diff --git a/ACNS/presentation/generalsss.tex b/ACNS/presentation/generalsss.tex index 807e2a96f8b5a1c556a725f26e0d0bbc2ee56629..ba9d357d76b8187d53db27b1b5939fb5f75fa00f 100644 --- a/ACNS/presentation/generalsss.tex +++ b/ACNS/presentation/generalsss.tex @@ -1,4 +1,20 @@ -\section{General Access Structures and Secret Sharing Schemes} +\section{General Secret Sharing Schemes} \begin{frame} + \frametitle{Necessary Characteristics for Compatibility} + \begin{itemize} + \item Independent reconstruction: a shareholder's input in reconstructing a secret is independent of other shares + \item Self-contained reconstruction: the shares of a secret live in the same space as the secret to enable two-level sharing + \item Compatibility with zero-knowledge proof and the piecewise verifiable proof in the HHS + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Examples} + \begin{itemize} + \item Shamir's polynomial secret sharing: compatible (our protocol was initially based on it) + \item Tassa's hierarchical threshold secret sharing \cite{DBLP:conf/tcc/Tassa04}: compatible (extension of Shamir's approach) + \item Damgard and Thorbek's linear integer secret sharing \cite{DBLP:conf/pkc/DamgardT06}: incompatible, since it is only computationally hiding + \item Additive secret sharing: incompatible, because superauthorised sets of shareholders do not exist + \end{itemize} \end{frame} diff --git a/ACNS/presentation/main.tex b/ACNS/presentation/main.tex index 85e1df67ff56f32c39954bad77d2a81c89846371..eca90406eb915b0fbfeb31b54e5068fea7c7383b 100644 --- a/ACNS/presentation/main.tex +++ b/ACNS/presentation/main.tex @@ -31,6 +31,6 @@ \section{References} \begin{frame}[allowframebreaks] \bibliographystyle{amsalpha} - \bibliography{pqc} + \bibliography{pqc,local_bib} \end{frame} \end{document} diff --git a/ACNS/presentation/motivation.tex b/ACNS/presentation/motivation.tex index d6bce6b45ddbe4250a2468dc40b5f198a51c879b..02f05b63dae78ab8287d37a369a41d09ac845cf7 100644 --- a/ACNS/presentation/motivation.tex +++ b/ACNS/presentation/motivation.tex @@ -38,9 +38,17 @@ \begin{frame} \frametitle{Secret Sharing Schemes} - - \begin{definition}[Superauthorises Sets] - + \begin{itemize} + \item Distribute a secret \(s\) among \(n\) shareholders via + \[ \mathcal S.\share\paren* s\] + \item Reconstruct a shared secret via + \[ \SH.\rec\paren*{\set{s_i}_{P_i \in S'}} \] + for an authorised set \(S'\in \Gamma\). + \end{itemize} + + \begin{definition}[Superauthorised Sets] + A \highlight{superauthorised set} of shareholders is a set \(S^\ast\), so that + \[\forall P \in S^\ast \colon S^\ast \setminus\set{P} \in \Gamma.\] \end{definition} \end{frame} diff --git a/ACNS/presentation/preamble.tex b/ACNS/presentation/preamble.tex index afdcc7742c654078d88614f2b8a5d605314c5ec2..162e8cb806dc6ded52ad91a79a7c77d27bfdf5e7 100644 --- a/ACNS/presentation/preamble.tex +++ b/ACNS/presentation/preamble.tex @@ -117,6 +117,7 @@ \newcommand\decaps{\mathsf{Decaps}} \newcommand\encaps{\mathsf{Encaps}} \newcommand\keygen{\mathsf{KeyGen}} +\providecommand\highlight[1]{\emph{#1}} \DeclarePairedDelimiter{\paren}{\lparen}{\rparen} \DeclarePairedDelimiter{\bracket}{[}{]} diff --git a/ACNS/presentation/signatures.tex b/ACNS/presentation/signatures.tex index abbe11a0ad315a428541a54b988cba82aecda6eb..b95a3774ad67295484eb7144215587218ee35a96 100644 --- a/ACNS/presentation/signatures.tex +++ b/ACNS/presentation/signatures.tex @@ -1,4 +1,16 @@ \section{Deriving a Signature Scheme} \begin{frame} + \begin{block}{Why actively secure signature schemes?} + Correctness of a signature is easily verified with the public key and the signed message. + + BUT: An incorrect signature does not identify the misbehaving shareholder. + \end{block} + \begin{block}{Signature Scheme} + \begin{itemize} + \item \(\keygen\): Keep \(\keygen\) of the key exchange mechanism, i.e., the secret key is two-level shared among parties \(P_1,\ldots,P_n\) + \item \(\sign\): Apply Fiat-Shamir-transform \cite{C:FiaSha86} to the decapsulation protocol, resulting in a signing protocol with secret shared secret key + \item \(\verify\): Arises naturally from the Fiat-Shamir-transformation + \end{itemize} + \end{block} \end{frame}