Distributed Ledger and Robust Consensus for Agreements
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The document discusses the design and implementation of a robust consensus algorithm for distributed ledger technology (DLT), focusing on cheat detection and performance. It outlines consensus processes, various types of failure interactions in networks, and methods for correcting deviations caused by malicious agents. The findings indicate the potential for achieving reliable consensus even in the presence of cheating, emphasizing the algorithm's limitations and applications.
![Introduction Cheat Detection Distributed Ledger Performance Conclusions
Consensus algorithm (Olfati, 2007)
1 each node has its initial
value
2 pass the value to its
neighbors
3 receive the values from its
neighbors
4 calculates the new value
1 2
3 4
x1 = 0.45 x2 = 0.425
x3 = 0.325 x4 = 0.6
x1 = 0.4
x(t + 1) = x(t) + ε
j∈Ni
[xj(t) − xi (t)]
@mrebollo UPV
Distributed Ledger and Robust Consensus for Agreements](https://image.slidesharecdn.com/mrebolloat18dltslides-181207131107/85/Distributed-Ledger-and-Robust-Consensus-for-Agreements-17-320.jpg)
![Introduction Cheat Detection Distributed Ledger Performance Conclusions
Altering Consensus
xi (t + 1) = xi (t) + ε
j∈Ni
[xj(t) − xi (t)] + ui (t)
1
23
4
5
6
7 8
9
10
0 10 20 30 40 50
time
0
2
4
6
8
10
xi
Consensus with Malicious Agent
10 agents, x = (1, 2, . . . , 10)T , ∆x5 = 4
@mrebollo UPV
Distributed Ledger and Robust Consensus for Agreements](https://image.slidesharecdn.com/mrebolloat18dltslides-181207131107/85/Distributed-Ledger-and-Robust-Consensus-for-Agreements-20-320.jpg)
![Introduction Cheat Detection Distributed Ledger Performance Conclusions
Altering Consensus
xi (t + 1) = xi (t) + ε
j∈Ni
[xj(t) − xi (t)] + ui (t)
1
23
4
5
6
7 8
9
10
0 10 20 30 40 50
time
0
2
4
6
8
10
xi
Consensus with Malicious Agent
10 agents, x = (1, 2, . . . , 10)T , ∆x5 = 4
@mrebollo UPV
Distributed Ledger and Robust Consensus for Agreements](https://image.slidesharecdn.com/mrebolloat18dltslides-181207131107/85/Distributed-Ledger-and-Robust-Consensus-for-Agreements-21-320.jpg)
![Introduction Cheat Detection Distributed Ledger Performance Conclusions
Cheat Detection
From
xi (t + 1) = xi (t) + ε
j∈Ni
[xj(t) − xi (t)]
clearing
0 = xi (t + 1) + (εdeg(i) − 1)xi (t) − ε
j∈Ni
xj(t)
dvi (t)
and the process must fulfil that
dvi (t) = 0 ∀t > 0
@mrebollo UPV
Distributed Ledger and Robust Consensus for Agreements](https://image.slidesharecdn.com/mrebolloat18dltslides-181207131107/85/Distributed-Ledger-and-Robust-Consensus-for-Agreements-22-320.jpg)
![Introduction Cheat Detection Distributed Ledger Performance Conclusions
Correction of the Deviations
xi (t + 1) = xi (t) + ε
j∈Ni
[xj(t) − xi (t)] + ui (t), with ui (t) > 0
ui (t) is divided into the neighbors as follows
the agent keeps (1 − εdeg(i))ui (t)
each neighbor receives εui (t)
therefore, dvi (t) = εui (t) → ui (t) = dvi (t)
ε
in general dvi (t)
ε = j∈Ni
uj(t)
total deviation Di (t) = t
s=0 dvi (s)
@mrebollo UPV
Distributed Ledger and Robust Consensus for Agreements](https://image.slidesharecdn.com/mrebolloat18dltslides-181207131107/85/Distributed-Ledger-and-Robust-Consensus-for-Agreements-23-320.jpg)
![Introduction Cheat Detection Distributed Ledger Performance Conclusions
Proof-of-concept
{ "@iot.count": 1,
"value": [{
"@iot.id": 1,
"phenomenonTime": 2018-10-05T08:55.08.504Z,
"result": 0.9058
}]}
Hash
0183A1ACBB765DB82EF98833872BA455F4D3B4037F...
@mrebollo UPV
Distributed Ledger and Robust Consensus for Agreements](https://image.slidesharecdn.com/mrebolloat18dltslides-181207131107/85/Distributed-Ledger-and-Robust-Consensus-for-Agreements-29-320.jpg)
![Introduction Cheat Detection Distributed Ledger Performance Conclusions
Malicious agent changes the block
[commandchars={}]
{ "@iot.count": 1,
"value": [{
"@iot.id": 1,
"phenomenonTime": 2018-10-05T08:55.08.504Z,
"result": 0.9312
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Hash
028AF8FD383E3E30EF73B141DB28100E2837DCA9B9...
@mrebollo UPV
Distributed Ledger and Robust Consensus for Agreements](https://image.slidesharecdn.com/mrebolloat18dltslides-181207131107/85/Distributed-Ledger-and-Robust-Consensus-for-Agreements-30-320.jpg)
Distributed Ledger and Robust Consensus for Agreements
- 1. Introduction Cheat Detection Distributed Ledger Performance Conclusions Distributed Ledger and Robust Consensus for Agreements M. Rebollo,C. Carrascosa, A. Palomares Grupo de Tec. Inform´atica – Inteligencia Artificial Universitat Polit`ecnica de Val`encia {mrebollo,carrasco,apalomares}@dsic.upv.es AT, Bergen 2018 c b a @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 2. Introduction Cheat Detection Distributed Ledger Performance Conclusions Overview 1 Introduction 2 Cheat Detection 3 Consensus for Distributed Ledger 4 Performance 5 Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 3. Introduction Cheat Detection Distributed Ledger Performance Conclusions What consensus is? @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 4. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 5. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 6. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 7. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 8. Introduction Cheat Detection Distributed Ledger Performance Conclusions What are consensus used for? @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 9. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 10. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 11. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 12. Introduction Cheat Detection Distributed Ledger Performance Conclusions @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 13. Introduction Cheat Detection Distributed Ledger Performance Conclusions Consensus algorithm (Olfati, 2007) Given undirected graph G = (V , E) set of initial values x = (x1, . . . , xn)T @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 14. Introduction Cheat Detection Distributed Ledger Performance Conclusions Consensus algorithm (Olfati, 2007) 1 each node has its initial value 1 2 3 4 x1 = 0.4 x2 = 0.2 x3 = 0.3 x4 = 0.9 x1 = 0.4 @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 15. Introduction Cheat Detection Distributed Ledger Performance Conclusions Consensus algorithm (Olfati, 2007) 1 each node has its initial value 2 pass the value to its neighbors 1 2 3 4 x1 = 0.4 x2 = 0.2 x3 = 0.3 x4 = 0.9 x1 = 0.4 x1 = 0.4 x1 = 0.4 @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 16. Introduction Cheat Detection Distributed Ledger Performance Conclusions Consensus algorithm (Olfati, 2007) 1 each node has its initial value 2 pass the value to its neighbors 3 receive the values from its neighbors 1 2 3 4 x1 = 0.4 x2 = 0.2 x3 = 0.3 x4 = 0.9 x2 = 0.2 x4 = 0.9 x3 = 0.3 @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 17. Introduction Cheat Detection Distributed Ledger Performance Conclusions Consensus algorithm (Olfati, 2007) 1 each node has its initial value 2 pass the value to its neighbors 3 receive the values from its neighbors 4 calculates the new value 1 2 3 4 x1 = 0.45 x2 = 0.425 x3 = 0.325 x4 = 0.6 x1 = 0.4 x(t + 1) = x(t) + ε j∈Ni [xj(t) − xi (t)] @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 18. Introduction Cheat Detection Distributed Ledger Performance Conclusions Consensus algorithm (Olfati, 2007) The network converges to the mean value lim t→∞ xi (t) = 1 n i xi (0) 0 5 10 15 20 25 30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 x = 0.45 @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 19. Introduction Cheat Detection Distributed Ledger Performance Conclusions Problem Failure detection on consensus process Only with one agent not following the algorithm, the network converges to a value different from the average @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 20. Introduction Cheat Detection Distributed Ledger Performance Conclusions Altering Consensus xi (t + 1) = xi (t) + ε j∈Ni [xj(t) − xi (t)] + ui (t) 1 23 4 5 6 7 8 9 10 0 10 20 30 40 50 time 0 2 4 6 8 10 xi Consensus with Malicious Agent 10 agents, x = (1, 2, . . . , 10)T , ∆x5 = 4 @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 21. Introduction Cheat Detection Distributed Ledger Performance Conclusions Altering Consensus xi (t + 1) = xi (t) + ε j∈Ni [xj(t) − xi (t)] + ui (t) 1 23 4 5 6 7 8 9 10 0 10 20 30 40 50 time 0 2 4 6 8 10 xi Consensus with Malicious Agent 10 agents, x = (1, 2, . . . , 10)T , ∆x5 = 4 @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 22. Introduction Cheat Detection Distributed Ledger Performance Conclusions Cheat Detection From xi (t + 1) = xi (t) + ε j∈Ni [xj(t) − xi (t)] clearing 0 = xi (t + 1) + (εdeg(i) − 1)xi (t) − ε j∈Ni xj(t) dvi (t) and the process must fulfil that dvi (t) = 0 ∀t > 0 @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 23. Introduction Cheat Detection Distributed Ledger Performance Conclusions Correction of the Deviations xi (t + 1) = xi (t) + ε j∈Ni [xj(t) − xi (t)] + ui (t), with ui (t) > 0 ui (t) is divided into the neighbors as follows the agent keeps (1 − εdeg(i))ui (t) each neighbor receives εui (t) therefore, dvi (t) = εui (t) → ui (t) = dvi (t) ε in general dvi (t) ε = j∈Ni uj(t) total deviation Di (t) = t s=0 dvi (s) @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 24. Introduction Cheat Detection Distributed Ledger Performance Conclusions Correction of the Deviation Consensus over (Di |wi ) Di cumulated deviation wi number of detected deviations Corrected value ˆxi(t) = xi (t) − Di (t) εwi (t) ci (t)) @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 25. Introduction Cheat Detection Distributed Ledger Performance Conclusions Failure Causes in Distributed Networks stop: the agent stops sending information byzantine failures: unexpected erratic behavior or deliberate errors unfair behavior, but admitted because of rationality, self-interest or incentive policies. @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 26. Introduction Cheat Detection Distributed Ledger Performance Conclusions Application to Distributed Ledger Technology (DLT) L1 L2 L3 L4 L5 L6 Hash 1+2 Hash 3+4 Hash 5+6 Hash 1+2+3+4 Hash 5+6 Hash 1+2+3+4+5+6 Distributed ledger stored in a Merkle tree only leaves have information each brach from root belongs to one agent @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 27. Introduction Cheat Detection Distributed Ledger Performance Conclusions Sample Merkle tree for 4 nodes @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 28. Introduction Cheat Detection Distributed Ledger Performance Conclusions DLT by consensus agent i creates a block with its transactions s inserts the block in its tree obtains the hash of the root hr generates (s|hr |yi = 1) the rest do ( | |yi = 0) @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 29. Introduction Cheat Detection Distributed Ledger Performance Conclusions Proof-of-concept { "@iot.count": 1, "value": [{ "@iot.id": 1, "phenomenonTime": 2018-10-05T08:55.08.504Z, "result": 0.9058 }]} Hash 0183A1ACBB765DB82EF98833872BA455F4D3B4037F... @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 30. Introduction Cheat Detection Distributed Ledger Performance Conclusions Malicious agent changes the block [commandchars={}] { "@iot.count": 1, "value": [{ "@iot.id": 1, "phenomenonTime": 2018-10-05T08:55.08.504Z, "result": 0.9312 }]} Hash 028AF8FD383E3E30EF73B141DB28100E2837DCA9B9... @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 31. Introduction Cheat Detection Distributed Ledger Performance Conclusions 0 20 40 60 80 100 time 1160 1180 1200 1220 1240 1260 x i DLT by Consensus with Cheating 10 15 20 25 30 1190 1200 1210 1220 1230 0 20 40 60 80 100 time 0 0.05 0.1 0.15 0.2 0.25 x i Evolution of Corrections for DLT @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 32. Introduction Cheat Detection Distributed Ledger Performance Conclusions Result after final correction {"iotcount":2,"readings":[{"iotid":1, "result":0.9058, "phenomenonTime":"2018-10-05T08:55.08.504Z"} {"iotcount":2,"readings":[{"iotid":1, "result":0.9058, "phenomenonTime":"2018-10-05T08:55.08.504Z"} {"iotcount":2,"readings":[{"iotid":1, "result":0.9058, "phenomenonTime":"2018-10-05T08:55.08.504Z"} ... @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 33. Introduction Cheat Detection Distributed Ledger Performance Conclusions Differences test over random networks if m cheat, then n ≥ 3 + 1 half the neighbors are confident @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 34. Introduction Cheat Detection Distributed Ledger Performance Conclusions Successful Corrections 1,000 repetitions corrections of 100% follow a Power-law with γ = −0.44 0 20 40 60 80 100 #cheating nodes 200 400 600 800 1000 freq. Successful corrections @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements
- 35. Introduction Cheat Detection Distributed Ledger Performance Conclusions Conclusions Extension of consensus algorithm robust algorithm for consensus in networks deviation from expected values detected correction mover the final result applied to DLT Limitations 1st exchange must be correct correction possible if m < n 3 and m < |Ni | 2 cheating agents undetected if only cheat once @mrebollo UPV Distributed Ledger and Robust Consensus for Agreements