Dfinity & BLS Threshold Signature

઒େش ΧϫλΠΩ !S@FUY ɾ౦ژ޻ۀେֶ෺ཧֶम࢜೥ ɾ#BODPS+BQBODPVOUSZNBOBHFS ɾ-*/&$ZCFS"HFOUΠϯλʔϯ Intro

Motivation ϚΠφʔͷগͳ͍PoWίΠϯʹ͸ Selfish Mining΍ిྗফඅͷ໰୊͕͋Δɻ ࠷ۙPoSʹ΋ਂࠁͳ໰୊͕ݟ͔ͭͬͨɻ ଞͷίϯηϯαεΞϧΰϦζϜ ϒϩοΫੜ੒ऀͷܾఆํ๏Λݕ౼͍ͨ͠ɻ

DfinityͰ࠾༻͞Ε͍ͯΔBlockੜ੒ऀͷ ܾఆํ๏ͱͦͷ࣮ݱํ๏ʹ͍ͭͯઆ໌͍͖ͯ͠·͢ɻ Idea

Idea PoWͰͷBlockੜ੒ऀͷܾఆํ๏ͱൺֱ͠ ཧղ͍ͯ͘͠ɻ

Idea PoW͸ɺ୭Ͱ΋͋Δ֬཰ͰBlockΛੜ੒Ͱ͖Δɻ Miner͸ɺܭࢉೳྗΛߴΊ ೳಈతʹ৚݅Λຬͨ͢nonceΛݟ͚ͭΔɻ 1P8

ؤுΕ͹Blockੜ੒ऀʹͳΕΔɻ αϘ͍ͬͯͨΒBlockੜ੒ऀʹͳΕͳ͍ Idea

ҰํɺDfinityͰ͸ϥϯμϜʹϒϩοΫੜ੒ऀΛܾΊΔ͜ͱ͕Ͱ͖Δɻ ϚΠφʔ͸ɺࢀՃऀ͕ੜ੒͢ΔϥϯμϜ஋ʹΑͬͯ डಈతʹϒϩοΫੜ੒ऀʹͳΔɻ Idea 1P4

Idea 1P8 %pOJUZ SBOEPNOVNCFS ೳಈత डಈత

Idea ϥϯμϜ஋ʹΑͬͯແ࡞ҝʹϒϩοΫੜ੒ऀΛ ܾఆ͢Δ͜ͱʹΑͬͯɺ ফඅిྗΛ཈͑ΕΔɺϑΥʔΫ͕ى͖ʹ͘͘ͳΔɻ

)PXJUXPSLT

ξh 3BOEPN ξh 3BOEPN (SPVQ Gh σh 4JHO TJHO IBTI ξh+1 3BOE ξh+1 3BOE (SPVQ Gh+1 σh+1 4JHO TJHO IBTI ξh+2 3BOE ξh+2 3BOE (SPVQ Gh+2 σh+2 4JHO TJHO TFMFDU TFMFDU #MPDL.BLFS h,0 #MPDL.BLFS h,1 #MPDL.BLFS h,2 TFMFDU #MPDL Bh,0 #MPDL Bh,1 TFMFDU DSFBUF #. h + 1,0 #MPDL Bh+1,0 #MPDL Bh+1,1 #MPDL DSFBUF Bh+1,2 #. h + 1,1 #. h + 1,2 ϥϯμϜ஋Λ༻͍ͯ#MPDLੜ੒ऀΛܾఆ ༏ઌॱҐΛ͚ͭΔ

ξh 3BOEPN ξh 3BOEPN (SPVQ Gh σh 4JHO TJHO IBTI ξh+1 3BOE ξh+1 3BOE (SPVQ Gh+1 σh+1 4JHO TJHO IBTI ξh+2 3BOE ξh+2 3BOE (SPVQ Gh+2 σh+2 4JHO TJHO TFMFDU TFMFDU #MPDL.BLFS h,0 #MPDL.BLFS h,1 #MPDL.BLFS h,2 TFMFDU #MPDL Bh,0 #MPDL Bh,1 TFMFDU DSFBUF #. h + 1,0 #MPDL Bh+1,0 #MPDL Bh+1,1 #MPDL DSFBUF Bh+1,2 #. h + 1,1 #. h + 1,2 ϥϯμϜ஋Λ༻͍ͯɺ ಉ࣌ʹϒϩοΫΛݕূ͢Δάϧʔϓ΋બͿɻ άϧʔϓ͸ɺάϧʔϓͷެ։伴Λ࡞੒͠ࣄલެ։͢Δ TFMFDU

ξh 3BOEPN (SPVQ Gh TJHO IBTI ξh+1 3BOE ξh+1 3BOE (SPVQ Gh+1 σh+1 4JHO TJHO IBTI ξh+2 3BOE ξh+2 3BOE (SPVQ Gh+2 σh+2 4JHO TJHO TFMFDU TFMFDU #MPDL.BLFS h,0 #MPDL.BLFS h,1 #MPDL.BLFS h,2 TFMFDU #MPDL Bh,0 #MPDL Bh,1 TFMFDU DSFBUF #. h + 1,0 #MPDL Bh+1,0 #MPDL Bh+1,1 #MPDL DSFBUF Bh+1,2 #. h + 1,1 #. h + 1,2 TFMFDU ξh 3BOEPN σh 4JHO ϒϩοΫΛݕূ͠ɺάϧʔϓʹॴଐ͢Δա൒਺ͷਓͷ ॺ໊ͷूΊΔ͜ͱʹΑͬͯάϧʔϓͷॺ໊͕࣮ߦͰ͖Δɻ

ෆਖ਼͕ى͖ͳ͍Α͏ʹάϧʔϓͰϥϯμϜ஋Λ࡞Δ ෳ਺ਓͷॺ໊Λ଍͠߹Θͤͯάϧʔϓͷॺ໊Λ ࡞੒͠άϧʔϓͷॺ໊Λߦ͏ɻ ·ͨͦͷॺ໊ΛϥϯμϜ஋ͱͯ͠ར༻͢Δɻ

ξh 3BOEPN (SPVQ Gh TJHO IBTI ξh+1 3BOE ξh+1 3BOE (SPVQ Gh+1 σh+1 4JHO TJHO IBTI ξh+2 3BOE ξh+2 3BOE (SPVQ Gh+2 σh+2 4JHO TJHO TFMFDU TFMFDU #MPDL.BLFS h,0 #MPDL.BLFS h,1 #MPDL.BLFS h,2 TFMFDU #MPDL Bh,0 #MPDL Bh,1 TFMFDU DSFBUF #. h + 1,0 #MPDL Bh+1,0 #MPDL Bh+1,1 #MPDL DSFBUF Bh+1,2 #. h + 1,1 #. h + 1,2 TFMFDU ξh 3BOEPN σh 4JHO άϧʔϓͷա൒਺Ͱ࡞Δॺ໊͕ ࣍ͷϥϯμϜ஋ ྫ͑͹ਓͷάϧʔϓ͔Β ਓͷॺ໊͕ू·Ε͹৘ใ͕෮ݩͰ͖Δɻ ϒϩοΫΛݕূ͠ɺάϧʔϓʹॴଐ͢Δա൒਺ͷਓͷ ॺ໊ͷूΊΔ͜ͱʹΑͬͯάϧʔϓͷॺ໊͕࣮ߦͰ͖Δɻ

ξh 3BOEPN (SPVQ Gh TJHO IBTI ξh+1 3BOE ξh+1 3BOE (SPVQ Gh+1 σh+1 4JHO TJHO IBTI ξh+2 3BOE ξh+2 3BOE (SPVQ Gh+2 σh+2 4JHO TJHO TFMFDU TFMFDU #MPDL.BLFS h,0 #MPDL.BLFS h,1 #MPDL.BLFS h,2 TFMFDU #MPDL Bh,0 #MPDL Bh,1 TFMFDU DSFBUF #. h + 1,0 #MPDL Bh+1,0 #MPDL Bh+1,1 #MPDL DSFBUF Bh+1,2 #. h + 1,1 #. h + 1,2 TFMFDU ξh 3BOEPN σh 4JHO ξh 3BOEPN σh 4JHO ξh 3BOEPN σh 4JHO ಉ͡ૢ࡞Λ܁Γฦ͢͜ͱͰ #MPDL͕ੜ੒͞ΕΔɻ

ξh 3BOEPN (SPVQ Gh TJHO IBTI ξh+1 3BOE ξh+1 3BOE (SPVQ Gh+1 σh+1 4JHO TJHO IBTI ξh+2 3BOE ξh+2 3BOE (SPVQ Gh+2 σh+2 4JHO TJHO TFMFDU TFMFDU #MPDL.BLFS h,0 #MPDL.BLFS h,1 #MPDL.BLFS h,2 TFMFDU #MPDL Bh,0 #MPDL Bh,1 TFMFDU DSFBUF #. h + 1,0 #MPDL Bh+1,0 #MPDL Bh+1,1 #MPDL DSFBUF Bh+1,2 #. h + 1,1 #. h + 1,2 TFMFDU ξh 3BOEPN σh 4JHO ξh 3BOEPN σh 4JHO ξh 3BOEPN σh 4JHO

ॺ໊͸ɺࣄલʹެ։͍ͯͨ͠ެ։伴Ͱ ؆୯ʹݕূͰ͖ΔΑ͏͍ͨ͠ɻ ͳͷͰ Ͳͷਓͷॺ໊ΛूΊͯ΋ ΋ಉ͡஋Λॺ໊͕Ͱ͖ΔΑ͏ʹ͍ͨ͠ɻ

άϧʔϓॴଐ͢ΔͲͷਓͷ৘ใΛूΊͯ΋ ಉ͡৘ใ͕෮ݩͰ͖Δ࢓૊Έ

ͦ͜Ͱɺগ͚ͩ͠ॺ໊ʹ͍ͭͯ෮श

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Ͳͷਓͷॺ໊ΛूΊͯ΋ ಉ͡৘ใΛ෮ݩͰ͖Δ࢓૊Έ͕ᮢ஋๏

෮ݩ͞ΕΔ৘ใͱͯ͠ɺؔ਺ͷ੾ยΛ༻͍Δɻ

(4,11) (1,5) s0 x y ᮢ஋๏

(4,11) (1,5) s0 x y ᮢ஋๏

s0 x y ᮢ஋๏

s0 x y ᮢ஋๏

(4,11) (1,5) s0 x y ಉؔ͡਺্ͷ఺Ͱ͋Ε͹ɺͲͷ఺Λ͖࣋ͬͯͯ΋ ಉؔ͡਺ ੾ย ͕෮ݩͰ͖Δɻ ᮢ஋๏

͜ͷ৔߹Ͱ͋Ε͹ɺࡾ࣍ؔ਺Ͱ͋ΔͷͰ Ͳͷͭͷ৘ใ͕ू·ͬͯҰͭͷؔ਺͕ܾ·Δɺ ಉ͡৘ใ͕෮ݩͰ͖Δ (x1 , y1 ) (x3 , y3 ) (x2 , y2 ) (x4 , y4 ) s0 x y ᮢ஋๏

Ͳͷਓͷॺ໊ΛूΊͯ΋ ಉ͡৘ใΛ෮ݩͰ͖Δ࢓૊Έ͕ᮢ஋๏ ࣍ؔ਺Λ࢖͑͹͍͍

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·ͱΊ ϥϯμϜ஋ʹΑͬͯແ࡞ҝʹϒϩοΫੜ੒ऀΛܾఆ͢Δɻ ফඅిྗΛ཈͑ΕΔ ϑΥʔΫ͕ى͖ʹ͘͘ͳΔ ॺ໊͸άϧʔϓͰߦ͍ɺͲͷϝϯόʔͷॺ໊ΛूΊͯ΋ ಉ͡ެ։伴ͰݕূͰ͖Δɻ %pOJUZͰ͸ɺ

͓஌Βͤ

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