diff --git a/hip2022/hip2022.tex b/hip2022/hip2022.tex
index a79a76c..119e065 100644
--- a/hip2022/hip2022.tex
+++ b/hip2022/hip2022.tex
@@ -439,7 +439,7 @@ Searching for functions \uncover<2->{with the following signatures}
 				\item generates $(\commitment_1,\dots,\commitment_\kappa)$ 
 					and $(\beta_1,\dots,\beta_\kappa)$ from $\commitment_0$\\
 					by calling $\kappa$ times $\Derive(\commitment_0, \pruf_0, \omega_i)$
-				\item calculates $h_0:=H\left(H(\commitment_1, \beta_1)||\dots||H(\commitment_\kappa, \beta_\kappa)\right)$
+				\item calculates $h_0:=H\left(H(\commitment_1, \beta_1)\parallel \dots\parallel H(\commitment_\kappa, \beta_\kappa)\right)$
 				\item sends $\commitment_0$ and $h_0$ to $\Exchange$
 			\end{enumerate}
 		\item[$\Exchange$:] 
@@ -453,7 +453,7 @@ Searching for functions \uncover<2->{with the following signatures}
 		\item[$\Exchange$:] 
 			\begin{enumerate}
 				\item[6.] compares $h_0$ and 
-			$H\left(H(\commitment_1, \beta_1)||...||h_\gamma||...||H(\commitment_\kappa, \beta_\kappa)\right)$
+			$H\left(H(\commitment_1, \beta_1)\parallel ...\parallel h_\gamma\parallel ...\parallel H(\commitment_\kappa, \beta_\kappa)\right)$
 				\item[7.] evaluates $\Compare(\commitment_0, \commitment_i, \beta_i)$ for all $i \neq \gamma$.
 			\end{enumerate}
 	\end{itemize}
@@ -710,7 +710,7 @@ Searching for functions \uncover<2->{with the following signatures}
 	\begin{description}
 		\item<2->[To \blue{Attest} a minimum age (group) $\blue{\minage} \leq \age$:]~\\
 			Sign a message with ECDSA using private key
-			$p_\blue{\minage}$.  The signature $\sigma$ is the
+			$p_\blue{\minage}$.  The signature $\sigma_\blue{\minage}$ is the
 			attestation.
 	\end{description}
 
@@ -720,11 +720,11 @@ Searching for functions \uncover<2->{with the following signatures}
 	Merchant gets 
 	\begin{itemize}
 		\item ordered public-keys $\Vcommitment = (q_1, \dots, q_\Age) $
-		\item Signature $\sigma$
+		\item Signature $\sigma_\blue{\minage}$
 	\end{itemize}
 	\begin{description}
-		\item<4->[To \blue{Verify} a minimum age (group) $\minage$:]~\\
-			Verify the ECDSA-Signature $\sigma$ with public key $q_\minage$.
+		\item<4->[To \blue{Verify} a minimum age (group) \blue{$\minage$}:]~\\
+			Verify the ECDSA-Signature $\sigma_\blue{\minage}$ with public key $q_\blue{\minage}$.
 	\end{description}
 	}
 	\vfill
@@ -785,15 +785,15 @@ Searching for functions \uncover<2->{with the following signatures}
 		\begin{minipage}{\textwidth}
 		\tiny
 		\begin{description}
-			\item[Game $\Game{FA}(\lambda)$: Forging an attest]~\\
-			 1. $(\age, \omega)	\drawfrom	\N_{\Age-1}\times\Omega(\lambda) $\\
+			\item[Game $\Game{FA}$: Forging an attest]~\\
+			 1. $(\age, \omega)	\drawfrom	\N_{\Age-1}\times\Omega $\\
 			 2. $(\commitment, \pruf)	\leftarrow	\Commit(\age, \omega) $\\
 			 3. $(\minage, \attest) \leftarrow \Adv(\age, \commitment, \pruf)$\\
 			 4. Return 0 if $\minage \leq \age$\\
 			 5. Return $\Verify(\minage,\commitment,\attest)$\\
 			\vfill
 		\item[Requirement:]~\\
-			$\Forall_{\Adv}: \Probability\Big[\Game{FA}(\lambda) = 1\Big] \le \negl(\lambda)$
+			$\Forall_{\Adv}: \Probability\Big[\Game{FA} = 1\Big] \le \negl$
 		\end{description}
 		\end{minipage}
 	\column{0.7\textwidth}
@@ -905,17 +905,16 @@ Searching for functions \uncover<2->{with the following signatures}
 	\label{fr:bindingToCoins}
 
 	To bind an age commitment $\commitment$ to a coin $C_p$, instead of
-	signing $H(C_p)$, $\Exchange$ now \hyperlink{fr:reminderBlindSignature}{blindly signs}
-	\begin{center}
-		$H(C_p, \orange{H(\commitment)})$
-	\end{center}
+	blindly signing \[ H(C_p), \]
+	$\Exchange$ now \hyperlink{fr:reminderBlindSignature}{blindly signs}
+	\[ H\left(C_p\parallel\orange{H(\commitment)}\right) \]
 
 	\vfill
-	Verfication of a coin now requires $H(\commitment)$, too:
-	\begin{center}
-		$1  \stackrel{?}{=}
-		\mathsf{SigCheck}\big(H(C_p, \orange{H(\commitment)}), D_p, \sigma_p\big)$
-	\end{center}
+	Therefore, verfication of a coin now requires $H(\commitment)$, too:
+	\[
+		1  \stackrel{?}{=}
+		\mathsf{SigCheck}\big(H\left(C_p\parallel\orange{H(\commitment)}\right), D_p, \sigma_p\big)
+	\]
 	\vfill
 \end{frame}
 
@@ -929,7 +928,7 @@ Searching for functions \uncover<2->{with the following signatures}
 		\node[circle,minimum size=25pt,fill=blue!15]  at (130:3) (Guardian) {$\Guardian$};
 
 		\draw[<->] (Guardian)   to  node[sloped,above,align=center]
-			{{\sf withdraw}\orange{, using}\\ $H(C_p\orange{, H(\commitment)})$} (Exchange);
+			{{\sf withdraw}\orange{, using}\\ $H(C_p\orange{\parallel H(\commitment)})$} (Exchange);
 		\draw[<->] (Client)   to node[sloped,below,align=center]
 			{{\sf refresh} \orange{ + }\\ \orange{$\DeriveCompare$}} (Exchange);
 		\draw[<->] (Client)   to node[sloped, below]
@@ -1108,14 +1107,15 @@ Searching for functions \uncover<2->{with the following signatures}
 			\end{itemize}
 		\item[B:]
 			\begin{itemize}
-				\item signs $m'$ by $\sigma' := m'^d \mod N$ {\hfill \scriptsize \textit{(B doesn't know $m$)}}
+				\item signs $m'$, by calculating 
+					$\sigma' := (m')^d \mod N$ {\hfill \scriptsize \textit{(B doesn't learn $m$)}}
 				\item sends $\sigma'$ to A.
-				\item[] \scriptsize Note: $m'^d = (m*b^e)^d = m^d*b^{ed} = m^d*b \mod N$
+				\item[] \scriptsize Note: $(m')^d = (m*b^e)^d = m^d*b^{ed} = m^d*b \mod N$
 			\end{itemize}
 		\item[A:]\begin{itemize}
 				\item unblinds $\sigma'$ by calculating 
 			\[ \sigma := \sigma'*b^{-1} (= m^d) \]
-			\item[]$\sigma$ is a valid RSA signature to message $m$.
+			\item[$\implies$]$\sigma$ is a valid RSA signature to message $m$.
 		\end{itemize}
 	\end{itemize}
 	\hfill \tiny back to \hyperlink{fr:GnuTaler}{\textit{taler}} or \hyperlink{fr:bindingToCoins}{\textit{binding}}