zec
/
zips
mirror of https://github.com/zcash/zips.git
1
0
Fork 0
Code Issues Projects Releases Wiki Activity

Update description of commitment scheme. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2016-09-03 04:03:28 +01:00
parent 7cc7ae34d1
commit d44f7d4959
1 changed files with 33 additions and 3 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

36
protocol/protocol.tex
View File

@ -146,6 +146,10 @@
\newcommand{\notes}{\term{notes}}
\newcommand{\Note}{Note}
\newcommand{\Notes}{Notes}
\newcommand{\commitmentScheme}{\term{commitment scheme}}
\newcommand{\commitmentTrapdoor}{\term{commitment trapdoor}}
\newcommand{\commitmentTrapdoors}{\term{commitment trapdoors}}
\newcommand{\trapdoor}{\term{trapdoor}}
\newcommand{\noteCommitment}{\term{note commitment}}
\newcommand{\noteCommitments}{\term{note commitments}}
\newcommand{\NoteCommitment}{\titleterm{Note Commitment}}
@ -338,10 +342,10 @@
% Commitments
\newcommand{\Commit}[1]{\mathsf{COMM}_{#1}}
\newcommand{\CommitOutputLength}{\mathsf{\ell_{COMM}}}
\newcommand{\CommitOutput}{\bitseq{\CommitOutputLength}}
\newcommand{\CommitTrapdoor}{\mathsf{COMM.Trapdoor}}
\newcommand{\CommitInput}{\mathsf{COMM.Input}}
\newcommand{\CommitOutput}{\mathsf{COMM.Output}}
\newcommand{\NoteCommit}{\mathtt{NoteCommitment}}
\newcommand{\commitmentTrapdoor}{\term{commitment trapdoor}}
\newcommand{\Uncommitted}{\mathsf{Uncommitted}}
% Symmetric encryption
@ -1122,6 +1126,32 @@ This is not considered to be a significant security weakness.
\todo{}
\nsubsubsection{Commitment} \label{abstractcomm}
A \commitmentScheme is a function that, given a random \commitmentTrapdoor
and an input, can be used to commit to the input in such a way that:
\begin{itemize}
\item no information is revealed about it without the \trapdoor (``hiding''),
\item given the \trapdoor and input, the commitment can be verified to ``open''
to that input and no other (``binding'').
\end{itemize}
\vspace{-3ex}
A \commitmentScheme $\Commit{}$ defines a type of inputs $\CommitInput$,
a type of commitments $\CommitOutput$, and a type of \commitmentTrapdoors
$\CommitTrapdoor$.
Let $\Commit{} \typecolon \CommitTrapdoor \times \CommitInput \rightarrow \CommitOutput$
be a function satisfying the following requirements, adapted from
...
\begin{securityrequirements}
\item \textbf{Computational Hiding:} ...
\item \textbf{Computational Binding:} ...
\end{securityrequirements}
\nsubsubsection{\ZeroKnowledgeProvingSystem}
A \zeroKnowledgeProvingSystem is a cryptographic protocol that allows