M slides/slides_lattices-intro.pdf → slides/slides_lattices-intro.pdf

M slides/slides_lattices-intro.tex → slides/slides_lattices-intro.tex

@@ -1068,17 +1068,6 @@ \end{column}
 
 \begin{column}{0.33\textwidth}
 
-% Move only this equation down, without affecting the frame layout
-% \raisebox{-1.4cm}[0pt][0pt]{%
-%   \makebox[\linewidth][c]{
-% \vspace*{2.5cm}
-  % $c\leftarrow C$\\
-  % \scriptsize{
-  %   (in practice, $c = H(M ||w)$)
-  % }
-%   }%
-% }
-
 
 \vspace*{2.5cm}
   \begin{align*}
@@ -1096,129 +1085,6 @@ \end{columns}
 \end{frame}
 
 
-
-% \begin{frame}{ML-DSA signatures}
-% %%%
-% \vspace{-0.5cm}
-% 
-% 
-% \scriptsize
-% 
-% $$
-% R_q = \mathbb{Z}_q[X]/(X^n+1)
-% $$
-% 
-% \vspace{-0.4cm}
-% 
-% \hspace*{-0.7cm}
-% \begin{tikzpicture}[
-%     >=Latex,
-%     every node/.style={font=\scriptsize},
-% ]
-% 
-% % =========================================================
-% % Headers
-% 
-% \node[anchor=west] at (0,0)
-%   {\textbf{Signer / Prover}};
-% 
-% \node[anchor=west] at (8.3,0)
-%   {\textbf{Verifier}};
-% 
-% % =========================================================
-% % Keys
-% 
-% \node[anchor=west, align=left] at (0,-0.8) {
-%   $s_1 \leftarrow S^\ell,~ s_2 \leftarrow S^k$
-%   \\[1mm]
-%   Public:\\
-%   $A \leftarrow R_q^{k\times\ell},~ t = As_1+s_2$
-% };
-% 
-% \node[anchor=west, align=left] at (8.3,-1.4) {
-%   Public key:\\
-%   $(A,t)$
-% };
-% 
-% \draw[->]
-%   (4.9,-1.5)
-%   --
-%   node[above] {$pk=(A,t)$}
-%   (8.0,-1.5);
-% 
-% % =========================================================
-% % Commitment
-% 
-% \node[anchor=west, align=left] at (0,-2.35) {
-%   Sample short vectors:\\
-%   $y_1\leftarrow Y^\ell,~
-%    y_2\leftarrow Y^k$
-%   \\[1mm]
-%   Compute:\\
-%   $w = Ay_1+y_2$
-% };
-% 
-% \draw[->]
-%   (4.9,-3.05)
-%   --
-%   node[above] {$w$}
-%   (8.0,-3.05);
-% 
-% % =========================================================
-% % Challenge
-% 
-% \node[anchor=west, align=left] at (8.3,-3.25) {
-%   $c\leftarrow C$\\
-%   \scriptsize{
-%     (in practice, $c = H(M ||w)$)
-%   }
-% };
-% 
-% \draw[<-]
-%   (4.9,-3.9)
-%   --
-%   node[above] {$c$}
-%   (8.0,-3.9);
-% 
-% % =========================================================
-% % Response
-% 
-% \node[anchor=west, align=left] at (0,-4.45) {
-%   Compute:\\
-%   $z_1=y_1+cs_1,~
-%    z_2=y_2+cs_2$
-%   \\[1mm]
-%   Reject if $z_1,z_2$ are not short.
-% };
-% 
-% \draw[->]
-%   (4.9,-5.55)
-%   --
-%   node[above] {$z_1,z_2$}
-%   (8.0,-5.55);
-% 
-% % =========================================================
-% % Verification
-% 
-% \node[anchor=west, align=left] at (8.3,-6.0) {
-%   Reconstruct:\\[1mm]
-%   $\begin{aligned}
-%   w'
-%     &= Az_1+z_2-ct \\
-%     &= A(y_1+cs_1)+(y_2+cs_2) \\
-%     &\qquad-c(As_1+s_2) \\
-%     &= Ay_1+y_2 \stackrel{?}{=} w
-%   \end{aligned}$
-%   \\[1mm]
-%   Accept if $z_1,z_2$ are short.
-% };
-% 
-% \end{tikzpicture}
-% 
-% 
-% %%%
-% 
-% \end{frame}
 
 \begin{comment}
 \begin{mayberm}