blockchain.md 2.1 KB
blockchain
blockchain $\mathbb{C}$ is a series of epochs, it's a tree of chains, $C_1$, $C_2$, $\dots$, $C_n$, the chain of the max length in $\mathbb{C}$ is the driving chain C
epoch
is multiple of blocks, some of those block might be empty due to the nature of the leader selection with VRF.
Genesis block
the first block in the epoch updates the stake for stakeholders, which influences weighted random leader selection algorithm, for epoch j, $S_j$ is the genesis block's data for n stakeholders of the blockchain: $$S_j=((U_1,v_1^{vrf},v_1^{kes},v_1^{dsig},s_1),\dots,(U_n,v_n^{vrf},v_n^{kes},v_n^{dsig},s_n)$$ $$\small\text{\emph{note that new stakeholders need to wait for the next epoch to be added to the genesis block}}$$
Block
block $\textbf{B}$ is the building block of the blockchain
block $B{i}=(st,d,sl,B{\pi},\rho, \sigma_s)$ created for slot i by stakeholder, and slot i leader $U_s$:
$$\textbf{\textcolor{red}{st}}: \text{state of the prebvious block, hash($B{i-1})$}$$ $$\textbf{\textcolor{red}{d}}: \text{data held by the block}$$ $$\textbf{\textcolor{red}{sl}}: \text{slot id generated by the beacon}$$ $$\textbf{\textcolor{red}{$B\pi$}}: \text{proof the stakeholder ${Us}$ is the owner, $B{\pi}=(U_s,y,\pi)$, y,$\pi$ are the output of the VRF}$$ $$\textbf{\textcolor{red}{$\rho$}}: \text{random seed for vrf, $\rho=(\rhoy,\rho{\pi})$}$$ $$\textbf{\textcolor{red}{$\sigma_{s}$}}: \text{owner signature on the block}$$
leader selection
at the onset of each slot each stakeholder needs to verify if it's the weighted random leader for this slot. $$y < T_{i}$$ $$\small\text{\emph{check if VRF output is less than some threshold}}$$ this statement might hold true for zero or more stakeholders, thus we might end up with multiple leaders for a slot, and other times no leader. also note that no one would know who is the leader, how many leaders are there for the slot, until you receive signed block with a proof claiming to be a leader. $$y = VRF(slotid||nonce)$$ $$\phi{f} = 1 - (1-f)^{\alphai}$$ $$T{i} = 2^{l{VRF}}\phi{f}(\alpha_i^j)$$