commit 015fae704db7a681aae56d7422a362bc7f62d98d
parent 93ed1b081170dd844ecb405e9ff4850347662094
Author: Pius Loosli <loosp2@bfh.ch>
Date: Mon, 23 Oct 2023 19:41:28 +0200
[doc] More details on signing, signing applications, BUDI-key-pair
Diffstat:
| M | doc/flows/main.tex | | | 66 | ++++++++++++++++++++++++++++++++++++++++++++---------------------- |
1 file changed, 44 insertions(+), 22 deletions(-)
diff --git a/doc/flows/main.tex b/doc/flows/main.tex
@@ -23,11 +23,28 @@
\begin{itemize}
\item \textbf{Cryptographic Hash Function} $H(m) = h$ where $m$ is a message and $h$ the resulting hash.
- \item \textbf{Signing Functions}
+ \item \textbf{Signing}
\begin{itemize}
- \item $\Sigma(m,k) = \sigma$ where $m$ is a message and $k$ is the private key used to sign the message (e.g. EdDSA).
-
- \item $\overline{\Gamma}(\overline{n},j) = \overline{\gamma}$ where $\overline{n}$ is a blinded message and $j$ is the private key used to blind sign the message (e.g. RSA/CS).
+ \item \textbf{Classic/lightweight signing (e.g. EdDSA):}
+ \begin{align}
+ \fbox{$\Sigma(m,k) = \sigma$}
+ \end{align}
+ where $m$ is a message and $k$ is the private key used to sign the message.\\
+ Applications:
+ \begin{itemize}
+ \item A charity signs a collection of $BKP$ before transfering them to the Donau to issue $Donation Receipt$s
+ \item The Donau computes the \emph{donation statement} signature for a donor for a specific year
+ \end{itemize}
+
+ \item \textbf{Blind signing(e.g. RSA/CS):}
+ \begin{align}
+ \fbox{$\overline{B}(\overline{m},k) = \overline{\beta}$}
+ \end{align}
+ where $\overline{m}$ is a blinded message and $k$ is the private key used to blind sign the message.\\
+ Application:
+ \begin{itemize}
+ \item The Donau blind signs \emph{BUDI}s received from the charity with the private key matching the public key in the received \emph{BKP}
+ \end{itemize}
\end{itemize}
\item \textbf{Donation Unit} $DU = (K_x^{pub}, K_x^{priv})$ where $x$ is the associated value (e.g. 2EUR):
@@ -36,9 +53,14 @@
\item \textbf{Unique Donor Identifier} $UDI = \langle H(\texttt{TAXID}, \texttt{SALT}), \texttt{NONCE} \rangle$
- \item \textbf{Blinded Unique Donor Identifier} $BUDI = \langle blinded$ $UDI, H(K_x^{pub}) \rangle$, blinded to protect the privacy of the donor
+ \item \textbf{Blinded Unique Donor Identifier} $BUDI = blinded$ $UDI$, blinded to protect the privacy of the donor
+
+ \begin{itemize}
+ \item \textbf{BUDI-key-pair} \emph{BKP} = $Pair(BUDI, H(K_x^{pub}))$
+ \end{itemize}
+
- \item \textbf{Donation Receipt} $DR = \langle UDI, \gamma, H(K_x^{pub}) \rangle$ where $\gamma$ is the unblinded signature: Sent to the Donau to get the donation Statement.
+ \item \textbf{Donation Receipt} $DR = \langle UDI, \beta, H(K_x^{pub}) \rangle$ where $\beta$ is the unblinded signature: Sent to the Donau to get the donation Statement.
\item \textbf{Donation Statement} $DS = \Sigma(\langle \texttt{AMOUNT}_{Total}, \texttt{YEAR}, H(\texttt{TAXID}, \texttt{SALT}) \rangle, D^{priv})$ where $D^{priv}$ is the private key from the Donau: Signature to attest the amount donated in a particular year by a specific donor.
@@ -73,22 +95,22 @@
\item The donor blinds the $UDI$'s using a \textbf{different} blinding factor $b$ for every $UDI_i$.
\begin{align}
- BUDI_1 &= \langle Blind(UDI_1, K_x^{pub}, b_i), H(K_x^{pub}) \rangle \\
+ BKP_1 &= \langle Blind(UDI_1, K_x^{pub}, b_1), H(K_x^{pub}) \rangle \\
... \\
- BUDI_i &= \langle Blind(UDI_i, K_x^{pub}, b_i), H(K_x^{pub}) \rangle
+ BKP_i &= \langle Blind(UDI_i, K_x^{pub}, b_i), H(K_x^{pub}) \rangle
\end{align}
-\item The donor sends the $BUDI$'s as well as the corresponding payment to the charity.
+\item The donor sends the $BKP$'s as well as the corresponding payment to the charity.
\end{enumerate}
-\subsubsection{Charity sends signed $BUDI$'s to Donau}
+\subsubsection{Charity sends signed $BKP$'s to Donau}
\begin{enumerate}
\item The charity verifies that the amount requested (based on the $H(K_x^{pub})$) for signing is lower or equal to the effective amount of the donation.
- \item The charity signs (using EdDSA) a structure containing all unsigned $BUDI$'s coming from the donor.
+ \item The charity signs (using EdDSA) a structure containing all unsigned $BKP$'s coming from the donor.
\begin{align}
- \sigma = \Sigma(\langle BUDI_1, BUDI_2, ..., BUDI_i \rangle, C^{priv})
+ \sigma_c = \Sigma(\langle BKP_1, BKP_2, ..., BKP_i \rangle, C^{priv})
\end{align}
\item The charity sends this structure and the signature $\sigma$ to the Donau.
@@ -98,34 +120,34 @@
\begin{enumerate}
\item The Donau:
\begin{enumerate}
- \item verifies the signature $\sigma$ on the structure.
+ \item verifies the signature $\sigma_c$ on the structure.
\item increments the current amount of donations received per year of the charity. This value is increased by the total amount of the $BUDI$'s, if the increment does not exceed the annual limit.
\item blind signs all the $blinded$ $UDI$'s using the $DU$ private keys $K_x^{priv}$ matching the public keys $H(K^{pub})$ used in the $BUDI$'s.
\begin{align}
- \overline{\gamma_1} = \overline{\Gamma}(blinded\ UDI_1, K_x^{priv}) \\
+ \overline{\beta_1} = \overline{B}(blinded\ UDI_1, K_x^{priv}) \\
... \\
- \overline{\gamma_i} = \overline{\Gamma}(blinded\ UDI_i, K_x^{priv})
+ \overline{\beta_i} = \overline{B}(blinded\ UDI_i, K_x^{priv})
\end{align}
- \item sends back the blind signatures $\overline{\gamma_1}, ..., \overline{\gamma_i}$ to the charity.
+ \item sends back the blind signatures $\overline{\beta_1}, ..., \overline{\beta_i}$ to the charity.
\end{enumerate}
\item The charity forwards the blind signatures to the donor.
- \item The donor unblinds the $BUDI$'s to get the signatures $\gamma_1, ..., \gamma_i$. This results in a collection of \textbf{Donation Receipts} $DR$'s each consisting of the $UDI$, the signature $\gamma$ and the Hash of the $DU$ public key $H(K_x^{pub})$.
+ \item The donor unblinds the signed $BUDI$'s $\overline{\beta_1}, ..., \overline{\beta_i}$ to get the signatures $\beta_1, ..., \beta_i$. This results in a collection of \textbf{Donation Receipts} $DR$'s each consisting of the $UDI$, the signature $\beta$ and the Hash of the $DU$ public key $H(K_x^{pub})$.
\begin{align}
- \gamma_1 &= Unblind(\overline{\gamma_1}, b_1) \\
+ \beta_1 &= Unblind(\overline{\beta_1}, b_1) \\
... \\
- \gamma_i &= Unblind(\overline{\gamma_i}, b_i)
+ \beta_i &= Unblind(\overline{\beta_i}, b_i)
\end{align}
\begin{align}
- DR_1 &= \langle UDI_1, \gamma_1, H(K_x^{pub}) \rangle \\
+ DR_1 &= \langle UDI_1, \beta_1, H(K_x^{pub}) \rangle \\
... \\
- DR_i &= \langle UDI_i, \gamma_i, H(K_x^{pub}) \rangle
+ DR_i &= \langle UDI_i, \beta_i, H(K_x^{pub}) \rangle
\end{align}
\end{enumerate}
@@ -136,7 +158,7 @@
\begin{itemize}
\item checks that $K_x^{pub}$ is known.
- \item verifies that the signature $\gamma$ is correct using the corresponding public key $K_x^{pub}$.
+ \item verifies that the signature $\beta$ is correct using the corresponding public key $K_x^{pub}$.
\item verifies that the hash of the $\texttt{TAXID}$ and the $\texttt{SALT}$ is the same as in other $DR$'s (With multiple wallets each wallet must simply obtain a separate $DS$!).
