diff options
| author | PO-CHUN KUO <39326293+kbjcobinhood@users.noreply.github.com> | 2019-03-18 15:51:13 +0800 |
|---|---|---|
| committer | PO-CHUN KUO <39326293+kbjcobinhood@users.noreply.github.com> | 2019-03-18 15:51:13 +0800 |
| commit | 8c11e889b093e9407169edee15d98ab80404fdd6 (patch) | |
| tree | 5d3026db5c5ffaae5249d9ff94e5ec90747b62ca | |
| parent | ea28ab35161b9b3540a17ebef8e6bb6f6e24d668 (diff) | |
| download | dexon-wiki-8c11e889b093e9407169edee15d98ab80404fdd6.tar dexon-wiki-8c11e889b093e9407169edee15d98ab80404fdd6.tar.gz dexon-wiki-8c11e889b093e9407169edee15d98ab80404fdd6.tar.bz2 dexon-wiki-8c11e889b093e9407169edee15d98ab80404fdd6.tar.lz dexon-wiki-8c11e889b093e9407169edee15d98ab80404fdd6.tar.xz dexon-wiki-8c11e889b093e9407169edee15d98ab80404fdd6.tar.zst dexon-wiki-8c11e889b093e9407169edee15d98ab80404fdd6.zip | |
Created Selection of the notary set size (markdown)
| -rw-r--r-- | Selection-of-the-notary-set-size.md | 35 |
1 files changed, 35 insertions, 0 deletions
diff --git a/Selection-of-the-notary-set-size.md b/Selection-of-the-notary-set-size.md new file mode 100644 index 0000000..b421aab --- /dev/null +++ b/Selection-of-the-notary-set-size.md @@ -0,0 +1,35 @@ +# Selection of the notary set size + +As mention in our consensus algorithm, we follow the hypergeometry distribution to decide the size of notary set. + +Given a node set of size N, the ratio of Byzantine nodes is R, and the notary set size n, then, the probability of more than 1/3 of notary set be Byzantine nodes is + +<p align="center"> + <img src="https://imgur.com/wszheq8.png" width="250"> +</p> + +We set the probability to be 10^-8; that is, there is one fault in more than 10000 years in expectation. +Assume R=1/5 and applying this equation, we can derive the size of notary set which is shown in the following figure. + + + + +We give two curves to approximate the data point. +The first one is y = 70.5 ln(x) - 264, which is the purple dash line and the second one is y = 74 ln(x) - 264, which is the green dash line. +Then, the following table is the resilience ratio to the Byzantine by giving the number of the size of notary set and probability 10^-8. + + + +| node set size | notary set size | resilience | notary set size | resilience | +| -------- | -------- | -------- | --- | --- | +| 200 | 110 | 0.199 | 123 | 0.220 | +| 400 | 159 | 0.197 | 174 | 0.207 | +| 600 | 187 | 0.194 | 203 | 0.202 | +| 800 | 208 | 0.197 | 224 | 0.202 | +| 1000 | 223 | 0.197 | 252 | 0.202 | +| 1500 | 252 | 0.199 | 270 | 0.204 | +| 2000 | 272 | 0.199 | 291 | 0.207 | +| 4000 | 321 | 0.207 | 342 | 0.209 | + + +DEXON mainnet will use y = 70.5 ln(x) - 264 to decide the notary set size from the node set size.
\ No newline at end of file |