staking.md 2.5 KB
title: tokens in stake author: ertosns
date: 24/3/2023
Staking in darkfi blockchain
The leadership winning mechanism is based off Ouroborous Crypsinous with some modifications. A stakeholder wins if some random value $y$, specific to the stakeholder and derived from the blockchain, is less than target value $T$. The probability of winning is quasi linear with the relative stake.
Least amount of DRK token required for staking
Accuracy of single leader per slot is affected by percentage of total DRK tokens in stake, in fact the relation is logarithmic.
Assume community $C$ owns 100% of DRK tokens.
The probability of $C$ winning the lottery at any slot is defined as:
\begin{align*} P(C=lead) &= y < 1 -(1-f)^\alpha \
&= y < 1 -(1-f) \\
&= y < f
\end{align*}
In our case f is targetting single leader per slot. An emulation of the leader election mechanism with PID controllers shows that f is oscillating around ~0.65 (depending on ration of tokens in stake).
Then,
\begin{align} P(C=lead)~=0.35 \end{align}
Linear independence
Given the linear independence property of the target function T, the probability of a node winning leadership at any slot with S staked tokens is the same as the probability of N nodes winning leadership at same slot, with same stake S for any S, N values.
Example
If the probability of stakeholder owning 0.1% of the tokens is 0.03, then the probability of a pool consisting of stakeholders owning 0.1% of tokens is also 0.03.
Tokens in stake
The probability of a pool of N% stake to win the leadership at any slot is:
\begin{align*} \frac{N}{100}P(C=lead) \end{align}
Example
Assume $P(C=lead)=33%$, then if only 10% of the total network token is staked the probability of having a single leader per slot is 0.03, or accuracy of 3%.
Ratio of staked tokens in different networks
| network | staked ratio |
|---|---|
| Etherum | 16% |
| Cardano | 69% |
| Solana | 71% |
| Bnb chain | 16% |
| Polygon | 40% |
| Polkadot | 47% |
Stake privacy leakage
From the graph above, and as a consequence of the linear independence property the accuracy of the controller leaks the percentage of token in stake.
Fix stake privacy leakage
Instant finality mechanism as khonsu would prevent such leakage.