Model

Let $\text{Bulla}$ be defined as in the section Bulla Commitments.

Let $P_p,{\mathbb{F}}_p,\mathcal{X},\mathcal{Y},\text{B⁶⁴2Fₚ}$ be defined as in the section Pallas and Vesta.

DAO

The DAO contains the main parameters that define DAO operation:

• The proposer limit $L$ is the minimum number of governance tokens of type $\tau$ required to create a valid proposal on chain. Note this minimum can come from multiple token holders.
• Quorum $Q$ specifies the absolute minimum number of tokens required for before a proposal can be accepted.
• The approval ratio $A^{\%}$ is a tuple that specifies the minimum theshold of affirmative yes votes for a proposal to become accepted.
• The public key $PK$ serves a dual role for both encrypted notes, and as a key to authorize accepted proposals to be executed. This key may be shared widely with all DAO members or within a privileged group.

Define the DAO params $$\begin{array}{rl}{\text{Params}}_{\text{DAO}}.L& \in N_{64}\\ {\text{Params}}_{\text{DAO}}.Q& \in N_{64}\\ {\text{Params}}_{\text{DAO}}.A^{\%}& \in N_{64}\times N_{64}\\ {\text{Params}}_{\text{DAO}}.\tau & \in {\mathbb{F}}_p\\ {\text{Params}}_{\text{DAO}}.\text{PK}& \in P_p\end{array}$$ where the approval ratio ${\text{Approval}}^{\%}=(q,d)$ defines the equivalence class $[\frac{q}{d}]$ of fractions defined by $q_1{d}_2=q_2{d}_1⟺[\frac{q_1}{d_1}]\sim [\frac{q_2}{d_2}]$.

/// DAOs are represented on chain as a commitment to this object
pub struct Dao {
    /// The minimum amount of governance tokens needed to open a proposal
    pub proposer_limit: u64,
    /// Minimal threshold of participating total tokens needed for a proposal to pass
    pub quorum: u64,
    /// The ratio of winning/total votes needed for a proposal to pass
    pub approval_ratio_quot: u64,
    pub approval_ratio_base: u64,
    /// DAO's governance token ID
    pub gov_token_id: TokenId,
    /// Public key of the DAO
    pub public_key: PublicKey,
    /// DAO bulla blind
    pub bulla_blind: BaseBlind,
}

$${\text{Bulla}}_{\text{DAO}}:{\text{Params}}_{\text{DAO}}\times {\mathbb{F}}_p\to {\mathbb{F}}_p$$ $${\text{Bulla}}_{\text{DAO}}(p,b_{\text{DAO}})=\text{Bulla}(N_{64}2{\mathbb{F}}_p(p.L),N_{64}2{\mathbb{F}}_p(p.Q),N_{64}2{\mathbb{F}}_p(p.A^{\%}),p.\tau ,\mathcal{X}(p.\text{PK}),\mathcal{Y}(p.\text{PK}),b_{\text{DAO}})$$

Proposals

Auth Calls

Let $\text{FuncId}$ be defined as in Function IDs.

Let $\text{BLAKE2b}$ be defined as in BLAKE2b Hash Function.

Define $\text{AuthCall}=(\text{FuncId},{\mathbb{B}}^{\ast })$. Each authorization call represents a child call made by the DAO. The auth data field is used by the child invoked contract to enforce additional invariants.

pub struct DaoAuthCall {
    pub contract_id: ContractId,
    pub function_code: u8,
    pub auth_data: Vec<u8>,
}

Define ${\text{Commit}}_{\text{Auth}}:{\text{AuthCall}}^{\ast }\to {\mathbb{F}}_p$ by $${\text{Commit}}_{{\text{Auth}}^{\ast }}(c)={\mathbb{B}}^{64}2{\mathbb{F}}_p({\text{BLAKE2b}}_{64}(\text{Encode}(c)))$$ which commits to a Vec<DaoAuthCall>.

Proposal

Define the proposal params $$\begin{array}{rl}{\text{Params}}_{\text{Proposal}}.C& \in {\text{AuthCall}}^{\ast }\\ {\text{Params}}_{\text{Proposal}}.t_0& \in N_{64}\\ {\text{Params}}_{\text{Proposal}}.D& \in N_{64}\\ {\text{Params}}_{\text{Proposal}}.\phi & \in {\mathbb{F}}_p\\ {\text{Params}}_{\text{Proposal}}.\text{DAO}& \in \text{Bulla}(\text{DAO2Fₚ}({\text{Params}}_{\text{DAO}}))\end{array}$$

pub struct DaoProposal {
    pub auth_calls: Vec<DaoAuthCall>,
    pub creation_blockwindow: u64,
    pub duration_blockwindows: u64,
    /// Arbitrary data provided by the user. We don't use this.
    pub user_data: pallas::Base,
    pub dao_bulla: DaoBulla,
    pub blind: BaseBlind,
}

$${\text{Bulla}}_{\text{Proposal}}:{\text{Params}}_{\text{Proposal}}\to {\mathbb{F}}_p^5$$ $${\text{Bulla}}_{\text{Proposal}}(p)=({\text{Commit}}_{{\text{Auth}}^{\ast }}(p.C),N_{64}2{\mathbb{F}}_p(p.t_0),N_{64}2{\mathbb{F}}_p(p.D),p.\phi ,p.\text{DAO})$$

Vote Nullifiers

Additionally for proposals, we keep track of nullifiers for each token weighted vote for or against a proposal.

Let $\text{PoseidonHash}$ be defined as in the section PoseidonHash Function.

Let $\mathcal{C}$ be the coin params, and $C$ be the coin commitment as defined in Money Contract.

Let $P$ be a proposal bulla as in the section Proposal.

Define ${\text{Nullifier}}_{\text{Vote}}:{\mathbb{F}}_p\times {\mathbb{F}}_p\times {\mathbb{F}}_p\to {\mathbb{F}}_p$ as follows: $${\text{Nullifier}}_{\text{Vote}}(\mathcal{C}.s,C,P)=\text{PoseidonHash}(\mathcal{C}.s,C,P)$$

Blockwindow

Time limits on proposals are expressed in 4 hour windows. Since proofs cannot guarantee which block they get into, we therefore must modulo the block height a certain number which we use in the proofs.

const _SECS_IN_HOUR: u64 = 60 * 60;
const _WINDOW_TIME_HR: u64 = 4;
// Precalculating the const for better performance
// WINDOW_TIME = WINDOW_TIME_HR * SECS_IN_HOUR
const WINDOW_TIME: u64 = 14400;

/// Blockwindow from block height and target time. Used for time limit on DAO proposals.
pub fn blockwindow(height: u32, target: u32) -> u64 {
    let timestamp_secs = (height as u64) * (target as u64);
    timestamp_secs / WINDOW_TIME
}

which can be used like this

    let current_blockwindow =
        blockwindow(wasm::util::get_verifying_block_height()?, wasm::util::get_block_target()?);