Tangle iota Tangle Tangle DAG Tangle Tangle 2 2 A B A B 2 A X B A B 2 Tangle Tangle Tangle Tangle 3 4 k 2 k
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1 The Tangle Serguei Popov October, 207. Version.3 IOTA IoT Tangle DAG Tangle M2M MCMC Tangle 6 Bitcoin IoT 2 Bitcoin IoT iota[] a.k.a. mthcl; author s contact information: e.monetki@gmail.com
2 Tangle iota Tangle Tangle DAG Tangle Tangle 2 2 A B A B 2 A X B A B 2 Tangle Tangle Tangle Tangle 3 4 k 2 k
3 IoT Bitcoin Bitcoin 0 iota Tangle 5 Tangle % ([4] )
4 2 2 (3 3. ) (4 ) DAG [3, 6, 7, 9, 2] [7] GHOST Bitcoin [9] DAG Tangle DAG [6] Tangle Tangle [8] DAG P2P Bitcoin [2, 0] 2 iota 3 n n 8 F A B C E F 9 =
5 3 0 D 6 F E 4 C 3 B A X 3 : X DAG F A B C E Tangle Tangle A C Tangle X A C X X 3 2 Tangle 5
6 D A 9 F 3 3 B G E 7 C 2: DAG A C 2 G F D B A 4 D A C A B D F G A = 9 C = 7 X X X 6
7 3 t L(t) L(t) 9 [] P[L(t) = k] as t k L(t) L(t) L(t) ( [] 5.3 ) λ h 2 ( 4. ) Tangle h Tangle t Tangle t + h L 0 > 0 λ 0 h L 0 t λh [t h, t) r t h L 0 = r + λh t h t λh r/(r + λh) r 9 7
8 λh 2r/(r + λh) r 2r(r + λh) = r = λh L 0 = 2λh. () 2 k L (k) 0 = kλh k. (2) L (k) 0 k λh λh 2 h + L 0 /2λ = 2h h 2λ/L 0 [] 5.3 t s [t, t + h(l 0, N)] 0 t Tangle DAG 0 8
9 3: Tangle 9
10 λ L 0 2λ/L 0 L 0 /(2λ).45h () 3 L 0 /2λ Tangle Θ(λ ) λ () 3 iota Tangle 0
11 Θ(h) h / / 3.? λ 6 λ Tangle H(t) t h K(t) t h := h(l 0, N) L 0 2 t t h 2 Tangle 2 ( K(t h) L 0 ) 2 = K(t h) L 0 ( 2 K(t h) L 0 ) 7 K( ) [] 6.4 λ > 0 6 7
12 K(t h) ( K(t h) ) H(t + δ) = H(t) + λδ 2 + o(δ). L 0 L 0 dh(t) dt K(t h) ( K(t h) ) = λ 2. (3) L 0 L 0 (3) K(t) t h t t h t 2 3 2λh h λh t K(t h)/2 A t t h K(t h)/2 B t K(t h)/2 p B A p 2 A p p 2 ( K(t h) ) 2 K(t h) ( p = + 2 2L 0 2L 0 ( K(t h) ) 2. p 2 = 2L 0 K(t h) ), L 0 p [ B ]+[ B 2 A B 2 ] (3) K(t) dk(t) dt K(t h) ( K(t h) ) = (p p 2 )λ = λ. (4) L 0 L 0 (4) K(t) ε > 0 εl 0 ( ε)l 0 K(t) L 0 (4) 2
13 8 λh L 0 = 2 (4) dk(t) dt K(t h). (5) 2h K(0) = K(t) = exp(c t h ) (5) K(t) = exp(c t h ) c (c h exp t ) ( h 2h exp c t ), h c ( K(t) = exp W ( 2 ) t ) ( exp t ). (6) h h W ( ) W 9 (6) K(t) εl 0 t 0 h W ( ) (ln L 0 ln ε ) 2.84 h ln L 0. (7) 2 (3) t 0 (7) t t 0 dh(t) dt 2λ K(t h) L 0 ( h exp ( W ( 2 )) exp W ( 2 = W ( ) ( 2 exp W ( ) t ) h 2 h ) t ) h ( H(t) W ( 2 ) t ) ( exp t ). (8) h h H(t) λ (8) 4 8 λ K(t h) L 0 9 x [ 0, + ) x = W (x) exp(w (x)) 3
14 β tan β = λ 0 4:. λw w 2. 2 H(t) (8) λw 4 3. (7) 4. 4
15 Sybil Attack Tangle Tangle Tangle 5 W (n) 3 n W (n) µ3 n 2 µ w 0 t 0 λw λ w w = λwt 0 x x n 0 = ln w ln 3 3 n 0 w 22 t 0 3 n 0 P[W (n 0) < t 0 ] = exp( t 0 µ3 n 0 ) exp( t 0 µw ) t 0µ w µ 3 n 22 w 3 n 0 w 5
16 5: t 0µ w n > n 0 3 n 3 n P[λwW (n) < 3 n ] = exp ( µ3 n 0 (3 n 0 /λw) ) = exp( µ/λw) µ λw. µ λw n 3 λw µ 23 3 t 0 w 0 λ 24 Tangle Tangle 23 t
17 µ G, G 2, G 3,... µ 25 i.i.d. V k = µg k k V, V 2, V 3,... i.i.d. t 0 w0 M(θ) = ( θ) [4] 7.7 α (0, ) 26 [ n ] P V k αn exp ( nφ(α) ). (9) k= φ(α) = ln α + α ln M( θ) α (0, ) φ(α) > 0 µt 0 w 0 < Tangle Tangle t 0 w 0 t 0 m w 0 (9) t 0 P [ w 0/m ] [ w 0 ] G k < t 0 = P V k < µt 0 k= = P k= [ w 0 k= V k < w 0 µt 0 w 0 ] exp ( w 0 φ ( µt 0 w 0 )). (0) w 0 m φ( µt 0 w 0 ) t t 0 w 0 + λ(t t 0 ) λ (0) 25 /µ 26 [3] [4] [5].9 7
18 t t 0 exp ( (w 0 + λ(t t 0 ))φ ( µt w 0 +λ(t t 0 ))). () λ µt 0 w 0 µ λ exp ( w 0 φ ( max( µt 0 w 0, µ λ ))). (2) µ = 2, λ = max( µt 0 w 0, µ λ ) = 3 4 φ( 3 4) (2) 0.29 µ = max( µt 0 w 0, µ λ ) = 3 8 φ( 3 8) (2) λ > µ (2) Tangle 2 4. Tangle Tangle ( 6) Tangle Tangle Tangle
19 6 Tangle Tangle 2 MCMC H x 2 Tangle 28. [W, 2W ] W N 3. x y y x Tangle [W, 2W ] [W, 5W ] t 0 2t 0 t
20 6: 2 5. y x y x P xy exp ( α(h x H y ) ) P xy = exp ( α(h x H y ) )( z:z x α > 0 3 exp ( α(h x H z ) )). (3) Tangle Tangle 6 P xy 6 Tangle Tangle Tangle 3 α = 20
21 6 Tangle MCMC Tangle Tangle α α Tangle 32 MCMC 32 Tangle 2
22 Bitcoin MCMC (3) f(s) = s 3 W N MCMC 4.2 Aviv Zohar MCMC Tangle MCMC MCRW MCRW Tangle MCMC 22
23 2 2 Bitcoin Tangle /2 2 /2 2 2 MCMC f 34 50% 2 Tangle MCMC (3) H x H y H x Tangle
24 . 2. Tangle 3. m m (2) (2) 4. Tangle 4. MCMC 5. MCMC 5 35 Bitcoin 2 68 Bitcoin Θ( N) [5] Θ(N) Bitcoin 2 68 =
25 iota = 8 36 iota Bitcoin Tangle Bartosz Kuśmierz Cyril Grünspan ver.0.6 James Brogan [] Iota: a cryptocurrency for Internet-of-Things. See and [2] bitcoinj. Working with micropayment channels. [3] people on nxtforum.org (204) DAG, a generalized blockchain. (registration at nxtforum.org required) [4] Moshe Babaioff, Shahar Dobzinski, Sigal Oren, Aviv Zohar (202) On Bitcoin and red balloons. Proc. 3th ACM Conf. Electronic Commerce, [5] Richard Durrett (2004) Probability Theory and Examples. Duxbury advanced series. [6] Sergio Demian Lerner (205) DagCoin: a cryptocurrency without blocks Θ( N) 0 N 25
26 [7] Yonatan Sompolinsky, Aviv Zohar (203) Accelerating Bitcoin s Transaction Processing. Fast Money Grows on Trees, Not Chains. [8] Yonatan Sompolinsky, Yoad Lewenberg, Aviv Zohar (206) SPECTRE: Serialization of Proof-of-work Events: Confirming Transactions via Recursive Elections. [9] Yoad Lewenberg, Yonatan Sompolinsky, Aviv Zohar (205) Inclusive Block Chain Protocols. btc.pdf [0] Joseph Poon, Thaddeus Dryja (206) The Bitcoin Lightning Network: Scalable Off-Chain Instant Payments. [] Sheldon M. Ross (202) Introduction to Probability Models. 0th ed. [2] David Vorick (205) Getting rid of blocks. slides.com/davidvorick/braids [3] Amir Dembo, Ofer Zeitouni (200) Large Deviations Techniques and Applications. Springer. [4] Sheldon M. Ross (2009) A First Course in Probability. 8th ed. [5] Gilles Brassard, Peter Høyer, Alain Tapp (998) Quantum cryptanalysis of hash and claw-free functions. Lecture Notes in Computer Science 380,
Tangle iota Tangle Tangle DAG Tangle Tangle 2 2 A B A B 2 A X B A B 2 Tangle Tangle Tangle Tangle 3 4 k 2 k
The Tangle Serguei Popov November 27, 207. Version.4. IOTA IoT Tangle DAG Tangle M2M MCMC Tangle 6 Bitcoin IoT 2 Bitcoin IoT iota[] a.k.a. mthcl; author s contact information: e.monetki@gmail.com Tangle
More information本論文では ブロックチェーンレス アプローチについて検討される これは現在 iota[1] において実装されているものである iota は最近 IoT 業界のための暗号通貨として設計された 当然 全ての理論解析はそのようなシステムが動作するバージョンからのフィードバックなしには成立しない 近日中にそ
The tangle Serguei Popov, for Jinn Labs April 3, 2016. Version 0.6 摘要 ( Abstract 本論文で iota IoT 業界の為の暗号通貨 のバックボーンとして利用されているテクノロジーを分 析する このテクノロジーはブロックチェーン技術の自然な後継であり 進化の次のステップであ る グローバルな規模で行われるマイクロ決済に必要な機能とともに公開される
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Title 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue 2012-06 Date Type Technical Report Text Version publisher URL http://hdl.handle.net/10086/23085 Right Hitotsubashi University Repository
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