大小链(BigSmallChains):一种失败的共识机制(1)

gentledog 海盗王 发布在 技术交流
 15229  2

大小链(BigSmallChains):一种失败的共识机制

本文尝试提出一种更具激励相容性的挖矿方案,以解决自私挖矿问题。但是,失败了。














































执行best_parameters.py(见附录1),可得:
γ=0.5 :

m w v α R 原来的R
2 3 3 0.480000 0.810210 0.831632
3 3 3 0.480000 0.766974 0.831632
4 3 3 0.480000 0.730639 0.831632
5 4 3 0.480000 0.730381 0.831632
6 4 3 0.480000 0.726512 0.831632
7 4 3 0.480000 0.721312 0.831632
8 4 3 0.480000 0.715421 0.831632
9 4 3 0.480000 0.709209 0.831632
10 4 0 0.480000 0.711430 0.831632
11 5 4 0.480000 0.707432 0.831632
12 5 4 0.480000 0.700616 0.831632
13 5 4 0.480000 0.694047 0.831632
14 5 4 0.480000 0.687740 0.831632
15 5 0 0.480000 0.684840 0.831632
16 6 5 0.480000 0.684044 0.831632
17 6 4 0.480000 0.680656 0.831632
18 6 4 0.480000 0.677406 0.831632
19 6 4 0.480000 0.674169 0.831632
20 6 4 0.480000 0.670961 0.831632
21 6 4 0.480000 0.667791 0.831632
22 6 0 0.480000 0.672224 0.831632
23 7 5 0.480000 0.669592 0.831632
24 7 5 0.480000 0.666312 0.831632
25 7 5 0.480000 0.663109 0.831632
26 7 5 0.480000 0.659984 0.831632
27 7 5 0.480000 0.656937 0.831632
28 7 0 0.480000 0.655298 0.831632
29 8 6 0.480000 0.657589 0.831632
30 8 5 0.480000 0.655372 0.831632
31 8 5 0.480000 0.653383 0.831632
32 8 5 0.480000 0.651414 0.831632
33 8 5 0.480000 0.649465 0.831632
34 8 5 0.480000 0.647540 0.831632
35 8 5 0.480000 0.645639 0.831632
36 8 0 0.480000 0.647201 0.831632
37 9 6 0.480000 0.648249 0.831632
38 9 6 0.480000 0.646281 0.831632
39 9 6 0.480000 0.644346 0.831632
40 9 6 0.480000 0.642444 0.831632
41 9 6 0.480000 0.640574 0.831632
42 9 6 0.480000 0.638738 0.831632
43 9 6 0.480000 0.636933 0.831632
44 9 0 0.480000 0.638949 0.831632
45 10 7 0.480000 0.638686 0.831632
46 10 6 0.480000 0.637173 0.831632
47 10 6 0.480000 0.635844 0.831632
48 10 6 0.480000 0.634528 0.831632
49 10 6 0.480000 0.633226 0.831632
50 10 6 0.480000 0.631937 0.831632

γ=1 :

m w v α R 原来的R
2 3 3 0.480000 0.818218 0.846920
3 3 3 0.480000 0.772499 0.846920
4 4 3 0.480000 0.766045 0.846920
5 4 3 0.480000 0.760078 0.846920
6 4 3 0.480000 0.752536 0.846920
7 4 3 0.480000 0.744340 0.846920
8 4 3 0.480000 0.735960 0.846920
9 5 4 0.480000 0.737941 0.846920
10 5 4 0.480000 0.729292 0.846920
11 5 4 0.480000 0.720994 0.846920
12 5 4 0.480000 0.713070 0.846920
13 5 4 0.480000 0.705523 0.846920
14 6 5 0.480000 0.706326 0.846920
15 6 4 0.480000 0.700546 0.846920
16 6 4 0.480000 0.696569 0.846920
17 6 4 0.480000 0.692625 0.846920
18 6 4 0.480000 0.688730 0.846920
19 6 4 0.480000 0.684900 0.846920
20 7 5 0.480000 0.689369 0.846920
21 7 5 0.480000 0.685422 0.846920
22 7 5 0.480000 0.681574 0.846920
23 7 5 0.480000 0.677828 0.846920
24 7 5 0.480000 0.674183 0.846920
25 7 5 0.480000 0.670639 0.846920
26 7 0 0.480000 0.671800 0.846920
27 8 6 0.480000 0.670386 0.846920
28 8 5 0.480000 0.667788 0.846920
29 8 5 0.480000 0.665478 0.846920
30 8 5 0.480000 0.663196 0.846920
31 8 5 0.480000 0.660945 0.846920
32 8 5 0.480000 0.658725 0.846920
33 8 0 0.480000 0.659597 0.846920
34 9 6 0.480000 0.660887 0.846920
35 9 6 0.480000 0.658624 0.846920
36 9 6 0.480000 0.656401 0.846920
37 9 6 0.480000 0.654219 0.846920
38 9 6 0.480000 0.652078 0.846920
39 9 6 0.480000 0.649976 0.846920
40 9 0 0.480000 0.648232 0.846920
41 9 0 0.480000 0.651307 0.846920
42 10 7 0.480000 0.649310 0.846920
43 10 6 0.480000 0.647290 0.846920
44 10 6 0.480000 0.645780 0.846920
45 10 6 0.480000 0.644286 0.846920
46 10 6 0.480000 0.642809 0.846920
47 10 6 0.480000 0.641348 0.846920
48 10 0 0.480000 0.640523 0.846920
49 10 0 0.480000 0.643193 0.846920
50 11 7 0.480000 0.642382 0.846920

γ=0.5 :

m w v α R 原来的R
2 3 3 0.250000 0.261894 0.250000
3 3 3 0.250000 0.261592 0.250000
4 3 3 0.250000 0.260355 0.250000
5 4 4 0.250000 0.258761 0.250000
6 4 4 0.250000 0.257851 0.250000
7 4 4 0.250000 0.257092 0.250000
8 4 4 0.250000 0.256457 0.250000
9 4 4 0.250000 0.255923 0.250000
10 4 4 0.250000 0.255468 0.250000
11 5 5 0.250000 0.254953 0.250000
12 5 4 0.250000 0.254847 0.250000
13 5 4 0.250000 0.254988 0.250000
14 5 4 0.250000 0.255065 0.250000
15 5 4 0.250000 0.255095 0.250000
16 6 5 0.250000 0.254601 0.250000
17 6 5 0.250000 0.254607 0.250000
18 6 5 0.250000 0.254593 0.250000
19 6 5 0.250000 0.254564 0.250000
20 6 5 0.250000 0.254523 0.250000
21 6 5 0.250000 0.254473 0.250000
22 6 5 0.250000 0.254417 0.250000
23 7 6 0.250000 0.254080 0.250000
24 7 6 0.250000 0.254033 0.250000
25 7 6 0.250000 0.253982 0.250000
26 7 6 0.250000 0.253929 0.250000
27 7 5 0.250000 0.253895 0.250000
28 7 5 0.250000 0.253925 0.250000
29 8 7 0.250000 0.253578 0.250000
30 8 6 0.250000 0.253606 0.250000
31 8 6 0.250000 0.253625 0.250000
32 8 6 0.250000 0.253637 0.250000
33 8 6 0.250000 0.253642 0.250000
34 8 6 0.250000 0.253643 0.250000
35 8 6 0.250000 0.253639 0.250000
36 8 5 0.250000 0.253651 0.250000
37 9 7 0.250000 0.253376 0.250000
38 9 7 0.250000 0.253371 0.250000
39 9 6 0.250000 0.253404 0.250000
40 9 6 0.250000 0.253435 0.250000
41 9 6 0.250000 0.253461 0.250000
42 9 6 0.250000 0.253481 0.250000
43 9 6 0.250000 0.253497 0.250000
44 9 5 0.250000 0.253535 0.250000
45 10 7 0.250000 0.253254 0.250000
46 10 6 0.250000 0.253273 0.250000
47 10 6 0.250000 0.253315 0.250000
48 10 6 0.250000 0.253351 0.250000
49 10 6 0.250000 0.253383 0.250000
50 10 6 0.250000 0.253411 0.250000

γ=1 :

m w v α R 原来的R
2 3 3 0.250000 0.285876 0.304878
3 3 3 0.250000 0.274910 0.304878
4 3 3 0.250000 0.268824 0.304878
5 3 0 0.250000 0.266301 0.304878
6 3 0 0.250000 0.271296 0.304878
7 3 0 0.250000 0.275234 0.304878
8 3 0 0.250000 0.278392 0.304878
9 5 4 0.250000 0.259297 0.304878
10 5 0 0.250000 0.261077 0.304878
11 5 0 0.250000 0.265123 0.304878
12 5 0 0.250000 0.268585 0.304878
13 5 0 0.250000 0.271569 0.304878
14 6 0 0.250000 0.266135 0.304878
15 6 0 0.250000 0.269033 0.304878
16 6 0 0.250000 0.271595 0.304878
17 6 0 0.250000 0.273870 0.304878
18 6 0 0.250000 0.275900 0.304878
19 6 0 0.250000 0.277719 0.304878
20 6 0 0.250000 0.279355 0.304878
21 6 0 0.250000 0.280833 0.304878
22 6 0 0.250000 0.282171 0.304878
23 6 0 0.250000 0.283389 0.304878
24 6 0 0.250000 0.284499 0.304878
25 6 0 0.250000 0.285515 0.304878
26 6 0 0.250000 0.286447 0.304878
27 7 0 0.250000 0.283734 0.304878
28 7 0 0.250000 0.284721 0.304878
29 7 0 0.250000 0.285635 0.304878
30 7 0 0.250000 0.286482 0.304878
31 7 0 0.250000 0.287268 0.304878
32 7 0 0.250000 0.288000 0.304878
33 7 0 0.250000 0.288683 0.304878
34 8 0 0.250000 0.286559 0.304878
35 8 0 0.250000 0.287282 0.304878
36 8 0 0.250000 0.287960 0.304878
37 8 0 0.250000 0.288597 0.304878
38 8 0 0.250000 0.289195 0.304878
39 8 0 0.250000 0.289758 0.304878
40 8 0 0.250000 0.290288 0.304878
41 8 0 0.250000 0.290789 0.304878
42 10 0 0.250000 0.286722 0.304878
43 10 0 0.250000 0.287342 0.304878
44 10 0 0.250000 0.287929 0.304878
45 10 0 0.250000 0.288486 0.304878
46 10 0 0.250000 0.289015 0.304878
47 10 0 0.250000 0.289517 0.304878
48 10 0 0.250000 0.289995 0.304878
49 10 0 0.250000 0.290449 0.304878
50 11 0 0.250000 0.288943 0.304878

从数据中可以看出,在糟糕情况下(α或γ取值较大),本方案似乎有明显的改进。
经过分析和对比,我决定选取(w,m)=(4,5),(5,11),(6,16),(7,23),(8,29),(9,37),(10,45)作为候选参数。









































图中,曲线“OSMA”表示采用本模型计算得到的上界,曲线“OSMO”表示采用文献[2]中的模型计算得到的下界,“OSMA-SIM”表示相应的模拟结果。从图中可以看出曲线“OSMA”和曲线“OSMO”非常接近。

十、结论

本方案没有明显的改进。
另外,增加大区块的期望收益、减少小区块的期望收益可能会对结果有一点点的改进。这需要更进一步的分析和更复杂的模型。

参考文献

[1]Ittay Eyal,Emin Gün Sirer: Majority is not Enough: Bitcoin Mining is Vulnerable
[2]Ayelet Sapirshtein,Yonatan Sompolinsky,and Aviv Zohar: Optimal Selfish Mining Strategies in Bitcoin

本文原创,转载请注明出处。

韭菜求生长。请各位大佬多多施肥:


BTC: bc1qrlqz880pmle25z23lhls659ffrcnqh5p7newmy
ETH: 0x2335f8Fa649b30292c3ffC8C81353A2593f550a1
DOT: 16NLd9SwbVCxW1subqjg1MWAsxpW5PHJ3PLKLKSDuCmDqFyx
LTC: ltc1qmg9me5d9n2le6kggmu3k3lxve5wu32szmmht0f
BCH: qzhf86vw0qfm5jkpxrah8mn485esl7pv9vknnhj5yw