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zeekay
abf99d05fc
Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
53 lines
2.3 KiB
TeX
53 lines
2.3 KiB
TeX
\section{Protocol Specification}
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\label{sec:protocol}
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\subsection{Deposit}
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\begin{algorithm}[H]
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\caption{Privacy Pool Deposit}
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\label{alg:deposit}
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\begin{algorithmic}[1]
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\Procedure{Deposit}{user, amount $v$}
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\State \textbf{require} $v \in \{0.1, 1, 10, 100, 1000\}$ LUX \Comment{Fixed denominations}
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\State User generates: $\mathsf{sk} \xleftarrow{\$} \mathbb{F}_p$, $r \xleftarrow{\$} \mathbb{F}_p$
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\State $\mathsf{pk} \gets \mathsf{sk} \cdot G$
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\State $\mathsf{commitment} \gets H(\mathsf{Commit}(v, r), \mathsf{pk})$
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\State Transfer $v$ LUX from user to PrivacyPool contract
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\State Insert $\mathsf{commitment}$ into Merkle tree at next leaf
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\State $\mathsf{leafIndex} \gets$ current leaf count
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\State User stores $(\mathsf{sk}, r, v, \mathsf{leafIndex})$ locally (secret note)
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\EndProcedure
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\end{algorithmic}
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\end{algorithm}
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Fixed denominations ensure all deposits of the same value are indistinguishable, maximizing the anonymity set.
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\subsection{Withdrawal}
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\begin{algorithm}[H]
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\caption{Privacy Pool Withdrawal}
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\label{alg:withdraw}
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\begin{algorithmic}[1]
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\Procedure{Withdraw}{secretNote, recipient, aspChoice}
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\State Retrieve $(\mathsf{sk}, r, v, \mathsf{leafIndex})$ from secretNote
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\State Compute $\mathsf{nf} \gets H_{\text{null}}(\mathsf{sk}, \mathsf{leafIndex})$
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\State Obtain current pool Merkle root $R$
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\State Obtain association set root $R_{\mathcal{A}}$ from chosen ASP
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\State Compute Merkle path for $\mathsf{leafIndex}$ in pool tree
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\State Compute Merkle path for $\mathsf{leafIndex}$ in association set tree
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\State Generate Groth16 proof $\pi$ for circuit $\mathcal{C}$:
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\State \quad Public: $(R, R_{\mathcal{A}}, \mathsf{nf}, \mathsf{recipient}, v)$
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\State \quad Private: $(\mathsf{sk}, r, \mathsf{leafIndex}, \text{paths})$
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\State Submit $(\pi, R, R_{\mathcal{A}}, \mathsf{nf}, \mathsf{recipient}, v)$ to contract
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\State Contract verifies:
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\State \quad (a) $\pi$ is valid for public inputs
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\State \quad (b) $\mathsf{nf}$ has not been used before
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\State \quad (c) $R$ is a valid (recent) pool root
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\State \quad (d) $R_{\mathcal{A}}$ is from a registered ASP
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\State If all checks pass: transfer $v$ LUX to $\mathsf{recipient}$
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\State Record $\mathsf{nf}$ as spent
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\EndProcedure
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\end{algorithmic}
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\end{algorithm}
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