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あなたの知らない乱数の世界
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Yosuke Furukawa
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August 18, 2017
Programming
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170
あなたの知らない乱数の世界
リクルートテクノロジーズの社内勉強会で発表した乱数の話です。
Yosuke Furukawa
PRO
August 18, 2017
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Transcript
͋ͳͨͷΒͳ͍ ཚͷੈք 2017/08/18 @ Recruit Tech Study
ͱཚ
ͦͦͷൃ
ৄ͍͠ܦҢͪ͜ΒΛ
RandඍົʹϥϯμϜ͡Όͳ͍ʁ
͜͜Ͱ͍͏Randͱ • ͓ͦΒ͘ MySQL ͔ Java ͔ͳʹ͔ͷ random ؔʁ •
ͩͱͨ͠ΒϥϯμϜ͡Όͳ͍ͱݴΘͳ͍͕ ࣭ͷѱ͍ϥϯμϜؔͰ͋Δ͜ͱ͔֬ɻ
͜͜Ͱ͍͏Randͱ • ͓ͦΒ͘ MySQL ͔ Java ͔ͳʹ͔ͷ random ؔʁ •
ͩͱͨ͠ΒϥϯμϜ͡Όͳ͍ͱݴΘͳ͍͕ ࣭ͷѱ͍ϥϯμϜؔͰ͋Δ͜ͱ͔֬ɻ ϥϯμϜؔͷ࣭ͱԿ͔ʁ
JavaͰMath.random() ͬͯ·͔͢ʁ
Math.random() ʹද͞ΕΔ ཚൃੜثٙࣅཚͰ͋Γɺ Javaͷٖࣅཚͷ࣮ ઢܗ߹ಉ๏
Javaͷ Math.random ͷΞϧΰ ϦζϜઢܗ߹ಉ๏ • "ܭࢉ୯७͕ͩ͋Μ·ΓϥϯμϜ͡Όͳ͍ཚ ੜث" • X[n+1] =
a * X[n] + b mod M
ઢܗ߹ಉ๏ const A = 1103515245 const B = 12345 const
M = 2^32 var X function rand() { X = (A * X + B) % M return X } // 32,21,18,11,6,17,20,27,32,21,18
ઢܗ߹ಉ๏ const A = 1103515245 const B = 12345 const
M = 2^32 var X function rand() { X = (A * X + B) % M return X } // 32,21,18,11,6,17,20,27,32,21,18 ۮ حͷॱʹฒΜͰΔ
ઢܗ߹ಉ๏ const A = 1103515245 const B = 12345 const
M = 2^32 var X function rand() { X = (A * X + B) % M return X } // 32,21,18,11,6,17,20,27,32,21,18 ۮ حͷॱʹฒΜͰΔ ࠷ॳͷ9<> ॳظ ͕ಉͩͬͨ͡Βඞͣಉ͡ྻ͕࡞ΒΕΔ
ઢܗ߹ಉ๏ const A = 1103515245 const B = 12345 const
M = 2^32 var X function rand() { X = (A * X + B) % M return X } // 32,21,18,11,6,17,20,27,32,21,18 ۮ حͷॱʹฒΜͰΔ ࠷ॳͷ9<> ॳظ ͕ಉͩͬͨ͡Βඞͣಉ͡ྻ͕࡞ΒΕΔ TFFEͱݴ͏
ઢܗ߹ಉ๏ • X[n+1] = a * X[n] + b mod
M • 1 : ۮحͷॱংͰฒͿ • 2 : ࠷ॳͷX[0](ॳظ) ͕ಉͩͬͨ͡Βඞ ͣಉ͡ྻ͕࡞ΒΕΔ
ઢܗ߹ಉ๏ • X[n+1] = a * X[n] + b mod
M • 1 : ۮحͷॱংͰฒͿ • 2 : ࠷ॳͷX[0](ॳظ) ͕ಉͩͬͨ͡Βඞ ͣಉ͡ྻ͕࡞ΒΕΔ ࣍ͷཚ͕༧ଌͰ͖Δɻ ཚʹنଇੑ͕͋Δɻ
ઢܗ߹ಉ๏ • X[n+1] = a * X[n] + b mod
M • 1 : ۮحͷॱংͰฒͿ • 2 : ࠷ॳͷX[0](ॳظ) ͕ಉͩͬͨ͡Βඞ ͣಉ͡ྻ͕࡞ΒΕΔ ࣍ͷཚ͕༧ଌͰ͖Δɻ ཚʹنଇੑ͕͋Δɻ ղ๏ΑΓΑ͍ΞϧΰϦζϜΛબͿ -JLFϝϧηϯψɾπΠελ 9034IJGU
ઢܗ߹ಉ๏ • X[n+1] = a * X[n] + b mod
M • 1 : ۮحͷॱংͰฒͿ • 2 : ࠷ॳͷX[0](ॳظ) ͕ಉͩͬͨ͡Βඞ ͣಉ͡ྻ͕࡞ΒΕΔ TFFEͱճ͔͑͞Ε ࣍ͷཚ͕༧ଌՄೳ
ઢܗ߹ಉ๏ • X[n+1] = a * X[n] + b mod
M • 1 : ۮحͷॱংͰฒͿ • 2 : ࠷ॳͷX[0](ॳظ) ͕ಉͩͬͨ͡Βඞ ͣಉ͡ྻ͕࡞ΒΕΔ TFFEͱճ͔͑͞Ε ࣍ͷཚ͕༧ଌՄೳ ٙࣅཚͱ͍͏ͷجຊ͜͏͍͏ͷ
randomؔͷ࣭ͱ • ٖࣅཚͰ͋Δ߹ɺཚ͕Ұ༷ʹ͢Δ ͜ͱʢಉ͡ࣈ͕ग़ʹ͍͘͜ͱʣ • نଇੑ͕ͳ͍͜ͱʢۮɾح͕ަޓʹग़ͨ Γ͠ͳ͍͜ͱʣ
randomؔͷ࣭ͱ • ٖࣅཚͰ͋Δ߹ɺཚ͕Ұ༷ʹ͢Δ ͜ͱʢಉ͡ࣈ͕ग़ʹ͍͘͜ͱʣ • نଇੑ͕ͳ͍͜ͱʢۮɾح͕ަޓʹग़ͨ Γ͠ͳ͍͜ͱʣ ࣭ͷྑ͍ϥϯμϜؔʢҰ༷ʹཚ͕͠ɺपظੑ͕͘ɺنଇੑ͕ͳ͍ͷʣ ͷྫɿϝϧηϯψɾπΠελɺ9034IJGU
randomؔͷ࣭ͱ • ٖࣅཚͰ͋Δ߹ɺཚ͕Ұ༷ʹ͢Δ ͜ͱʢಉ͡ࣈ͕ग़ʹ͍͘͜ͱʣ • نଇੑ͕ͳ͍͜ͱʢۮɾح͕ަޓʹग़ͨ Γ͠ͳ͍͜ͱʣ ࣭ͷྑ͍ϥϯμϜؔʢҰ༷ʹཚ͕͠ɺपظੑ͕͘ɺنଇੑ͕ͳ͍ͷʣ ͷྫɿϝϧηϯψɾπΠελɺ9034IJGU
randomؔͷ࣭ͱ • ٖࣅཚͰ͋Δ߹ɺཚ͕Ұ༷ʹ͢Δ ͜ͱʢಉ͡ࣈ͕ग़ʹ͍͘͜ͱʣ • نଇੑ͕ͳ͍͜ͱʢۮɾح͕ަޓʹग़ͨ Γ͠ͳ͍͜ͱʣ ࣭ͷྑ͍ϥϯμϜؔʢҰ༷ʹཚ͕͠ɺपظੑ͕͘ɺنଇੑ͕ͳ͍ͷʣ ͷྫɿϝϧηϯψɾπΠελɺ9034IJGU ͪͳΈʹ7ͷ.BUISBOEPN
͜ͷ9034IJGU
͞Βʹຊ
ݫີʹϥϯμϜͳrandomؔͱ͔ͳ͍?
ຊͩΖ͏͔ʁ
ٙࣅ͡Όͳ͍ཚ͋Δ • ϋʔυΣΞཚੜثʢӳޠͩͱTrue Random Number Generator TRNG) • /dev/random •
ࡶԻ • ์ࣹੑ࣭ͷ่յ • ͳͲͳͲɺଞʹͨ͘͞Μ͋Δ
/dev/random ΩʔϘʔυϚεɺσΟεΫૢ࡞ͱ͍ͬͨૢ࡞هΛݩʹ৭Μͳ ใΛஷΊ͓͖ͯɺ͔ͦ͜ΒϥϯμϚΠζ͞ΕͨใΛग़͢
/dev/random ΩʔϘʔυϚεɺσΟεΫૢ࡞ͱ͍ͬͨૢ࡞هΛݩʹ৭Μͳ ใΛஷΊ͓͖ͯɺ͔ͦ͜ΒϥϯμϚΠζ͞ΕͨใΛग़͢ ૢ࡞ه͕Ұఆஷ·Βͳ͍ͱ ػೳ͠ͳ͍
ࡶԻΛͬͨํ๏ ిؾճ࿏Ͱ0/Ͱ0''Ͱͳ͍ঢ়گΛ࡞͓ͬͯ͘ɻ ͦͷ্ͰࡶԻͱ͍͏ཧݱΛͬͯPS͕ϥϯμϜʹग़ΔΑ͏ʹ͢Δɻ )JHI )JHI
ࡶԻΛͬͨํ๏ *OUFM*WZ#SJEHFʹ࣮ࡁΈɻ
ࡶԻΛͬͨํ๏ *OUFM*WZ#SJEHFʹ࣮ࡁΈɻ ͨͩ͠ɺࡶԻʹΑΔํ๏ిྗফඅྔ͕ܹ͍͠ ΤωϧΪʔ͕খ͗ͯ͢͞ภΓ͕͋ΔɺͦͷͨΊιϑτΣΞͷิॿ͕ඞཁ
ݪࢠ่֩յΛͬͨํ๏
ݪࢠ่֩յΛͬͨํ๏ ”70ஹݸͷݪࢠͷݪࢠ่֩յΛར༻ͨ͠ͷͰɺߏ୯७ɻ” ”ઢݯͷۙ͘ʹμΠΦʔυΛઃஔ͠ɺ͜͜ͰύϧεΛݕ͢Δɻ”
ݪࢠ่֩յΛͬͨํ๏ ”70ஹݸͷݪࢠͷݪࢠ่֩յΛར༻ͨ͠ͷͰɺߏ୯७ɻ” ”ઢݯͷۙ͘ʹμΠΦʔυΛઃஔ͠ɺ͜͜ͰύϧεΛݕ͢Δɻ”
ʊਓਓਓਓਓʊ ʼɹύϧεɹʻ ʉY^Y^Y^Yʉ
͑ɺͦΕඃരɾɾɾ
ඃര͠ͳ͕ΒཚΛऔΔͷ ࠷ߴʹϩοΫ
"ݪࢠ่֩յͱ͍͏ͱɺ์ࣹઢ ඃΛࢥ͍ු͔ͯ͠·͏͕ɺ ઢྔݶΓͳ͘͘ɺਓମʹ Өڹ͢ΔϨϕϧͰͳ͍ɻ"
·ͱΊ • ཚܯ • ٖࣅཚͷྑ͠ѱ͠ • ϋʔυΣΞཚੜثͱ͍͏ਅͷཚΛ࡞ Δͷ͋Δ • ཚԞਂ͍ɺΈΜͳ৭ʑௐͯΈΔͱָ͍͠