topics.tex

\documentclass{zkdl-template}

\begin{document}

\section*{ZKDL Camp Topics}

\subsection*{Basic Topics (Preliminaries)}

\begin{enumerate}
    \item \textbf{Mathematics for cryptographers.}
    \begin{enumerate}
        \item Basics of number theory, RSA case study.
        \item Definition of a group. Subgroups, cyclic groups, isomorphisms and automorphisms. Applications.
        \item Vector spaces.
        \item Polynomials.
        \item Definition of a field. Finite fields.
    \end{enumerate}
    \item \textbf{Elliptic Curves.}
    \begin{enumerate}
        \item Defining a group structure.
        \item Points addition in affine form.
        \item Scalar multiplication, effective implementation in $O(\log_2(k))$.
        \item Twisted Curves.
        \item Useful endomorphism.
        \item Examples of widely used curves.
    \end{enumerate}
    \item \textbf{Elliptic Curve Pairings} (\textit{might simply redirect to the zksync lecture}).
    \begin{enumerate}
        \item Definition and applications.
        \item Finite field extensions $\mathbb{F}_{p^n}$.
        \item \textit{(optional, possibly advanced topic)} Implementation details: divisors, ate pairing, Miller Loop.
    \end{enumerate}
    \item \textbf{Cryptographic Commitments}.
    \begin{enumerate}
        \item Hash and Pedersen commitments.
        \item Functional commitments: Polynomial commitments.
        \item KZG commitment scheme.
        \item $\tau$ ceremony.
    \end{enumerate}
\end{enumerate}

\subsection*{Medium Topics}
\begin{enumerate}
    \item Introduction: What are zero-knowledge proofs? Basic examples.
    \item Succinct Non-Interactive Arguments of Knowledge (SNARK): what succinctness means and security definitions. 
    \item Arithmetic Circuits. Rank-1 Constraint Systems. Quadratic Arithmetic Programs.
    \item Programming SNARKs. Circom. Solving real-world problems with Circom and many practical examples.
    \item Zero-knowledge proving systems case studies:
    \begin{enumerate}
        \item Groth16 
        \item Plonk 
        \item Range proofs + Bulletproofs + Bulletproofs+ + Bulletproofs++
        \item STARKs 
    \end{enumerate}
\end{enumerate}

\subsection*{Advanced topics}
\begin{enumerate}
    \item Low-level arithmetic and optimizations.
    \item Halo2.
    \item Nova, Supernova, Hypernova.
    \item Folding schemes.
\end{enumerate}

\end{document}