spec: DAO::propose() nullifier

doc/latex-macros.txt

@@ -2,4 +2,5 @@
 \hash:{\textrm{hash}}
 \t:{\textrm{#1}}
 \~:{\sim}
+\cN:{\mathcal{N}}
 

doc/src/spec/contracts/dao/contract.md

@@ -74,6 +74,7 @@ $$ \begin{aligned}
 
 Define the DAO propose input function params
 $$ \begin{aligned}
+  \t{ProposeInput}.\cN &∈ 𝔽ₚ \\
   \t{ProposeInput}.V &∈ ℙₚ \\
   \t{ProposeInput}.R_\t{coin} &∈ 𝔽ₚ \\
   \t{ProposeInput}.\t{PK}_σ &∈ ℙₚ
@@ -129,11 +130,15 @@ claimed in the *proposer limit threshold met* check.
 
 For each input $i ∈ 𝐢$,
 
+  **Unused nullifier**   check that $\cN$ does not exist in the
+money contract nullifiers DB.
+
   **Valid input coins merkle root**   check that $i.R_\t{coin}$ is a
 previously seen merkle root in the money contract merkle roots DB.
 
   Let there be a prover auxiliary witness inputs:
 $$ \begin{aligned}
+  x_c &∈ 𝔽ₚ \\
   x_σ &∈ 𝔽ₚ \\
   c &∈ \t{Params}_\t{Coin} \\
   bᵥ &∈ 𝔽ᵥ \\
@@ -142,12 +147,13 @@ $$ \begin{aligned}
 \end{aligned} $$
   Attach a proof $π_i$ such that the following relations hold:
 
+  **Nullifier integrity**   $\cN = \t{PoseidonHash}(x_c, C)$.
+
   **Coin value commit**   $i.V = \t{PedersenCommit}(c.v, bᵥ)$.
 
   **Token commit**   $T = \t{PoseidonHash}(c.τ, b_τ)$.
 
-  **Valid coin**   let $C = \t{Commit}(c)$. Check
-$i.R_\t{coin} = \t{MerkleRoot}(ψᵢ, Πᵢ, C)$.
+  **Valid coin**   Check $c.P = \t{DerivePubKey}(x_c)$. Let $C = \t{Commit}(c)$. Check $i.R_\t{coin} = \t{MerkleRoot}(ψᵢ, Πᵢ, C)$.
 
   **Proof of signature public key ownership**   $i.\t{PK}_σ = \t{DerivePubKey}(x_σ)$.
 

doc/src/spec/contracts/dao/model.md

@@ -9,7 +9,7 @@ Let $ℙₚ, 𝔽ₚ, \mathcal{X}, \mathcal{Y}, \t{𝔹⁶⁴2𝔽ₚ}$ be defin
 The DAO contains the main parameters that define DAO operation:
 
 * The proposer limit $L$ is the minimum number of governance tokens of type
-  $T$ required to create a valid proposal on chain. Note this minimum can
+  $τ$ 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.