update folding-sonobe slides

slides_sonobe-zkbarcelona.tex

@@ -89,17 +89,16 @@
 \end{frame}
 
 
-\section[Preliminaries]{Preliminaries}
-\begin{frame}{Homomorphic commitments}
-  [TODO] Homomorphic commitment definition
-
+\section[Folding]{Folding}
+\begin{frame}{Homomorphic commitments and RLC}
+  We rely on homomorphic commitments\\
   ie. Pedersen commitments\\
   Let $g \in \mathbb{G}^n,~ v \in \mathbb{F}_r^n$,\\
   $$Com(v) = \langle g, v \rangle =g_1 \cdot v_1 + g_2 \cdot v_2 + \ldots + g_n \cdot v_n$$
 
   % \pause
 
-  RLC\\
+  RLC:\\
   Let $v_1, v_2 \in \mathbb{F}_r^n$, set $cm_1 = Com(v_1),~ cm_2=Com(v_2)$.
   \\then,
   \begin{align*}
@@ -111,7 +110,6 @@
 
 \end{frame}
 
-\section[Folding]{Folding}
 \begin{frame}{Relaxed R1CS}
   R1CS instance: $(\{A, B, C\} \in \mathbb{F}^{n \times n},~ io,~ n,~ l)$, such that for $z=(io \in \mathbb{F}^l, 1, w \in \mathbb{F}^{n-l-1}) \in \mathbb{F}^n$,
 
@@ -130,13 +128,16 @@ for $u \in \mathbb{F},~~ E \in \mathbb{F}^n$.
 Committed Relaxed R1CS instance: $CI = (\overline{E}, u, \overline{W}, x)$\\
 Witness of the instance: $WI=(E, W)$
 
+\vspace{0.5cm}
+\footnotesize{(We don't have time for it now, but there is a simple reasoning for the RelaxedR1CS usage explained in Nova paper)}
+
 
 \end{frame}
 
 \begin{frame}{NIFS - Non Interactive Folding Scheme}
   \scriptsize{
   \begin{align*}
-    CI_1 &=(\overline{E}_1, u_1, \overline{W}_1, x_1) ~~~~~~WI_1=(E_1, W_1)\\
+    CI_1 &=(\overline{E}_1 \in \mathbb{G}, u_1 \in \mathbb{F}, \overline{W}_1 \in \mathbb{G}, x_1 \in \mathbb{F}^n) ~~~~~~WI_1=(E_1 \in \mathbb{F}^n, W_1 \in \mathbb{F}^n)\\
     CI_2 &=(\overline{E}_2, u_2, \overline{W}_2, x_2) ~~~~~~WI_2=(E_2, W_2)
   \end{align*}
   where $\overline{V}=Com(V)$
@@ -186,7 +187,7 @@ New folded witness: $(E, W)$
   
   \small{
   F':\\
-  i) execute a step of the incremental computation, $z_i+1 = F(z_i)$\\
+  i) execute a step of the incremental computation, $z_{i+1} = F(z_i)$\\
   ii) invoke the NIFS.V to fold $U_i, u_i$ into $U_{i+1}$\\
   iii) other checks to ensure that the IVC is done properly
   }
@@ -288,6 +289,29 @@ New folded witness: $(E, W)$
 \end{frame}
 
 \begin{frame}{Code example}
+  [show code with a live demo]
+  \vspace{0.5cm}
+
+  Some numbers (still optimizations pending):
+  \begin{itemize}
+  \item AugmentedFCircuit: $\sim 80k$ R1CS constraints
+  \item DeciderEthCircuit: $\sim 9.6M$ R1CS constraints
+  \begin{itemize}
+    \item $<3$ minutes in a 32GB RAM 16 core laptop
+  \end{itemize}
+  \item gas costs (DeciderEthCircuit proof): $\sim 800k$ gas
+  \begin{itemize}
+    \item mostly from G16, KZG10, public inputs processing
+    \item will be reduced by hashing the public inputs
+    \item expect to get it down to $< 600k$ gas.
+  \end{itemize}
+  \end{itemize}
+
+  \vspace{0.3cm}
+
+Recall, this proof is proving that applying $n$ times the function $F$ (the circuit that we're folding) to an initial state $z_0$ results in the state $z_n$.
+\\In Srinath Setty words, you can prove practically unbounded computation onchain by 800k gas (and soon $< 600k$).
+
 
 \end{frame}
 
@@ -299,7 +323,9 @@ New folded witness: $(E, W)$
   \item \href{https://privacy-scaling-explorations.github.io/sonobe-docs/}{https://privacy-scaling-explorations.github.io/sonobe-docs/}
 \end{itemize}
 
+\begin{center}
   \includegraphics[width=4cm]{qr-sonobe-repo-link}
+\end{center}
 
 \tiny{
   $$\text{2024-04-22}$$