟ࣮ J൪ͷਓʢJOʣࣗͷϥϯ μϜϊϯεSJΛܾΊͯɺޓ͍ʹ3JSJ(ͱ ެ։伴9JΛڞ༗͢Δ ڞ༗ใ͔ΒOݸͷެ։伴9JͷͰ͋Δ 9 3JͷͰ͋Δ3Λܭࢉ͢Δ ͦΕͧΕͷॺ໊ऀ TJSJ )
9 3 N YJΛܭࢉ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূT(3 ) 9 3 N 9 ڞ༗ใ SSS 33 3 3 99 9 9 3J 9J ڞ༗ใͷ࡞ɾڞ༗
୯७ͳϚϧνγάωνϟ࣮ ڞ༗ใ SSS 33 3 3 99 9 9 3
9 3J TJ SJ( SJ ) 9 3 N YJ J൪ͷਓʢJOʣࣗͷϥϯ μϜϊϯεSJΛܾΊͯɺޓ͍ʹ3JSJ(ͱ ެ։伴9JΛڞ༗͢Δ ڞ༗ใ͔ΒOݸͷެ։伴9JͷͰ͋Δ 9 3JͷͰ͋Δ3Λܭࢉ͢Δ ͦΕͧΕͷॺ໊ऀ TJSJ ) 9 3 N YJΛܭࢉ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূT(3 ) 9 3 N 9
୯७ͳϚϧνγάωνϟ࣮ 3 T 3 T 3 T ݕূऀ T(3 )
9 3 N 9 J൪ͷਓʢJOʣࣗͷϥϯ μϜϊϯεSJΛܾΊͯɺޓ͍ʹ3JSJ(ͱ ެ։伴9JΛڞ༗͢Δ ڞ༗ใ͔ΒOݸͷެ։伴9JͷͰ͋Δ 9 3JͷͰ͋Δ3Λܭࢉ͢Δ ͦΕͧΕͷॺ໊ऀ TJSJ ) 9 3 N YJΛܭࢉ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূT(3 ) 9 3 N 9
୯७ͳϚϧνγάωνϟ࣮ 3 T 3 T 3 T ݕূऀ T(3 )
9 3 N 9 J൪ͷਓʢJOʣࣗͷϥϯ μϜϊϯεSJΛܾΊͯɺޓ͍ʹ3JSJ(ͱ ެ։伴9JΛڞ༗͢Δ ڞ༗ใ͔ΒOݸͷެ։伴9JͷͰ͋Δ 9 3JͷͰ͋Δ3Λܭࢉ͢Δ ͦΕͧΕͷॺ໊ऀ TJSJ ) 9 3 N YJΛܭࢉ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূT(3 ) 9 3 N 9
୯७ͳϚϧνγάωνϟ࣮ 3 T 3 T 3 T ݕূऀ T(3 )
9 3 N 9 J൪ͷਓʢJOʣࣗͷϥϯ μϜϊϯεSJΛܾΊͯɺޓ͍ʹ3JSJ(ͱ ެ։伴9JΛڞ༗͢Δ ڞ༗ใ͔ΒOݸͷެ։伴9JͷͰ͋Δ 9 3JͷͰ͋Δ3Λܭࢉ͢Δ ͦΕͧΕͷॺ໊ऀ TJSJ ) 9 3 N YJΛܭࢉ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূT(3 ) 9 3 N 9 ֤ਓͷॺ໊ू͞Εɺݕূ ࣌ʹू͞Εͨެ։伴9ͷ ΈΘΕ͍ͯΔɻ֤ਓͷެ։ 伴9JΘΕ͍ͯͳ͍ɻ
୯७ͳϚϧνγάωνϟ࣮ʹΑΔ伴ू ϚϧνγάΞΧϯτͷެ։伴͕9ʹू͞Εɺૹۚ࣌ʹ̍ͭͷ伴 9ʹඥ͍ͨΞυϨεΛࢦఆ͢Δ͚ͩͰྑ͍ɻ ݕূ4DSJQU͕γϯάϧγάͱಉαΠζʢߴʣ ϚϧνγάΞΧϯτ ެ։伴9 9 9 9 TJH49
6OMPDLJOH 4DSJQU %61)"4)9)BTI&26"-7&3*':$)&$,4*( -PDLJOH4DSJQU 伴ूૹۚ࣌ॲཧ͕ಛघͰͳ͘ɺίϯύΫτɺ͔ͭߴݕূ
3PHVF,FZ߈ܸ w ͜ͷ୯७ͳ伴ू๏͋Δॺ໊ऀ͕ެ։伴ΛِΔ͜ͱͰɺͻͱΓ Ͱॺ໊ݕূΛޭͤ͞Δ߈ܸ͕࣮ݱՄೳ ΞϦεʢެ։伴9"ʣͱϘϒʢެ։伴9#ʣͷϚϧνγάʹͯɺϘ ϒ͕ѱऀͳ߹Λߟ͑Δ ެ։伴Λڞ༗͢Δஈ֊ͰɺΞϦεͷެ։伴9"͔Β9#`9#9" Λٯࢉͯ͠ɺ9#`ΛϘϒͷެ։伴ͱͯ͠ެ։͢Δ
ݕূऀʹΑΔ伴ूͰɺ99#` 9"9#9" 9"9# ͱͳΓɺϘϒͷൿີ伴ͷΈͰॺ໊ݕূ͕௨ͬͯ͠·͏ w ͜ͷ3PVHF,FZ߈ܸΛ͙ʹɺͦΕͧΕͷެ։伴ʹରԠ͢Δൿ ີ伴Λॴ༗͍ͯ͠Δ͜ͱΛఏࣔ͢Δඞཁ͕͋Δ͕ɺ͜Ε໘ɻ ެ։伴ͷΈͷอ༗Ͱྑ͍؆ૉެ։伴Ϟσϧ 1MBJO1VCMJD,FZ .PEFM Λຬͨ͢ΞϧΰϦζϜ͕CFUUFS
#FMMBSF/FWFOʹΑΔϚϧνγά࣮ ڞ༗ใ SSʜ 33 3 ʜ -) 9 9 ʜ
9J ) 3J 3J J൪ͷਓʢJOʣࣗ ͷϥϯμϜϊϯεSJΛܾΊͯɺޓ͍ ʹ9J ) 3JSJ( 3JΛڞ༗ ڞ༗͞Εͨใ͔Βɺ-ͱू͞Ε ͨ3ΛಘΔ ͦΕͧΕͷॺ໊ऀ TJSJ ) - 9J 3 N YJΛ࡞ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূ T(3 ) - 9 3 N 9 ) - 9 3 N 9 ʜ ʜ
#FMMBSF/FWFOʹΑΔϚϧνγά࣮ ڞ༗ใ SSʜ 33 3 ʜ -) 9 9 ʜ
9J ) 3J 3J J൪ͷਓʢJOʣࣗͷ ϥϯμϜϊϯεSJΛܾΊͯɺޓ͍ʹ 9J ) 3JSJ( 3JΛڞ༗ ڞ༗͞Εͨใ͔Βɺ-ͱू͞Ε ͨ3ΛಘΔ ͦΕͧΕͷॺ໊ऀ TJSJ ) - 9J 3 N YJΛ࡞ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূ T(3 ) - 9 3 N 9 ) - 9 3 N 9 ʜ ʜ
#FMMBSF/FWFOʹΑΔϚϧνγά࣮ ڞ༗ใ SSʜ 33 3 ʜ -) 9 9 ʜ
- 3 TJSJ ) - 9J 3 N YJ J൪ͷਓʢJOʣࣗͷ ϥϯμϜϊϯεSJΛܾΊͯɺޓ͍ʹ 9J ) 3JSJ( 3JΛڞ༗ ڞ༗͞Εͨใ͔Βɺ-ͱू͞Ε ͨ3ΛಘΔ ͦΕͧΕͷॺ໊ऀ TJSJ ) - 9J 3 N YJΛ࡞ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূ T(3 ) - 9 3 N 9 ) - 9 3 N 9 ʜ ʜ
J൪ͷਓʢJOʣࣗͷ ϥϯμϜϊϯεSJΛܾΊͯɺޓ͍ʹ9J ) 3JSJ( 3JΛڞ༗ ڞ༗͞Εͨใ͔Βɺ-ͱू͞Εͨ 3ΛಘΔ ͦΕͧΕͷॺ໊ऀ TJSJ
) - 9J 3 N YJΛ࡞ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূ #FMMBSF/FWFOʹΑΔϚϧνγά࣮ 3 T 3 T ݕূऀ T(3 ) - 9 3 N 9 ) - 9 3 N 9 ʜ 33 3 ʜ -) 9 9 ʜ ʜ ʜ
J൪ͷਓʢJOʣࣗͷ ϥϯμϜϊϯεSJΛܾΊͯɺޓ͍ʹ9J ) 3JSJ( 3JΛڞ༗ ڞ༗͞Εͨใ͔Βɺ-ͱू͞Εͨ 3ΛಘΔ ͦΕͧΕͷॺ໊ऀ TJSJ
) - 9J 3 N YJΛ࡞ ݕূऀू͞Εͨॺ໊ ʢ3 Tʣ TT T ʜTO Λऔಘ ݕূ #FMMBSF/FWFOʹΑΔϚϧνγά࣮ 3 T 3 T ݕূऀ T(3 ) - 9 3 N 9 ) - 9 3 N 9 ʜ 33 3 ʜ -) 9 9 ʜ ʜ ʜ
J൪ͷਓʢJOʣࣗͷ ϥϯμϜϊϯεSJΛܾΊͯɺޓ͍ʹ9J ) 3JSJ( 3JΛڞ༗ ڞ༗͞Εͨใ͔Βɺ-ͱू͞Εͨ 3ΛಘΔ ͦΕͧΕͷॺ໊ऀ TJSJ
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J൪ͷਓʢJOʣࣗͷϥϯ μϜϊϯεSJΛܾΊͯɺޓ͍ʹ 3JSJ(Λڞ༗͢Δ -) 9 9ʜ ΛٻΊΔ 9) - 9
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