Effective Selfish Mining Defense Strategies to Improve Bitcoin Dependability
<p>State transition diagram (0: initial state, 0′: double branches, 1: one-block lead, 2: two-block lead, 3: three-block lead, and 4: attack success).</p> "> Figure 2
<p>Bitcoin dependability before and after the application of the DDAA under sets <span class="html-italic">a</span> and <span class="html-italic">a</span>′.</p> "> Figure 3
<p>Bitcoin dependability before and after application of the DDAA under sets <span class="html-italic">b</span> and <span class="html-italic">b</span>′.</p> "> Figure 4
<p>Bitcoin dependability before and after application of the DDAA under sets <span class="html-italic">c</span> and <span class="html-italic">c</span>′.</p> "> Figure 5
<p><span class="html-italic">p</span>-value results when <span class="html-italic">β</span> varies from 1.1 to 1.6 under the DDAA.</p> "> Figure 6
<p>Bitcoin dependability before and after the application of the ALP.</p> "> Figure 7
<p><span class="html-italic">p</span>-value results when <span class="html-italic">γ</span> varies from 0.6 to 0.9 under the ALP.</p> "> Figure 8
<p>Bitcoin dependability under the DDAA, ALP, and TM.</p> ">
Abstract
:1. Introduction
2. CTMC-Based Dependability Analysis
3. Dynamic Difficulty Adjustment Algorithm (DDAA)
3.1. Effects of the DDAA on Bitcoin Dependability
3.2. Optimal Parameter Selection for Parameter β
4. Acceptance Limitation Policy (ALP)
5. Comparative Studies
6. Conclusions and Future Directions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Rate | Set a | Set b | Set c | Set a′ | Set b′ | Set c′ |
---|---|---|---|---|---|---|
λ01 | 0.03 | 0.12 | 0.34 | 0.024 | 0.096 | 0.272 |
λ0′1 | 0.11 | 0.11 | 0.11 | 0.088 | 0.088 | 0.088 |
λ12 | 0.06 | 0.18 | 0.56 | 0.048 | 0.144 | 0.448 |
λ23 | 0.04 | 0.04 | 0.04 | 0.032 | 0.032 | 0.032 |
λ34 | 0.36 | 0.36 | 0.36 | 0.288 | 0.288 | 0.288 |
0.24 | 0.24 | 0.24 | 0.24 | 0.24 | 0.24 | |
0.12 | 0.12 | 0.12 | 0.12 | 0.12 | 0.12 | |
0.31 | 0.31 | 0.31 | 0.31 | 0.31 | 0.31 |
t (hrs) | Set a | Set a′ | a–a′ | Set b | Set b′ | b–b′ | Set c | Set c′ | c–c′ |
---|---|---|---|---|---|---|---|---|---|
6 | 0.9995 | 0.9998 | 0.0003 | 0.9950 | 0.9977 | 0.0027 | 0.9745 | 0.9868 | 0.0123 |
12 | 0.9964 | 0.9983 | 0.0019 | 0.9705 | 0.9847 | 0.0142 | 0.8887 | 0.9335 | 0.0448 |
18 | 0.9907 | 0.9954 | 0.0047 | 0.9334 | 0.9631 | 0.0297 | 0.7911 | 0.8646 | 0.0735 |
24 | 0.9835 | 0.9915 | 0.0080 | 0.8924 | 0.9379 | 0.0455 | 0.7007 | 0.7961 | 0.0954 |
30 | 0.9755 | 0.9872 | 0.0117 | 0.8515 | 0.9117 | 0.0602 | 0.6202 | 0.7319 | 0.1117 |
36 | 0.9670 | 0.9826 | 0.0156 | 0.8119 | 0.8855 | 0.0736 | 0.5489 | 0.6726 | 0.1237 |
Set a vs. Set a′ | Set b vs. Set b′ | Set c vs. Set c′ | |
---|---|---|---|
F-test | 0.1914 | 0.3090 | 0.5277 |
t-test | 0.0164 | 0.0097 | 0.0034 |
β | 1.1 | 1.25 | 1.43 | 1.6 |
---|---|---|---|---|
p-value | 0.0191 | 0.0164 | 0.0145 | 0.0173 |
Rate | λ01 | λ0′1 | λ12 | λ23 | λ34 | |||
---|---|---|---|---|---|---|---|---|
Set a | 0.03 | 0.11 | 0.06 | 0.04 | 0.36 | 0.24 | 0.12 | 0.31 |
Set a″ | 0.03 | 0.11 | 0.06 | 0.04 | 0.36 × γ | 0.24 | 0.12 | 0.31 |
γ | 0.6 | 0.7 | 0.8 | 0.9 |
---|---|---|---|---|
p-value | 0.0049 | 0.0044 | 0.0033 | 0.0057 |
Set | λ01 | λ0′1 | λ12 | λ23 | λ34 | |||
---|---|---|---|---|---|---|---|---|
DDAA-a | 0.03/β | 0.11/β | 0.06/β | 0.04/β | 0.36/β | 0.24 | 0.12 | 0.31 |
ALP-a | 0.03 | 0.11 | 0.06 | 0.04 | 0.36×γ | 0.24 | 0.12 | 0.31 |
TM-a | 0.03 | 0.11 | 0.06 | 0.04 | 0.36 | 0.24×ω | 0.12×ω | 0.31×ω |
t (hrs) | β = 1.2 | γ = 1/1.2 | ω = 1.2 | β = 1.4 | γ = 1/1.4 | ω = 1.4 | β = 1.6 | γ = 1/1.6 | ω = 1.6 |
---|---|---|---|---|---|---|---|---|---|
6 | 0.9997 | 0.9995 | 0.9995 | 0.9998 | 0.9996 | 0.9996 | 0.9999 | 0.9996 | 0.9996 |
12 | 0.9980 | 0.9967 | 0.9969 | 0.9988 | 0.9969 | 0.9972 | 0.9992 | 0.9971 | 0.9976 |
18 | 0.9948 | 0.9912 | 0.9922 | 0.9968 | 0.9917 | 0.9934 | 0.9979 | 0.9921 | 0.9944 |
24 | 0.9905 | 0.9842 | 0.9866 | 0.9940 | 0.9848 | 0.9889 | 0.9960 | 0.9854 | 0.9907 |
30 | 0.9857 | 0.9762 | 0.9804 | 0.9909 | 0.9769 | 0.9840 | 0.9938 | 0.9776 | 0.9868 |
36 | 0.9805 | 0.9678 | 0.9739 | 0.9875 | 0.9678 | 0.9790 | 0.9914 | 0.9693 | 0.9828 |
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Zhou, C.; Xing, L.; Liu, Q.; Wang, H. Effective Selfish Mining Defense Strategies to Improve Bitcoin Dependability. Appl. Sci. 2023, 13, 422. https://doi.org/10.3390/app13010422
Zhou C, Xing L, Liu Q, Wang H. Effective Selfish Mining Defense Strategies to Improve Bitcoin Dependability. Applied Sciences. 2023; 13(1):422. https://doi.org/10.3390/app13010422
Chicago/Turabian StyleZhou, Chencheng, Liudong Xing, Qisi Liu, and Honggang Wang. 2023. "Effective Selfish Mining Defense Strategies to Improve Bitcoin Dependability" Applied Sciences 13, no. 1: 422. https://doi.org/10.3390/app13010422