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.

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

Vesting Configuration

The vesting configuration contains the main parameters that define the vesting operation:

• The vesting authority public key $VAPK$ controls the vesting configuration.
• The vestee public key $VPK$ for withdrawls.
• The shared secret public key $SPK$ controls who can use the vested coin.
• Token $t$ is the token type of the to-be-vested input coins.
• Total $T$ is the total amount of the to-be-vested input coins.
• Cliff $C$ is the amount unlocked at the start blockwindow $S$.
• Start $S$ and end $E$ are the blockwindows defining when vesting starts and ends.
• Blockwindow value $V$ is the amount unlocked on each blockwindow.

Define the vesting configuration $VC$ params: $$\begin{array}{rl}{\text{Params}}_{\text{VC}}.\text{VAPK}& \in P_p\\ {\text{Params}}_{\text{VC}}.\text{VPK}& \in P_p\\ {\text{Params}}_{\text{VC}}.\text{SPK}& \in P_p\\ {\text{Params}}_{\text{VC}}.\tau & \in {\mathbb{F}}_p\\ {\text{Params}}_{\text{VC}}.T& \in N_{64}\\ {\text{Params}}_{\text{VC}}.C& \in N_{64}\\ {\text{Params}}_{\text{VC}}.S& \in N_{64}\\ {\text{Params}}_{\text{VC}}.E& \in N_{64}\\ {\text{Params}}_{\text{VC}}.V& \in N_{64}\end{array}$$

TODO: add model definition path

$${\text{Bulla}}_{\text{VC}}:{\text{Params}}_{\text{VC}}\times {\mathbb{F}}_p\to {\mathbb{F}}_p$$ $$\begin{array}{r}{\text{Bulla}}_{\text{VC}}(p,b_{\text{VC}})=\text{Bulla}(\\ \mathcal{X}(p.\text{VAPK}),\mathcal{Y}(p.\text{VAPK}),\\ \mathcal{X}(p.\text{VPK}),\mathcal{Y}(p.\text{VPK}),\\ \mathcal{X}(p.\text{SPK}),\mathcal{Y}(p.\text{SPK}),\\ p.\tau ,\\ N_{64}2{\mathbb{F}}_p(p.T),\\ N_{64}2{\mathbb{F}}_p(p.C),\\ N_{64}2{\mathbb{F}}_p(p.S),\\ N_{64}2{\mathbb{F}}_p(p.E),\\ N_{64}2{\mathbb{F}}_p(p.V),\\ b_{\text{VC}}\\ )\end{array}$$

Note: Since a vesting configuration bulla is derived using a random blinding factor, it’s safe to use the same parameters to generate different vesting configurations.

Blockwindow

Time limits on vesting configurations are expressed in 1 day 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.

TODO: add definition path

which can be used like this:

TODO: add usage example path