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II. Consensus AlgorithmEthash - PoW Algorithm for Ethereum 1.0
https://github.com/ethereum/wiki/wiki/Ethash
Block # Date Difficulty Target
9,000,000 2019-11-26 2,573,664,196,528,490 0x0000000000001bff809762e524...
8,000,000 2019-06-21 2,037,888,242,889,388 0x000000000000235be453641714...
6,000,000 2018-07-21 3,483,739,548,912,554 0x00000000000014af19378e94eb
3,000,000 2017-01-16 103,975,266,902,792 0x000000000002b506bb4c196d40
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Keccak(header, transactions, nonce) = 0x0000...
def mine(full_size, dataset, header, difficulty):
target = zpad(encode_int(2**256 // difficulty), 64)[::-1]
from random import randint
nonce = randint(0, 2**64)
while hashimoto_full(full_size, dataset, header, nonce) > target:
nonce = (nonce + 1) % 2**64
return nonce
difficulty x target = 2256](https://image.slidesharecdn.com/basicconsensusalgorithms-200313061047/85/Basic-Consensus-Algorithms-15-320.jpg)
Basic Consensus Algorithms
- 1. Basic Consensus Algorithms Mar. 2020 Sangmoon Oh (halfface@chollian.net) v1.0
- 2. 2 목차 • Byzantine Fault • Byzantine Fault Tolerance (BFT) • 3m + 1 Processors Algorithm • pBFT • Proof of Work (PoW) • Ethash • PoW Finality Problem • Casper FFG
- 3. 3 II. Consensus AlgorithmByzantine Fault (Byzantine General Problem) Enemy attack retreat retreat retreat retreat retreat attack attack attack attack Agree on Attack/Retreat Protocol or Algorithm SIFT: design and analysis of a fault-tolerant computer for aircraft control (1978)
- 4. 4 II. Consensus AlgorithmByzantine Fault - Simple Example 2 Loyal Generals with 1 Unknown Traitor 1 3 2 Traitor att att att ret att att (att,att,att) Attack (att,ret,att) Attack 1 3 2 Traitor att ret ret ret ret ret 1 3 2 Traitor att att att ret ret ret (ret,att,ret) Retreat (att,att,ret) Attack (ret,ret,ret) Retreat (att,ret,ret) Retreat Not Agreed !! Case 1) Case 2) Case 3)
- 5. 5 II. Consensus AlgorithmByzantine Fault Tolerance (BFT) Enemy General Traitor General Traitor General General Attack G T G T G G Attack Attack Attack Retreat G T G T G G Retreat Retreat Retreat Algorithm 1 Retreat Attack G T G T G G Attack Attack Retreat G T G T G G Retreat Retreat RetreatAlgorithm 2 Always Agreement No Agreement Possible A1: BTF A2: Not BTF
- 6. 6 II. Consensus AlgorithmByzantine Fault Revisited Enemy Synchronous or Asynchronous Message Delivery Forgeable vs. Unforgeable Message Level of Connectivity Option Space Is BTF Possible ? What Algorithms ?
- 7. 7 II. Consensus Algorithm3m + 1 Processors Algorithm - Overview With m faulty processors, Min. (3m +1) processors are needed to tolerate the fault. Algorithm OM(m) n 3m + 1 General Traitor General General General GeneralTraitor General General General General Traitor Traitor General General General General Traitor Traitor General m=1, n=3 (< 3m+1) m=1, n=4 ( 3m+1) m=2, n=6 (< 3m+1) m=2, n=7 ( 3m+1) (Synchronized message delivery, Forgeable message, Full connected) OM(1) OM(2)
- 8. 8 II. Consensus Algorithm3m + 1 Processors Algorithm - Instructions m nmin Instruction 1 4 OM(0), OM(1) 2 7 OM(0), OM(1), OM(2) 3 10 OM(0), OM(1), OM(2), OM(3) Recursive Relay v:1:4 v:1:2:4 v:1:2 v:1:2:3 v:1:2:3:4 4 1 2 3 v:1:4 v:1:2:4 v:1:3:4 v:1:2:3:4 v:1:3:2:4 1 + 2C1 + 2C11C1 = 5 v:1:::4
- 9. 9 II. Consensus Algorithm3m + 1 Processors Algorithm - Simplest Case Case v:2:1 v:2:3:1 v:2:4:1 v:2:::1 v:2:3 v:2:1:3 v:2:4:3 v:2:::3 v:2:4 v2:1:4 v:2:3:4 v:2:::4 1) A A R 2A + R A A R 2A + R R A A 2A + R 2) A R A 2A + R R A A 2A + R A A R 2A + R 3) A R R A + 2R R A R A + 2R R A R A + 2R 4) R A A 2A + R A R A 2A + R A R A 2A + R 5) R A R A + 2R A R R A + 2R R R A A + 2R 6) R R A A + 2R R R A A + 2R A R R A + 2R
- 10. 10 II. Consensus Algorithm3m + 1 Processors Algorithm - Complexity General General GeneralTraitor General General General General Traitor Traitor General Faulty Total Recursion Number of Message 1 4 OM(0), OM(1) 4*3 + 4*3*2 2 7 OM(0), OM(1), OM(2) 7*6 + 7*6*5 + 7*6*5*4 3 10 OM(0), OM(1), OM(2), OM(3) 10*9 + 10*9*8 + 10*9*8*7 + 10*9*8*7*6 m 3m + 1 OM(0), OM(1), , OM(m) (3m+1)*3m + (3m+1)*3m*(3m-1) + + (3m+1)*3m2m Complexity : O(nm) General General General General Traitor Traitor
- 11. 11 II. Consensus AlgorithmState Machine Replication a : 100 b : 100 c : 100 a : 120 b : 110 c : 70 a : 90 b : 100 c : 110 tx1 tx3 tx4 tx2 tx1 : b a, 20 tx2 : b c, 10 tx3 : c b, 30 tx4 : a c, 30 a : 100 b : 100 c : 100 a : 120 b : 110 c : 70 a : 90 b : 100 c : 110 tx1 tx3 tx4 tx2 a : 100 b : 100 c : 100 a : 120 b : 110 c : 70 a : 90 b : 100 c : 110 tx1 tx3 tx4 tx2 Ordering Txs Decentralized way Communication and Corporation
- 12. 12 II. Consensus AlgorithmpBFT (Practical Byzantine Fault Tolerance) 1 2 3 4 client Pre-prepare (~ n) Prepare (~ n(n-1)) Commit (~ n(n-1)) Primary Create and share next state candidate Backups Validate next state candidate Pre-prepare Sender Share validated(accepted) next state candidate Receiver Collect the acceptance of the other nodes Commit if enough nodes accepted ( > 2𝑛+1 3 ) Prepare, Commit tx
- 13. 13 II. Consensus AlgorithmProof of Work (PoW) 4 3 2 1 5 Compute Solve Send Send Send Send Compute Compute Compute Verify Verify Verify Verify Compute Try a puzzle hard to solve but easy to verify. Competition Reward
- 14. 14 II. Consensus Algorithm 4 3 2 1 5 Compute Solve Send Send Send Send Compute Compute Compute Verify Verify Verify Verify Compute Hash based PoW Data + Nonce SHA-256(Data + Nonce) Hello, world! 0x315f5bdb76d078c43b8ac0064e4a0164612b1fce77c869345bfc94c75894edd3 Hello, world!0 0x1312af178c253f84028d480a6adc1e25e81caa44c749ec81976192e2ec934c64 Hello, world!1 0xe9afc424b79e4f6ab42d99c81156d3a17228d6e1eef4139be78e948a9332a7d8 Hello, world!2 0xae37343a357a8297591625e7134cbea22f5928be8ca2a32aa475cf05fd4266b7 Hello, world!4248 0x6e110d98b388e77e9c6f042ac6b497cec46660deef75a55ebc7cfdf65cc0b965 Hello, world!4249 0xc004190b822f1669cac8dc37e761cb73652e7832fb814565702245cf26ebb9e6 Hello, world!4250 0x0000c3af42fc31103f1fdc0151fa747ff87349a4714df7cc52ea464e12dcd4e9 Puzzle: Find Nonce for SHA-256(Data, Nonce) to Start with 0000
- 15. 15 II. Consensus AlgorithmEthash - PoW Algorithm for Ethereum 1.0 https://github.com/ethereum/wiki/wiki/Ethash Block # Date Difficulty Target 9,000,000 2019-11-26 2,573,664,196,528,490 0x0000000000001bff809762e524... 8,000,000 2019-06-21 2,037,888,242,889,388 0x000000000000235be453641714... 6,000,000 2018-07-21 3,483,739,548,912,554 0x00000000000014af19378e94eb 3,000,000 2017-01-16 103,975,266,902,792 0x000000000002b506bb4c196d40 4 3 2 1 5 Compute Solve Send Send Send Send Compute Compute Compute Verify Verify Verify Verify Compute Keccak(header, transactions, nonce) = 0x0000... def mine(full_size, dataset, header, difficulty): target = zpad(encode_int(2**256 // difficulty), 64)[::-1] from random import randint nonce = randint(0, 2**64) while hashimoto_full(full_size, dataset, header, nonce) > target: nonce = (nonce + 1) % 2**64 return nonce difficulty x target = 2256
- 16. 16 II. Consensus AlgorithmPoW - Finality Problem Solve Bm Solve Bn Bm Two different miners may generate a block simultaneously. Bm Bn Bn
- 17. 17 II. Consensus AlgorithmPoW - Finality Problem Solve Bm2 Solve Bn2 Bm Another two different miners may generate a block simultaneously again. Bm Bn Bn Bn2 Bn2Bm2 Bm2
- 18. 18 II. Consensus AlgorithmPoW - Finality Problem Bm Bn Bm Bn Bm Bn Bm Bn Bn txb(b a, 10) txb(b a, 10)
- 19. 19 II. Consensus AlgorithmCasper FFG - Finality System "Casper FFG" paper by Vitalik and Virgil PoS based Finality System which Overlays an existing PoW blockchain. Accountability : Penalty Dynamic validators Modular overlay : a partial consensus mechanism
- 20. 20 II. Consensus AlgorithmCasper FFG - Process 1) Voting Vote for link(edge) 2 Commandments (Slashing conditions) 2) Justifying 2/3 votes 3) Finalizing Canonical chain 1) 2) 3)
- 21. 21 AppendixReferences Consensus Byzantine fault Reaching Agreement in the Presence of Faults (1980, M. PEASE, R, SHOSTAK, AND L. LAMPORT) The Byzantine Generals Problem (1982, LESLIE LAMPORT, ROBERT SHOSTAK, and MARSHALL PEASE) Practical Byzantine Fault Tolerance (1999, Miguel Castro and Barbara Liskov) pBFT— Understanding the Consensus Algorithm Proof-of-Work, Explained Hashcash Ethash