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doc/blockchain: Proper formatting and wrapping.
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# Dynamic Proof of Stake
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## blockchain
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## Blockchain
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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
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Blockchain $\mathbb{C}$ is a series of epochs: it's a tree of chains,
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$C_1$, $C_2$, $\dots$, $C_n$, the chain of the max length in
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$\mathbb{C}$ is the driving chain C.
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## epoch
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is multiple of blocks, some of those block might be empty due to the nature of the leader selection with VRF.
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## Epoch
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An epoch is a multiple of blocks. Some of those blocks might be empty
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due to the nature of the leader selection with VRF.
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## Genesis block
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the first block in the epoch updates the stake for stakeholders, which influences weighted random leader selection algorithm, for epoch j, the pair ($S_j,\eta_j$) is the genesis block's data for n stakeholders of the blockchain:
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$$S_j=((U_1,v_1^{vrf},v_1^{kes},v_1^{dsig},s_1),\dots,(U_n,v_n^{vrf},v_n^{kes},v_n^{dsig},s_n)$$
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$$\eta_j \leftarrow \{0,1\}^\lambda$$
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$$\small\text{\emph{note that new stakeholders need to wait for the next epoch to be added to the genesis block}}$$
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The first block in the epoch updates the stake for stakeholders, which
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influences the weighted random leader selection algorithm. For epoch j,
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the pair ($S_j,\eta_j$) is the genesis block's data for n stakeholders
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of the blockchain:
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$$ S_j=((U_1,v_1^{vrf},v_1^{kes},v_1^{dsig},s_1),\dots,(U_n,v_n^{vrf},v_n^{kes},v_n^{dsig},s_n) $$
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$$ \eta_j \leftarrow \{0,1\}^\lambda $$
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<sup><strong>Note that new stakeholders need to wait for the next epoch
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to be added to the genesis block</strong></sup>
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## Block
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block $\textbf{B}$ is the building block of the blockchain
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block $B_{i}=(st,d,sl,B_{\pi},\rho, \sigma_s)$ created for slot i by stakeholder, and slot i leader $U_s$:
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A block $\textbf{B}$ is the building block of the blockchain.
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$$\textbf{\textcolor{red}{st}}: \text{state of the prebvious block, Hash(head($\mathbb{C}$}$$
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Block $B_{i}=(st, d, sl, B_{\pi}, \rho, \sigma_s)$ created for slot i
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by a stakeholder, and slot i leader $U_s$:
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$$\textbf{\textcolor{red}{st}}: \text{state of the prebvious block, Hash(head($\mathbb{C}$))}$$
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$$\textbf{\textcolor{red}{d}}: \text{data held by the block}$$
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$$\textbf{\textcolor{red}{sl}}: \text{slot id generated by the beacon}$$
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$$\textbf{\textcolor{red}{$B_\pi$}}: \text{proof the stakeholder ${U_s}$ is the owner, $B_{\pi}=(U_s,y,\pi)$, y,$\pi$ are the output of the VRF}$$
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@@ -27,92 +40,100 @@ $$\textbf{\textcolor{red}{$\rho$}}: \text{random seed for vrf, $\rho=(\rho_y,\rh
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$$\textbf{\textcolor{red}{$\sigma_{s}$}}: \text{owner signature on the block}$$
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## Leader selection
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At the onset of each slot each a stakeholder needs to verify if it's
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the weighted random leader for this slot.
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## leader selection
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at the onset of each slot each stakeholder needs to verify if it's the weighted random leader for this slot.
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$$y < T_{i}$$
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$$\small\text{\emph{check if VRF output is less than some threshold}}$$
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this statement might hold true for zero or more stakeholders, thus we might end up with multiple leaders for a slot, and other times no leader.
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also note that no one would know who is the leader, how many leaders are there for the slot, until you receive signed block with a proof claiming to be a leader.
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<center><sup><strong>check if VRF output is less than some threshold
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</strong></sup></center>
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This statement might hold true for zero or more stakeholders, thus we
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might end up with multiple leaders for a slot, and other times no
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leader. Also note that no one would know who the leaderis , how many
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leaders are there for the slot, until you receive a signed block with
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a proof claiming to be a leader.
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$$y = VRF(\eta||sid)$$
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$$\small\text{\emph{$\eta$ is random nonce generated from the blockchain, $\textbf{sid}$ is block id}}$$
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<center><sup><strong>$\eta$ is random nonce generated from the
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blockchain, $\textbf{sid}$ is block id</strong></sup></center>
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$$\phi_{f} = 1 - (1-f)^{\alpha_i}$$
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$$T_{i} = 2^{l_{VRF}}\phi_{f}(\alpha_i^j)$$
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note that $\phi_f(1)=f$, \textbf{f}: the active slot coefficient is the probability that a party holding all the stake will be selected to be a leader.
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stakeholder is selected as leader for slot j with probability $\phi_f(\alpha_i)$, $\alpha_i$ is $U_i$ stake.
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## leaky non-resettable beacon
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built on top of globally synchronized clock, that leaks the nonce $\eta$ of the next epoch a head of time (thus called leaky), non-resettable in the sense that the random nonce is deterministic at slot s, while assuring security against adversary controlling some stakeholders.
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for an epoch j, the nonce $\eta_j$ is calculated by hash function H, as:
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Note that $\phi_f(1)=f$, $\textbf{f}$: the active slot coefficient is
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the probability that a party holding all the stake will be selected to
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be a leader. Stakeholder is selected as leader for slot j with
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probability $\phi_f(\alpha_i)$, $\alpha_i$ is $U_i$ stake.
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## Leaky non-resettable beacon
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Built on top of globally synchronized clock, that leaks the nonce
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$\eta$ of the next epoch a head of time (thus called leaky),
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non-resettable in the sense that the random nonce is deterministic at
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slot s, while assuring security against adversary controlling some
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stakeholders.
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For an epoch j, the nonce $\eta_j$ is calculated by hash function H,
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as:
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$$\eta_j = H(\eta_{j-1}||j||v)$$
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v is the concatentation of the value $\rho$ in all blocks from the beginning of epoch $e_{i-1}$ to the slot with timestamp up to $(j-2)R + \frac{16k}{1+\epsilon}$, note that k is a persistence security parameter, R is the epoch length in terms of slots.
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v is the concatentation of the value $\rho$ in all blocks from the
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beginning of epoch $e_{i-1}$ to the slot with timestamp up to
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$(j-2)R + \frac{16k}{1+\epsilon}$, note that k is a persistence
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security parameter, R is the epoch length in terms of slots.
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# Protocol
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# Appendix
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This section gives further details about the structures that will be used by the protocol. Since Streamlet consensus protocol will be used at early stages of the Blockchain development, we created hybrid structures, to enable seemless transition from one protocol to the other, without the need of a blockchain forking.
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This section gives further details about the structures that will be
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used by the protocol. Since Streamlet consensus protocol will be used
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at early stages of the Blockchain development, we created hybrid
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structures, to enable seemless transition from one protocol to the
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other, without the need of a blockchain forking.
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## Blockchain
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\begin{tabular}{||c c c||}
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\hline
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Field & Type & Description \\ [0.5ex]
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\hline\hline
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blocks & Vec<Block> & Series of blocks consisting the Blockchain. \\ [1ex]
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\hline
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\end{tabular}
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| Field | Type | Description |
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|----------|--------------|--------------------------------------------|
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| `blocks` | `Vec<Block>` | Series of blocks consisting the Blockchain |
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## Block
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\begin{tabular}{||c c c||}
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\hline
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Field & Type & Description \\ [0.5ex]
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\hline\hline
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st & String & Previous block hash. \\
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\hline
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sl & u64 & Slot uid, generated by the beacon. \\
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\hline
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txs & Vec<Transaction> & Transactions payload. \\
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\hline
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metadata & Metadata & Additional block information. \\ [1ex]
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\hline
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\end{tabular}
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| Field | Type | Description |
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|------------|--------------------|-----------------------------------|
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| `st` | `String` | Previous block hash |
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| `sl` | `u64` | Slot UID, generated by the beacon |
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| `txs` | `Vec<Transaction>` | Transactions payload |
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| `metadata` | `Metadata` | Additional block information |
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## Metadata
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\begin{tabular}{||c c c||}
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\hline
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Field & Type & Description \\ [0.5ex]
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\hline\hline
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om & OuroborosMetadata & Block information used by Ouroboros consensus. \\
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\hline
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sm & StreamletMetadata & Block information used by Streamlet consensus. \\
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\hline
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timestamp & Timestamp & Block creation timestamp. \\ [1ex]
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\hline
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\end{tabular}
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## Ouroboros\_Metadata
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\begin{tabular}{||c c c||}
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\hline
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Field & Type & Description \\ [0.5ex]
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\hline\hline
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proof & VRFOutput & Proof the stakeholder is the block owner. \\
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\hline
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r & Seed & Random seed for VRF. \\
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\hline
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s & Signature & Block owner signature. \\ [1ex]
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\hline
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\end{tabular}
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| Field | Type | Description |
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|-------------|---------------------|-----------------------------------------------|
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| `om` | `OuroborosMetadata` | Block information used by Ouroboros consensus |
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| `sm` | `StreamletMetadata` | Block information used by Streamlet consensus |
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| `timestamp` | `Timestamp` | Block creation timestamp |
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## Streamlet\_Metadata
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\begin{tabular}{||c c c||}
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\hline
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Field & Type & Description \\ [0.5ex]
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\hline\hline
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votes & Vec<Vote> & Epoch votes for the block. \\
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\hline
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notarized & bool & Block notarization flag. \\
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\hline
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finalized & bool & Block finalization flag. \\ [1ex]
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\hline
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\end{tabular}
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## Ouroboros Metadata
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| Field | Type | Description |
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|-------------|---------------------|-----------------------------------------------|
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| `proof` | `VRFOutput` | Proof the stakeholder is the block owner |
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| `r` | `Seed` | Random seed for the VRF |
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| `s` | `Signature` | Block owner signature |
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## Streamlet Metadata
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| Field | Type | Description |
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|-------------|---------------------|-----------------------------------------------|
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| `votes` | `Vec<Vote>` | Epoch votes for the block |
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| `notarized` | `bool` | Block notarization flag |
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| `finalized` | `bool` | Block finalization flag |
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