mirror of https://github.com/zcash/zips.git
Protocol spec: more vertical spacing fixes.
Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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@ -1991,7 +1991,7 @@ electronic commerce and payment, financial privacy, proof of work, zero knowledg
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\Large \coauthora\affiliation — \coauthorb\affiliation — \coauthorc\affiliation}
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\date{\today}
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\maketitle
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\vspace{-6ex}
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\vspace{-6ex}\sprout{\vspace{-3ex}}
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\notsprout{
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\begin{center}
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@ -2012,7 +2012,7 @@ succinct non-interactive arguments of knowledge (\zkSNARKs). It attempted
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to address the problem of mining centralization by use of the \Equihash
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memory-hard proof-of-work algorithm.
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\vspace{1.5ex}
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\notsprout{\vspace{1.5ex}}
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\sprout{\noindent This specification defines the \Zcash consensus protocol
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as it was at launch, and explains its differences from \Zerocash and \Bitcoin.
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It is a historical document and no longer specifies the current \Zcash
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@ -2026,7 +2026,7 @@ at launch, and after each of the upgrades codenamed \Overwinter, \Sapling, and
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\Blossom. It is a work in progress. Protocol differences from \Zerocash and
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\Bitcoin are also explained.}
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\vspace{2.5ex}
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\sprout{\vspace{1ex}}\notsprout{\vspace{2.5ex}}
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\noindent \textbf{Keywords:}~ \StrSubstitute[0]{\keywords}{,}{, }.
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\ifxetex
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@ -2043,6 +2043,7 @@ This document was built with Lua\TeX, which is \href{https://github.com/zcash/zi
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\end{abstract}
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\sprout{\vspace{-2ex}}
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\phantompart{Contents}{contents}
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\renewcommand{\contentsname}{}
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@ -6325,6 +6326,7 @@ No other security properties commonly associated with \hashFunctions are needed.
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These \hashFunctions are \emph{not} \collisionResistant for variable-length inputs.
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}
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\introlist
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\theoremlabel{thmpedersenencodeinjective}
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\begin{theorem}[The encoding function $\PedersenEncode{\paramdot}$ is injective]\end{theorem}
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@ -6368,6 +6370,7 @@ is \collisionResistant under the same assumptions and security bounds.
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Because $\ExtractJ$ is injective, it follows that $\PedersenHash$ is equally
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\collisionResistant\!.
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\introlist
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\theoremlabel{thmnohashtouncommittedsapling}
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\begin{theorem}[$\UncommittedSapling$ is not in the range of $\PedersenHash$]\end{theorem}
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@ -7623,6 +7626,7 @@ $\SubgroupJ$ is of odd-prime order.}
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% <https://github.com/zcash/zcash/issues/2234#issuecomment-333360977>
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\vspace{-2ex}
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\introlist
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\theoremlabel{lemmasubgroupnegation}
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\begin{lemma}[Let $P = (u, \varv) \in \SubgroupJ$. Then $(u, -\varv) \notin \SubgroupJ$]\end{lemma}
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@ -7642,6 +7646,7 @@ since $\SubgroupJ$ is of odd order \cite{KvE2013}).
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\end{proof}
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\vspace{-3ex}
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\introlist
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\theoremlabel{thmselectuinjective}
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\begin{theorem}[$\Selectu$ is injective on $\SubgroupJ$]\end{theorem}
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@ -11321,6 +11326,7 @@ We will need the theorem below about $y$-coordinates of points on
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\fact{$\ParamM{A}^2 - 4$ is a nonsquare in $\GF{\ParamS{r}}$.}
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\vspace{-1ex}
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\introlist
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\theoremlabel{thmmontynotzero}
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\begin{theorem}[$(0, 0)$ is the only point with $y = 0$ on certain \MontgomeryCurves]
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@ -11718,6 +11724,7 @@ a point on the relevant curve. If that is the case, the theorems below
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enumerate all exceptional inputs that may violate the side-conditions.
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\vspace{-1ex}
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\introlist
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\theoremlabel{thmconversiontomontnoexcept}
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\begin{theorem}[Exceptional points (ctEdwards $\rightarrow$ Montgomery)]
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@ -11733,6 +11740,7 @@ obtain $\varv = \pm 1$, and by substituting $\varv = 1$ and using $a \neq d$ we
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\end{proof}
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\vspace{-4ex}
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\introlist
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\theoremlabel{thmconversiontoedwardsnoexcept}
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\begin{theorem}[Exceptional points (Montgomery $\rightarrow$ ctEdwards)]
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