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勉強会 #3
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titech.crypto
May 27, 2018
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勉強会 #3
ハッシュ関数について①
titech.crypto
May 27, 2018
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Transcript
ϋογϡؔ ୈճ$SZQ(FFLษڧձ 5",&)*,00),"8"
ϋογϡؔͷͭͷಛ ҙͷϝοηʔδΛೖྗ͢ ΔͱɺϝοηʔδΛද͢Δ ݻఆͷΛग़ྗ͢Δؔ ಉ͡ϋογϡؔʹಉ͡ϝο ηʔδ͕ೖྗ͞Εͨͱ͖ɺಉ ͡ϋογϡ͕ग़ྗ͢Δؔ ೖྗ͕େ͖ͯ͘ߴͰϋο γϡΛܭࢉͰ͖Δؔ ੑ࣭ᶃ
ੑ࣭ᶄ ੑ࣭ᶅ
ཧతͳϋογϡؔ w ϝοηʔδNΛ҉߸Խ͠ɺOϏοτͷ ϋογϡIΛग़ྗ͢Δ߹ w ͜ͷཧతͳϋογϡؔݟ͔ͭͬͯ ͳ͍ɻ ੑ࣭ᶅΛແࢹ͢ΕߏͰ͖Δ
ϋογϡؔͷඪ४తͳ҆શੑ Ұํੑ ݪ૾ܭࢉࠔੑ ୈݪ૾ܭࢉࠔੑ িಥࠔੑ
Ұํੑ ݪ૾ܭࢉࠔੑ 0OFXBZOFTT 1SFJNBHF3FTJTUBODF • ߈ܸऀɺh (=H(m)) Λೖྗͱͯ͠༩͑ΒΕͨͱ͖ɺh = H(m’)
Λຬͨ͢m’ Λग़ྗ͢Δ͜ͱ͕ࠔͰ͋Δ͜ͱɻ͜ ͷ߹ɺm Ҏ֎ͷ m’ Λग़ྗͯ͠ɺϋογϡ͕ h Ͱ͋Εɺ߈ܸʹޭͨ͜͠ͱʹͳΓ·͢ɻ
ୈݪ૾ܭࢉࠔੑ 4FDPOE1SFJNBHF3FTJTUBODF • ͋Δϝοηʔδʢୈ1ݪ૾ʣͱͦͷϋογϡ ͕༩͑ΒΕͨͱ͖ʹɺಉҰͷϋογϡ ʹͳΔผͷϝοηʔδʢୈ2ݪ૾ʣΛܭࢉ͢ Δ͜ͱ͕ࠔͰ͋Δ͜ͱɻ • ऑ͍ҙຯͰͷিಥࠔੑͱݺΕΔɻ
িಥࠔੑ 4FDPOE1SFJNBHF3FTJTUBODF • ɹಉ͡ϋογϡʹͳΔΑ͏ͳ2ͭͷҟͳ ΔϝοηʔδΛٻΊΔ͜ͱ͕ࠔͰ͋Δ͜ ͱɻ߈ܸऀࢦఆ͞Εͨিಥ͢Δϋογϡ ΛٻΊΔඞཁͳ͘ɺিಥ͑͢͞Ε ҙͷϋογϡͰΑ͍͜ͱʹͳΓ·͢ɻ • ɹڧ͍ҙຯͰͷিಥࠔੑ
N N` I ϝοηʔδۭؒ ϋογϡۭؒ
҆શੑͷڧऑ • ୈ2ݪ૾ܭࢉࠔੑΛഁΔ͜ͱʢୈ2ݪ૾ΛٻΊΔ͜ͱʣͱɺিಥࠔ ੑΛഁΔ͜ͱʢҙͷিಥϖΞΛݟ͚ͭΔ͜ͱʣΛൺֱͨ͠߹ɺ߈ ܸऀʹͱͬͯޙऀͷํ͕࣮ݱ͍͢͠ɻ • ϋογϡ͕ؔিಥࠔੑΛ࣋ͭͳΒɺҰํੑΛ࣋ͪ·͢ɻ • Ұํੑ, ୈ̎ݪ૾ܭࢉࠔੑ
< িಥࠔੑ
িಥϖΞ͕ٻ·Δ݅ɾ֬ w QݸͷϘʔϧͱOݸͷശ͕͋ΓɺശʹϥϯμϜʹϘʔϧΛೖΕͨ࣌ʹɺি ಥ͢Δ֬1 Q O P(p, n) = (
1 (p > n ͷͱ͖.) 1 n n n 1 n n 2 n · · · n p+1 n (p n ͷͱ͖.) P(p, 365) ͷ߹ 8JLJQFEJBੜͷύϥυοΫε 㲋O
িಥϖΞ͕ٻ·Δ݅ɾ֬ w Qճͷϋογϡܭࢉ LϏοτ ͷࢼߦɺOLͷऔΓ͏Δϋογϡɻ w ോͷݪཧLϏοτͷϋογϡL ճͷܭࢉͰඞͣɺিಥϖΞ͕ ٻ·Δɻ w
ܭࢉճ͕LճҎԼͷ࣌㲋OLͷͱ͖ɺিಥϖΞ͕ٻ·Δ֬ Ҏ্ʹͳΔɻ
ͭͷ҆શੑΛഁΔͨΊͷܭࢉճ ҆શੑͷछྨ ഁΔͨΊʹඞཁͳܭࢉճ Ұํੑ 2k-1 ճఔ ୈ2ݪ૾ܭࢉࠔੑ 2k-1 ճఔ িಥࠔੑ
2k/2 ճఔ ૯ͨΓ߈ܸͷ߹ͷฏۉతͳܭࢉճ