\chapter{Protocol Specification}
\label{chap:spec}
The proposed Taler protocols using the Clause Blind Schnorr Signature Scheme will be implemented as an additional option besides the existing \gls{RSABS} variant of the protocol as suggested by Christian Grothoff.
A Taler Exchange operator should be able to configure whether he wants to use \gls{RSABS} or \gls{CSBS}.
\\This variant allows to choose the signature scheme globally or per denomination.
Furthermore, it allows a change of signature scheme in a non-breaking way by revoking (or letting expire) a denomination and offering new denominations with the other scheme.
\\
The following key points are specified in this chapter:
\begin{itemize}
  \item Architecture of the different components
  \item Explain and specify needed changes
  \item Data strucutures
  \item Public \acp{API}
  \item Persistence
  \item Used libraries
\end{itemize}

\section{Architecture}
Before specifying the implementation of the different protocols, a deeper understanding of the technical architecture of Talers components is needed.
this section introduces the architecture of the exchange and wallet components and explains where the needed changes need to be implemented on a high-level.

\subsection{Exchange}
An introduction to the exchange can be found in section \ref{sec:exchange}.
An exchange operator needs to run and maintain some additional services besides Taler's exchange.
Although this is not directly relevant for the implementation, it helps to better understand the environment in which the exchange runs.
The perspective of an exchange operator can be seen in figure \ref{fig:taler:exchange-operator-architecture}.

\begin{figure}[h!]
  \begin{adjustbox}{max totalsize={.9\textwidth}{.7\textheight},center}
    \begin{tikzpicture}
      \tikzstyle{def} = [node distance= 5em and 6.5em, inner sep=1em, outer sep=.3em];
      \node (origin) at (0,0) {};
      \node (exchange) [def,above=of origin,draw]{Exchange};
      \node (nexus) [def, draw, below right=of exchange] {Nexus};
      \node (corebanking) [def, draw, below left=of nexus] {Core Banking};
      \node (nginx) [def, draw, above=of exchange]{Nginx};
      \node (postgres) [def, draw, below left=of exchange]{Postgres};
      \node (postgres-nexus) [def, draw, below right=of nexus]{Postgres};

      \tikzstyle{C} = [color=black, line width=1pt]

      \draw [<-, C] (exchange) -- (nginx) node [midway, above, sloped] (TextNode) {REST API};
      \draw [<-, C] (postgres) -- (exchange) node [midway, above, sloped] (TextNode) {SQL};
      \draw [<-, C] (postgres-nexus) -- (nexus) node [midway, above, sloped] (TextNode) {SQL};
      \draw [<-, C] (nexus) -- (exchange) node [midway, above, sloped] (TextNode) {Internal REST API};
      \draw [<-, C] (corebanking) -- (nexus) node [midway, above, sloped] (TextNode) {EBICS/FinTS};

    \end{tikzpicture}
  \end{adjustbox}
  \caption{Taler exchange operator architecture (source: \cite{taler-presentation})}
  \label{fig:taler:exchange-operator-architecture}
\end{figure}

The software architecture of the exchange can be seen in figure \ref{fig:taler:exchange-architecture}.
The API runs under the httpd service, where the API endpoints need to be adjusted/added to incorporate the changes of this thesis.
The httpd server has no access to the private keys of the denomination and  online signing keys.
Only the corresponding security module can perform operations requiring the private key.
Further the keys are also managed by these security modules.
To support \gls{CSBS} a new security module, which performs signature operations, is added.
To persist the new data structures, the postgres helpers need to be adjusted to serialize/deserialize the new \gls{CSBS} data structures.
More details on what changes are needed in these places is discussed in the following sections.

\begin{figure}[h!]
  \begin{center}
    \begin{tikzpicture}
      \tikzstyle{def} = [node distance=2em and 2.5em, inner sep=1em, outer sep=.3em];
      \node (origin) at (0,0) {};
      \node [blue] (httpd) [def,above=of origin,draw]{httpd};
      \node (secmod-rsa) [def, draw, right=of httpd] {secmod-rsa};
      \node (secmod-eddsa) [def, draw, left=of httpd] {secmod-eddsa};
      \node [blue](postgres) [def, draw, below=of httpd]{Postgres};
      \node [mGreen] (secmod-cs) [def, draw, left=of postgres]{secmod-cs};
      \node (aggregator) [def, draw, right=of postgres]{aggregator};
      \node (transfer) [def, draw, below left=of postgres]{transfer};
      \node (wirewatch) [def, draw, below right=of postgres]{wirewatch};
      \node (nexus) [def, draw, below=of postgres]{Nexus};

      \tikzstyle{C} = [color=black, line width=1pt]

      \draw [<->, C] (httpd) -- (postgres) node [midway, above, sloped] (TextNode) {};
      \draw [<->, C] (httpd) -- (secmod-rsa) node [midway, above, sloped] (TextNode) {};
      \draw [<->, C] (httpd) -- (secmod-eddsa) node [midway, above, sloped] (TextNode) {};
      \draw [<->, C] (httpd) -- (secmod-cs) node [midway, above, sloped] (TextNode) {};
      \draw [<->, C] (aggregator) -- (postgres) node [midway, above, sloped] (TextNode) {};
      \draw [<->, C] (wirewatch) -- (postgres) node [midway, above, sloped] (TextNode) {};
      \draw [<->, C] (transfer) -- (postgres) node [midway, above, sloped] (TextNode) {};
      \draw [->, C] (transfer) -- (nexus) node [midway, above, sloped] (TextNode) {};
      \draw [<-, C] (wirewatch) -- (nexus) node [midway, above, sloped] (TextNode) {};
    \end{tikzpicture}
  \end{center}
  \caption{Taler exchange architecture (source: \cite{taler-presentation})}
  \label{fig:taler:exchange-architecture}
\end{figure}

\subsection{Wallet}
The architecture of the wallet implementation (as seen in figure \ref{fig:taler:wallet-architecture}) is quite straightforward.
To add support for \gls{CSBS} in the wallet, the cryptographic routines need to be reimplemented in Typescript.
Taler uses tweetnacl \cite{bern:tweetnacl} which provides functionality for the group operations.
There are existing \gls{hkdf} and \gls{fdh} implementations, that can be reused.\\
Furthermore, the Taler protocols need to be adjusted to support \gls{CSBS} in the wallet-core.

\begin{figure}[h!]
  \begin{center}
    \begin{tikzpicture}
      \tikzstyle{def} = [node distance= 5em and 4.5em, inner sep=1em, outer sep=.3em];
      \node (origin) at (0,0) {};
      \node (gui) [def,above=of origin,draw]{wallet-gui};
      \node [blue](core) [def,below=of gui,draw]{wallet-core};
      \node (sync) [def, draw, below left=of core] {Sync};
      \node (taler) [def, draw, below right=of core] {Taler};
      \node (anastasis) [def, draw, below=of core] {Anastasis};

      \tikzstyle{C} = [color=black, line width=1pt]
      \draw [<->, C] (gui) -- (core) node [midway, above, sloped] (TextNode) {};
      \draw [<->, C] (core) -- (sync) node [midway, above, sloped] (TextNode) {Backup};
      \draw [<->, C] (core) -- (taler) node [midway, above, sloped] (TextNode) {Payment};
      \draw [<->, C] (core) -- (anastasis) node [midway, above, sloped] (TextNode) {Key Escrow};
    \end{tikzpicture}
  \end{center}
  \caption{Taler wallet architecture (source: \cite{taler-presentation})}
  \label{fig:taler:wallet-architecture}
\end{figure}

\section{Persistence}
The Clause Blind Schnorr Signature scheme is quite different to \gls{RSABS}.
Despite the differences, the database model does not need to be changed.
The only change needed an additional type field, specifying whether RSA or CS is used as signature algorithm.
To persist the new structs introduced with the support for \gls{CSBS}, only the postgres helpers need to support serialization and deserialization of the new structs.

\section{Testing}
We will partially use test-driven development, meaning that we will write tests (at least for the known good case) before implementing functions, and extend them during and after development.
This allows us to check the functionality (code section, function(s)) during development, while being able to extend testing whenever we identify new test cases during development.

Test cases can be used to verify different aspects of a functionality.
These are the ones we will focus on.
\begin{itemize}
  \item \textbf{Known good}:
        Known good cases test whether a functionality works as expected.
        They are the most useful during development, because they indicate whether the code is working as expected.
  \item \textbf{Known Bad}:
        Known bad cases test whether functionality that is known not to work behaves as expected.
  \item \textbf{Determinism}:
        This case type checks whether the same input leads to the same output.
        It is important for code that must work deterministic (same output), non-deterministic (e.g. random output) or based on a state that impacts the functionality.
  \item \textbf{Performance testing}:
        Performance testing is used to gather timing information that can be used to identify functionality with long duration, or to  compare performance between different implementations or major changes.
        We will restrict performance testing to the comparison of the Blind RSA Signature Scheme and the Clause Blind Schnorr Signature Scheme.
\end{itemize}


\section{Signature Scheme Operations in GNUnet}
\label{sec:specification-signature-scheme}

The signature scheme operations implemented are needed in all other parts of the implementation.
Taler's cryptographic primitives (e.g. \gls{RSABS}, \gls{hkdf}, hash functions) are mostly implemented in GNUnet utils, therefore the Clause Blind Schnorr Signature routines will be implemented in GNUnet too.
It is important to provide a clear API for the cryptographic routines and to test them thoroughly.
Libsodium will be used for finite field arithmetic (\cite{libsodium:finite-field-arithmetic}) and for other functionality when available (e.g. for key generation).
Thus, a widely used and well tested cryptographic library is used for group operations.

For \acl{FDH} and \gls{hkdf} existing implementations provided by GNUnet are used.
The \gls{hkdf} is used with SHA-512 for the extraction phase and SHA-256 for the expansion phase.

\subsection{Data Structures}
Libsodium represents Ed25519 points and scalars as 32-byte char arrays.
To provide a more user-friendly \ac{API}, structs were created to represent each type.
For example \texttt{struct GNUNET\_CRYPTO\_CsPrivateKey} or  \texttt{struct GNUNET\_CRYPTO\_RSecret}
The main reason is to increase readability and to prevent misusage of the \ac{API}.
Unlike RSA, our \gls{CSBS} on Ed25519 data structures have a fixed sizes.
The different data structures can be found in table \ref{tab:datastruct-crypto}.

\begin{table}[ht]
  \centering
  \resizebox{0.95\textwidth}{!}{\begin{minipage}{\textwidth}
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Values} & \textbf{Data Structure} & \textbf{Data Type} \\\hline
      Curve25519 Scalar & {\small GNUNET\_CRYPTO\_Cs25519Scalar} & 32 byte char array\\\hline
      Curve25519 Point & {\small GNUNET\_CRYPTO\_Cs25519Point} & 32 byte char array\\\hline
      Private Key & {\small GNUNET\_CRYPTO\_CsPrivateKey} & {\small GNUNET\_CRYPTO\_Cs25519Scalar}\\\hline
      Public Key & {\small GNUNET\_CRYPTO\_CsPublicKey} & {\small GNUNET\_CRYPTO\_Cs25519Point}\\\hline
      $\alpha, \beta$ & {\small GNUNET\_CRYPTO\_CsBlindingSecret} & {\footnotesize 2x GNUNET\_CRYPTO\_Cs25519Scalar}\\\hline
      $r$ & {\small GNUNET\_CRYPTO\_CsRSecret} & {\small GNUNET\_CRYPTO\_Cs25519Scalar}\\\hline
      $R$ & {\small GNUNET\_CRYPTO\_CsRPublic} & {\small GNUNET\_CRYPTO\_Cs25519Point}\\\hline
      $c$ & {\small GNUNET\_CRYPTO\_CsC} & {\small GNUNET\_CRYPTO\_Cs25519Scalar}\\\hline
      $s$ & {\small GNUNET\_CRYPTO\_CsBlindS} & {\small GNUNET\_CRYPTO\_Cs25519Scalar}\\\hline
      $s'$ & {\small GNUNET\_CRYPTO\_CsS} & {\small GNUNET\_CRYPTO\_Cs25519Scalar}\\\hline
      $\sigma := \langle s',R' \rangle$ & {\small GNUNET\_CRYPTO\_CsSignature} & {\small GNUNET\_CRYPTO\_Cs25519Scalar}\\
      & & {\small GNUNET\_CRYPTO\_Cs25519Point}\\\hline
      Nonce & {\small GNUNET\_CRYPTO\_CsNonce} & 32 byte char array\\\hline
  \end{tabular}
  \caption{Data structures for cryptographic routines}
  \label{tab:datastruct-crypto}
\end{minipage}}
\end{table}



\subsection{Library API}
The public \ac{API} and related data structures are specified in the C header file \url{src/include/gnunet_crypto_lib.h} in the GNUnet repository \cite{gnunet-git}.
It was developed in multiple iterations based on feedback from Christian Grothoff.
The complete C header \ac{API} can be found in the repository.
This section provides an overview of the implemented crypto API.

Some design decisions need to be explained further:
\begin{itemize}
  \item In order to prevent misusage of our implementation and increase readability, the functions that represent different stages in the signature scheme takes different data types as in- and output.
        Internally most variables are either scalars or curve points (except for nonces, secrets and messages).
  \item Operations that are performed twice in the Clause Blind Schnorr Signature Scheme (e.g. derivation of $ r $) do not have to be called twice.
        Instead, the API returns an array of two instead of a single value.\\
        For these functions, we also optimized the \gls{hkdf} (as proposed by Christian Grothoff).
        Instead of calling \gls{hkdf} twice (with different salts, e.g. "r0" and "r1"), we call it one time (e.g. with salt "r") and double the output length.
  \item The cryptographic hash function used to derive $ c' $ (hash of $ R' $ and message) must map the results into the main subgroup for scalars, meaning that it has to be a \gls{fdh} (see \ref{sec:rsa-fdh}).
\end{itemize}

The following API examples should provide an overview on how the API works and how to use it.

First of all the API must provide functionality to create a \gls{25519} keypair as in listing \ref{lst:crypto-keypair-api}

\begin{lstlisting}[style=bfh-c,language=C, caption={GNUnet create keypair API}, label={lst:crypto-keypair-api}]
/**
 * Create a new random private key.
 *
 * @param[out] priv where to write the fresh private key
 */
void
GNUNET_CRYPTO_cs_private_key_generate (
    struct GNUNET_CRYPTO_CsPrivateKey *priv);


/**
 * Extract the public key of the given private key.
 *
 * @param priv the private key
 * @param[out] pub where to write the public key
 */
void
GNUNET_CRYPTO_cs_private_key_get_public (
    const struct GNUNET_CRYPTO_CsPrivateKey *priv,
    struct GNUNET_CRYPTO_CsPublicKey *pub);
\end{lstlisting}

The signer needs an API to generate his secret $r$ and calculate his public point $R$.
As specified in the redesign of the protocols, the r must not be chosen randomly because we need to provide \textit{\gls{abort-idempotency}}. However, the secret $r$ still needs to be \textit{unpredictable} and look random to the client.
The r\_derive API derives such a secret $r$ from a nonce and a long-term secret with \gls{hkdf}.
Further, the API ensures that a caller must generate two secret $r$ as in the Clause Blind Schnorr Signature scheme. This should discourage people from using the unsecure Blind Schnorr Signature scheme. See \ref{lst:crypto-rderive-api}.


\begin{lstlisting}[style=bfh-c,language=C, caption={GNUnet r derive API}, label={lst:crypto-rderive-api}]
 /**
  * Derive a new secret r pair r0 and r1.
  * In original papers r is generated randomly
  * To provide abort-idempotency, r needs to be derived but still needs to be UNPREDICTABLE
  * To ensure unpredictability a new nonce should be used when a new r needs to be derived.
  * Uses HKDF internally.
  * Comment: Can be done in one HKDF shot and split output.
  * 
  * @param nonce is a random nonce
  * @param lts is a long-term-secret in form of a private key
  * @param[out] r array containing derived secrets r0 and r1
  */
 void
 GNUNET_CRYPTO_cs_r_derive (const struct GNUNET_CRYPTO_CsNonce *nonce,
                            const struct GNUNET_CRYPTO_CsPrivateKey *lts,
                            struct GNUNET_CRYPTO_CsRSecret r[2]);
 
 
/**
  * Extract the public R of the given secret r.
  *
  * @param r_priv the private key
  * @param[out] r_pub where to write the public key
  */
 void
 GNUNET_CRYPTO_cs_r_get_public (const struct GNUNET_CRYPTO_CsRSecret *r_priv,
                                struct GNUNET_CRYPTO_CsRPublic *r_pub);
\end{lstlisting}


Same as the r\_derive, the blinding secrets are also derived and not generated randomly.
The blinding secrets are generated by a client who provides a secret as seed to derive the secrets from as in listing \ref{lst:crypto-blinding-secrets-api}.

\begin{lstlisting}[style=bfh-c,language=C, caption={GNUnet blinding secrets derive API}, label={lst:crypto-blinding-secrets-api}]
/**
 * Derives new random blinding factors.
 * In original papers blinding factors are generated randomly
 * To provide abort-idempotency, blinding factors need to be derived but still need to be UNPREDICTABLE
 * To ensure unpredictability a new nonce has to be used.
 * Uses HKDF internally
 * 
 * @param secret is secret to derive blinding factors
 * @param secret_len secret length
 * @param[out] bs array containing the two derivedGNUNET_CRYPTO_CsBlindingSecret
 */
void
GNUNET_CRYPTO_cs_blinding_secrets_derive (
    const struct GNUNET_CRYPTO_CsNonce *blind_seed,
    struct GNUNET_CRYPTO_CsBlindingSecret bs[2]);
\end{lstlisting}

Further the Clause Blind Schnorr API provides an API to calculate the two blinded c of the message with the two public $R$, the blinding factors and the public key as in listing \ref{lst:crypto-calc-c-api}.

\begin{lstlisting}[style=bfh-c,language=C, caption={GNUnet calculate blinded c API}, label={lst:crypto-calc-c-api}]
/**
 * Calculate two blinded c's
 * Comment: One would be insecure due to Wagner's algorithm solving ROS
 * 
 * @param bs array of the two blinding factor structs each containing alpha and beta
 * @param r_pub array of the two signer's nonce R
 * @param pub the public key of the signer
 * @param msg the message to blind in preparation for signing
 * @param msg_len length of message msg
 * @param[out] blinded_c array of the two blinded c's
 */
void
GNUNET_CRYPTO_cs_calc_blinded_c (
    const struct GNUNET_CRYPTO_CsBlindingSecret bs[2],
    const struct GNUNET_CRYPTO_CsRPublic r_pub[2],
    const struct GNUNET_CRYPTO_CsPublicKey *pub,
    const void *msg,
    size_t msg_len,
    struct GNUNET_CRYPTO_CsC blinded_c[2]);
\end{lstlisting}

The sign function in our API is called sign\_derive, since we derive $b \in \{0,1\}$ from the long-term secret and then calculate the signature scalar of $c_b$.
See listing \ref{lst:crypto-sign-api}.

\begin{lstlisting}[style=bfh-c,language=C, caption={GNUnet sign API}, label={lst:crypto-sign-api}]
/**
 * Sign a blinded c
 * This function derives b from a nonce and a longterm secret
 * In original papers b is generated randomly
 * To provide abort-idempotency, b needs to be derived but still need to be UNPREDICTABLE.
 * To ensure unpredictability a new nonce has to be used for every signature
 * HKDF is used internally for derivation
 * r0 and r1 can be derived prior by using GNUNET_CRYPTO_cs_r_derive
 * 
 * @param priv private key to use for the signing and as LTS in HKDF
 * @param r array of the two secret nonce from the signer
 * @param c array of the two blinded c to sign c_b
 * @param nonce is a random nonce
 * @param[out] blinded_signature_scalar where to write the signature
 * @return 0 or 1 for b (see Clause Blind Signature Scheme)
 */
int
GNUNET_CRYPTO_cs_sign_derive(
    const struct GNUNET_CRYPTO_CsPrivateKey *priv,
    const struct GNUNET_CRYPTO_CsRSecret r[2],
    const struct GNUNET_CRYPTO_CsC c[2],
    const struct GNUNET_CRYPTO_CsNonce *nonce,
    struct GNUNET_CRYPTO_CsBlindS *blinded_signature_scalar);
\end{lstlisting}

The API for the unblind operation can be called with the blinding secrets and the signature scalar received from the signer as in listing \ref{lst:crypto-unblind-api}.

\begin{lstlisting}[style=bfh-c,language=C, caption={GNUnet unblind API}, label={lst:crypto-unblind-api}]
  /**
 * Unblind a blind-signed signature using a c that was blinded
 *
 * @param blinded_signature_scalar the signature made on the blinded c
 * @param bs the blinding factors used in the blinding
 * @param[out] signature_scalar where to write the unblinded signature
 */
void
GNUNET_CRYPTO_cs_unblind (
    const struct GNUNET_CRYPTO_CsBlindS *blinded_signature_scalar,
    const struct GNUNET_CRYPTO_CsBlindingSecret *bs,
    struct GNUNET_CRYPTO_CsS *signature_scalar);
\end{lstlisting}

The verify API takes the message and its signature with the public key and returns GNUNET\_OK for a valid signature and GNUNET\_SYSERR otherwhise.
See listing \ref{lst:crypto-verify-api}.

\begin{lstlisting}[style=bfh-c,language=C,, caption={GNUnet verify API}, label={lst:crypto-verify-api}]
  /**
  * Verify whether the given message corresponds to the given signature and the
  * signature is valid with respect to the given public key.
  *
  * @param sig signature that is being validated
  * @param pub public key of the signer
  * @param msg is the message that should be signed by @a sig  (message is used to calculate c)
  * @param msg_len is the message length
  * @returns #GNUNET_YES on success, #GNUNET_SYSERR if signature invalid
  */
 enum GNUNET_GenericReturnValue
 GNUNET_CRYPTO_cs_verify (const struct GNUNET_CRYPTO_CsSignature *sig,
                          const struct GNUNET_CRYPTO_CsPublicKey *pub,
                          const void *msg,
                          size_t msg_len);
\end{lstlisting}

\subsection{Testing}
For digital signature schemes, the most important test case is the \textit{known good} case where a signature is created and successfully validated.
This test case already tests very much in a digital signature scheme.
When the signature creation or verification has a bug, a test will not succeed, because the mathematic operations need to be correct to be validated correctly.

The cryptographic operations are further tested for deterministicy (where it applies), meaning that multiple function calls with the same input must lead to the same output.

Since libsodium is used for the finite field arithmetic operations and is a well tested library, many cryptographic tests are already done in libsodium.

The performance is measured in a benchmark to see how performant \gls{CSBS} are in comparison to the RSA Blind Signature Scheme.

\section{Taler Cryptographic Utilities}
Taler provides utility functions to support cryptographic operations.\\
This chapter provides an overview of these utility functions and about the functionality they provide.

\subsection{Planchet Creation}
In crypto.c many utility functions are provided to create planchets (for planchet details see \ref{fig:coin:states}), blinding secrets and much more.
One difference between \gls{RSABS} and \gls{CSBS} is, that the coin private key and RSA blinding secret can be created at the same point in time, since the RSA blinding secret is created randomly.
However, for Clause Blind Schnorr secrets an additional step is needed, the public $R_0$ and $R_1$ are required to calculate the blinding seed to derive the secrets.

A planchet in the Clause Blind Schnorr Signature Scheme can be created as followed (implementation details ommited).

\begin{enumerate}
  \item Create planchet with new \ac{EdDSA} private key
  \item Derive withdraw nonce
  \item Request public $R_0, R_1$ from signer
  \item Derive blinding seed
  \item Prepare (blind) the planchet
\end{enumerate}

After the planchet is created, it is sent to the exchange to be signed.

\subsection{Taler CS Security Module}
The exchange segregates access to the private keys with separate security module processes.
The security module has sole access to the private keys of the online signing keys and thus, only a security module can create signatures.
The different \textit{taler-exchange-secmod} processes (separated by signature scheme) are managing the exchanges online signing keys. The RSA denomination keys for example are managed with \textit{taler-exchange-secmod-rsa}.

Now a new \textit{taler-exchange-secmod-cs} needs to be created for managing the \gls{CSBS} denomination keys.
These security modules run on the same machine as the httpd process and they use UNIX Domain Sockets as method for \acl{IPC}.
A short introduction about UNIX Domain Sockets can be found in the blog post \cite{matt:unix-domain-sockets}.
Furthermore, the security modules are used to protect the online signing keys by performing the actual signing operations in the dedicated taler-secmod-cs process.
This abstraction makes it harder for an attacker who has already compromised the http daemon to gain access to the private keys.
However, such an attacker would still be able to sign arbitrary messages (see \cite{taler-documentation:exchange-operator-manual}).
A crypto helper exists for each security module, these functions can be called inside the exchange for operations requiring the private online signing keys.
The new Clause Schnorr security module and corresponding crypto helper provides the following functionality:
\begin{itemize}
  \item Private Key Management and creation
  \item Request public $R_0, R_1$
  \item Request a signature of a $c_0,c_1$ pair
  \item Revoke an online signing key
\end{itemize}

\subsection{Testing}
All of the operations have tests and are included in unit tests.
As a template for testing, the existing RSA tests were used and adjusted for \gls{CSBS}.


\section{Denomination Key Management}
Since we introduce a type of denomination keys, related operations like connection to the \gls{CSBS} security module, making the denominations available for customers, persisting them in the database and offline signing using the exchange's offline signature key have to be extended to incorporate the \acl{CS}.

The exchange offline signer requests the future, not yet signed keys by calling GET \url{/management/keys} as described in table \ref{tab:management-keys-get}. \\\\
\framebox[1.1\width]{\color{blue}\texttt{GET /management/keys}}
\begin{table}[ht]
  \centering
  \resizebox{0.9\textwidth}{!}{\begin{minipage}{\textwidth}
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{ll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Value} \\
      future\_denoms & Information about denomination keys \\
      future\_signkeys & Information about exchange online signing keys \\
      master\_pub & Exchange's master public key \\
      denom\_secmod\_public\_key & RSA security module public key \\
      denom\_secmod\_cs\_public\_key & \gls{CSBS} security module public key \\
      signkey\_secmod\_public\_key & Online singing security module public key \\
  \end{tabular}
  \caption{GET \url{/management/keys} response data}
  \label{tab:management-keys-get}
\end{minipage}}
\end{table}

It then signs the keys and returns them using POST on the same \ac{URL} with the data described in table  \ref{tab:management-keys-post}. \\\\
\framebox[1.1\width]{\color{blue}\texttt{POST /management/keys}}
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{ll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Value} \\
      denom\_sigs & Denomination key signatures \\
      signkey\_sigs & Online signing key signatures \\
  \end{tabular}
  \caption{POST \url{/management/keys} response data}
  \label{tab:management-keys-post}
\end{table}

Wallets can then call GET \url{/keys} to obtain the current denominations and other information, the response is described in table \ref{tab:keys-get}. \\\\
\framebox[1.1\width]{\color{blue}\texttt{GET /keys}}
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{ll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Value} \\
      version & Exchange's protocol version \\
      currency & Currency \\
      master\_public\_key & Exchange's master public key \\
      reserve\_closing\_delay & Delay before reserves are closed \\
      signkeys & Exchange's online signing public keys \\
      recoup & Revoked keys \\
      denoms & List of denominations \\
      auditors & Auditors for this exchange \\
      list\_issue\_date & Timestamp \\
      eddsa\_pub & Exchange's online signing public key \\
      eddsa\_sig & Signature (use "eddsa\_pub" for verification) \\
  \end{tabular}
  \caption{GET \url{/keys} response data}
  \label{tab:keys-get}
\end{table}


\section{New Endpoint for $R$}
The withdraw and refresh protocols using the  Claude Blind Schnorr Signature Scheme introduce an additional round trip.
In this round trip, the customer requests two $ R $ from the exchange.
The exchange uses a secret $ r $ to calculate $ R := rG $.
\\
In contrast to the plain Clause Blind Schnorr Signature Scheme (see \ref{sec:clause-blind-schnorr-sig}), $ r $ isn't generated randomly but instead derived using a \gls{hkdf} with a nonce from the customer and a denomination private key (secret only known by the exchange).
This still ensures that the private $ r $ can't be anticipated, but has multiple advantages regarding \gls{abort-idempotency}.
\Gls{abort-idempotency} means that a withdraw or refresh operation can be aborted in any step and later tried again (using the same values) without yielding a different result.
The challenge for $ r, R $ regarding \gls{abort-idempotency} is to ensure that the same $ r $ is used during the complete signature creation process.

The only drawback of this process is that we have to ensure that the same nonce and secret aren't used for different withdraw- or refresh-operations.
This is done during signature creation and will be described in the withdraw protocol section \ref{sec:specification-withdraw}.


\subsection{Public APIs and Data Structures}
This is a new functionality, meaning a new endpoint accessible to customers has to be introduced.
It will be made available in the exchange HTTP server under \framebox[1.1\width]{\color{blue}\texttt{POST /csr}} and will take the input parameters described in table \ref{tab:csr-request-data} (as \ac{JSON}).
\begin{table}[ht]
  \centering
  \resizebox{0.9\textwidth}{!}{\begin{minipage}{\textwidth}
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Type} & \textbf{Value} \\
      nonce & String & 32 Bytes encoded in Crockford base32 Hex \\
      denom\_pub\_hash & String & Denomination Public Key encoded in Crockford base32 Hex \\
  \end{tabular}
  \caption{POST \url{/csr} request data}
  \label{tab:csr-request-data}
\end{minipage}}
\end{table}

The exchange will then check the denomination and return one of these HTTP status codes:
\begin{itemize}
  \item \textbf{200 (HTTP\_OK)}: Request Successful
  \item \textbf{400 (BAD\_REQUEST)}: Invalid input parameters
  \item \textbf{404 (NOT\_FOUND)}: Denomination unknown or not Clause Schnorr
  \item \textbf{410 (GONE)}: Denomination revoked/expired
  \item \textbf{412 (PRECONDITION\_FAILED)}: Denomination not yet valid
\end{itemize}

When the request was successful, the exchange returns the data described in table \ref{tab:csr-response-data} (as \ac{JSON}).
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Type} & \textbf{Value} \\
      r\_pub\_0 & String & 32 Bytes encoded in Crockford base32 Hex \\
      r\_pub\_1 & String & 32 Bytes encoded in Crockford base32 Hex \\
  \end{tabular}
  \caption{POST \url{/csr} response data}
  \label{tab:csr-response-data}
\end{table}


\subsection{Persistence}
This API does not persist anything.
This is because the resulting $R_0, R_1$ are derived and can be derived in a later step.


\section{Withdraw Protocol}
\label{sec:specification-withdraw}
The withdraw protocol has been introduced in section \ref{sec:withdrawal}.
For the \acl{CS} necessary adjustments are described in section \ref{sec:withdraw-protocol-schnorr}.


\subsection{Public APIs and Data Structures}
\label{sec:specification-withdraw-public-api}
The existing endpoint is available under \texttt{POST /reserves/[reserve]/withdraw} where "reserve" is the reserve public key encoded as Crockford base32.
It takes the following input parameters described in table \ref{tab:withdraw-request-data} as JSON.\\\\
\framebox[1.1\width]{\color{blue}\texttt{POST /reserves/[reserve]/withdraw}}
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{ll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Value} \\
      denom\_pub\_hash & Denomination Public Key \\
      coin\_ev & RSA blinded coin public key \\
      reserve\_sig & Signature over the request using the reserve's private key \\
  \end{tabular}
  \caption{Withdraw request data}
  \label{tab:withdraw-request-data}
\end{table}

In order to facilitate parsing, Christian Grothoff suggested to include the cipher type in the "coin\_ev" field, thus creating a nested \ac{JSON} (as described in table \ref{tab:withdraw-coin-ev-rsa}).
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Type} & \textbf{Value} \\
      cipher & Integer & Denomination cipher: 1 stands for RSA \\
      rsa\_blinded\_planchet & String & RSA blinded coin public key \\
  \end{tabular}
  \caption{Withdraw "coin\_ev" field (RSA)}
  \label{tab:withdraw-coin-ev-rsa}
\end{table}

For the Clause Schnorr implementation, the field "rsa\_blinded\_planchet" will be replaced with the necessary values as described in table \ref{tab:withdraw-coin-ev-cs}.
\begin{table}[ht]
  \centering
  \resizebox{0.85\textwidth}{!}{\begin{minipage}{\textwidth}
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
    \rowcolor{BFH-tablehead}
    \textbf{Field} & \textbf{Type} & \textbf{Value} \\
    cipher & Integer & Denomination cipher: 2 stands for \gls{CSBS} \\
    cs\_nonce & String & 32 Bytes encoded in Crockford base32 Hex \\
    cs\_blinded\_c0 & String & 32 Bytes encoded in Crockford base32 Hex \\
    cs\_blinded\_c1 & String & 32 Bytes encoded in Crockford base32 Hex \\
  \end{tabular}
  \caption{Withdraw "coin\_ev" field (\gls{CSBS})}
  \label{tab:withdraw-coin-ev-cs}
\end{minipage}}
\end{table}

The exchange will then process the withdraw request and return one of these HTTP status codes:
\begin{itemize}
  \item \textbf{200 (HTTP\_OK)}: Request Successful
  \item \textbf{400 (BAD\_REQUEST)}: Invalid input parameters (can also happen if denomination cipher doesn't match with cipher in "coin\_ev")
  \item \textbf{403 (FORBIDDEN)}: Signature contained in "reserve\_sig" invalid
  \item \textbf{404 (NOT\_FOUND)}: Denomination unknown
  \item \textbf{410 (GONE)}: Denomination revoked/expired
  \item \textbf{412 (PRECONDITION\_FAILED)}: Denomination not yet valid
\end{itemize}

When the request was successful, the exchange returns the RSA signature as JSON (described in table \ref{tab:withdraw-response-rsa}).
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Type} & \textbf{Value} \\
      cipher & Integer & Denomination cipher: 1 stands for RSA \\
      blinded\_rsa\_signature & String & RSA signature \\
  \end{tabular}
  \caption{Withdraw response (RSA)}
  \label{tab:withdraw-response-rsa}
\end{table}

Table \ref{tab:withdraw-response-cs} describes the response for \gls{CSBS}.
\begin{table}[ht]
  \centering
  \resizebox{0.85\textwidth}{!}{\begin{minipage}{\textwidth}
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Type} & \textbf{Value} \\
      cipher & Integer & Denomination cipher: 2 stands for \gls{CSBS} \\
      b & Integer & \gls{CSBS} signature session identifier (either 0 or 1) \\
      s & String & signature scalar (32 Bytes encoded in Crockford base32 Hex) \\
  \end{tabular}
  \caption{Withdraw response (\gls{CSBS})}
  \label{tab:withdraw-response-cs}
\end{minipage}}
\end{table}


\subsection{Persistence}
Persistence for withdrawing is implemented in the function \texttt{postgres\_do\_withdraw} in \texttt{src/exchangedb/plugin\_exchangedb\_postgres.c}
For \gls{CSBS}, persisting the blinded signature must be implemented.


\section{Deposit Protocol}
For the deposit protocol (described in section \ref{sec:deposit-protocol}) only the handling and verification of \gls{CSBS} signatures has to be added.

\subsection{Public APIs and Data Structures}
Deposit is an existing endpoint available under \texttt{POST /coins/[coin public key]/deposit} where "coin public key" is encoded as Crockford base32.
Additional parameters are passed as JSON (as described in table \ref{tab:spend-request}).\\\\
\framebox[1.1\width]{\color{blue}\texttt{POST /coins/[coin public key]/deposit}}
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{ll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Value} \\
      % cipher & Denomination cipher: 2 stands for \gls{CSBS} \\
      % b & \gls{CSBS} signature session identifier (either 0 or 1) \\
      % s & signature scalar (32 Bytes encoded in Crockford base32 Hex) \\
      merchant\_payto\_uri & Account that is credited  \\
      wire\_salt & Salt used by the merchant \\
      contribution & Amount to use for payment (for one specific coin) \\
      denom\_pub\_hash & Denomination public key hash \\
      ub\_sig & (unblinded) denomination signature of coin \\
      merchant\_pub & Merchant public key \\
      h\_contract\_terms & Contract terms hash \\
      coin\_sig & Deposit permission signature \\
      timestamp & Timestamp of generation \\
      refund\_deadline (optional) & Refund deadline \\
      wire\_transfer\_deadline (optional) & Wire transfer deadline \\
  \end{tabular}
  \caption{Spend request}
  \label{tab:spend-request}
\end{table}

Relevant field for the \gls{CSBS} implementation is the field "ub\_sig" containing the unblinded denomination signature of the coin.
For RSA, the (nested) \ac{JSON} is described in table \ref{tab:spend-request-ubsig-rsa}.
\begin{table}[ht]
  \centering
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Type} & \textbf{Value} \\
      cipher & Integer & Denomination cipher: 1 stands for RSA \\
      rsa\_signature & String & Unblinded RSA signature \\
  \end{tabular}
  \caption{ub\_sig (RSA)}
  \label{tab:spend-request-ubsig-rsa}
\end{table}

Table \ref{tab:spend-request-ubsig-cs} describes the values in "ub\_sig" required for \gls{CSBS}.
\begin{table}[ht]
  \centering
  \resizebox{0.85\textwidth}{!}{\begin{minipage}{\textwidth}
  \colorlet{BFH-table}{BFH-MediumBlue!10}
  \colorlet{BFH-tablehead}{BFH-MediumBlue!50}
  \setupBfhTabular
  \begin{tabular}{lll}
      \rowcolor{BFH-tablehead}
      \textbf{Field} & \textbf{Type} & \textbf{Value} \\
      cipher & Integer & Denomination cipher: 2 stands for \gls{CSBS} \\
      cs\_signature\_r & String & Curve point $ R' $ (32 Bytes encoded in Crockford base32 Hex) \\
      cs\_signature\_s & String & Signature scalar (32 Bytes encoded in Crockford base32 Hex) \\
  \end{tabular}
  \caption{ub\_sig (\gls{CSBS})}
  \label{tab:spend-request-ubsig-cs}
\end{minipage}}
\end{table}


\subsection{Persistence}
Persistence is handled in the functions \texttt{postgres\_insert\_deposit} and\\ \texttt{postgres\_have\_deposit} located in \url{src/exchangedb/plugin_exchangedb_postgres.c}.
However, these functions are not containing \gls{CSBS}-specific persistence.
\\What needs to be adjusted however, is the function \texttt{postgres\_ensure\_coin\_known} called by the function \texttt{TEH\_make\_coin\_known} (located in \url{src/exchange/taler-exchange-httpd_db.c}).


% \section{Tipping}
% \subsection{Public APIs and Data Structures}
% \subsection{Code Location}
% \subsection{Persistence}
% \subsection{Used Libraries}

% \section{Payback Protocol}
% \subsection{Public APIs and Data Structures}
% \subsection{Code Location}
% \subsection{Persistence}
% \subsection{Used Libraries}


% sollte ein Product Backlog das Ziel dieser Phase sein?
