mirror of https://github.com/zcash/zips.git
Protocol spec: cosmetics.
Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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Daira Hopwood
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2766855113
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@ -2246,9 +2246,9 @@ $\vproduct{i=1}{\rmN} a_i$ means the product of $a_{\allN{}}$.\;
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$\vxor{i=1}{\rmN} a_i$ means the bitwise exclusive-or of $a_{\allN{}}$.
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When $N = 0$ these yield the appropriate neutral element, i.e.
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\smash{$\vsum{i=1}{0} a_i = 0$, $\vproduct{i=1}{0} a_i = 1$, and
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$\vxor{i=1}{0} a_i = 0$} or the all-zero bit sequence of the
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appropriate length given by the type of $a$.
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$\ssum{i=1}{0} a_i = 0$, $\sproduct{i=1}{0} a_i = 1$, and
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$\sxor{i=1}{0} a_i = 0$ or the all-zero bit sequence of length given
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by the type of $a$.
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\notsprout{
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$\ssqrt{a}$, where $a \typecolon \GF{q}$, means the positive
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@ -5015,7 +5015,7 @@ For details of the form and encoding of \spendStatement proofs, see \crossref{gr
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\begin{pnotes}
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\item Public and \auxiliaryInputs{} \MUST be constrained to have the types specified. In particular,
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see \crossref{ccteddecompressvalidate} for implementation of validity checks on compressed
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see \crossref{ccteddecompressvalidate}, for required validity checks on compressed
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representations of \jubjubCurve points.
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The $\ValueCommitOutput$ and $\SpendAuthSigPublic$ types also represent points, i.e. $\GroupJ$.
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@ -5094,7 +5094,7 @@ For details of the form and encoding of \outputStatement proofs, see \crossref{g
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\begin{pnotes}
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\item Public and \auxiliaryInputs{} \MUST be constrained to have the types specified. In particular,
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see \crossref{ccteddecompressvalidate} for implementation of validity checks on compressed
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see \crossref{ccteddecompressvalidate}, for required validity checks on compressed
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representations of \jubjubCurve points.
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The $\ValueCommitOutput$ type also represents points, i.e. $\GroupJ$.
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@ -6222,10 +6222,10 @@ $\UncommittedSapling = \ItoLEBSPOf{\MerkleHashLengthSapling}{1}$ is not in the r
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\end{theorem}
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\begin{proof}
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By injectivity of $\ItoLEBSP{\MerkleHashLengthSapling}$ and the definitions of
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By injectivity of $\ItoLEBSP{\MerkleHashLengthSapling}$ and definitions of
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$\PedersenHash$ and $\ExtractJ$, $\ItoLEBSPOf{\smash{\MerkleHashLengthSapling}}{1}$
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can be in the range of $\PedersenHash$ only if there exist
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$(D \typecolon \byteseq{8}$, $M \typecolon \bitseq{\PosInt})$ such that $\Selectu\Of{\PedersenHashToPoint(D, M)} = 1$.
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$(D \typecolon \smash{\byteseq{8}}$, $M \typecolon \smash{\bitseq{\PosInt}})$ such that $\Selectu\Of{\PedersenHashToPoint(D, M)} = 1$.
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The latter can only be the affine-ctEdwards $u$-coordinate of a point in $\strut\GroupJ$.
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We show that there are no points in $\GroupJ$ with affine-ctEdwards $u$-coordinate $1$.
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Suppose for a contradiction that $(u, \varv) \in \GroupJ$ for $u = 1$ and some
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@ -6640,8 +6640,8 @@ Define $\KASaplingAgree(\sk, P) := \scalarmult{\ParamJ{h} \mult \sk}{P}$.
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\begin{lrbox}{\kdfsaplinginputbox}
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\setsapling
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\begin{bytefield}[bitwidth=0.07em]{544}
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\sbitbox{256}{$\LEBStoOSPOf{256}{\reprJ\Of{\DHSecret{}}\hairspace}$} &
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\sbitbox{256}{$\LEBStoOSPOf{256}{\reprJ\Of{\EphemeralPublic}\hairspace}$}
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\sbitbox{256}{$\LEBStoOSPOf{256}{\reprJ\Of{\DHSecret{}}\kern 0.02em}$} &
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\sbitbox{256}{$\LEBStoOSPOf{256}{\reprJ\Of{\EphemeralPublic}\kern 0.02em}$}
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\end{bytefield}
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\end{lrbox}
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@ -7266,7 +7266,7 @@ The \representedPairing $\BLSCurve$ is defined in this section. Parameters are t
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\cite{Bowe2017}.
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\introlist
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Let $\ParamS{q} :=\;$\scalebox{0.81}[1]{$4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787$.}
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Let $\ParamS{q} :=\;$\scalebox{0.805}[1]{$4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787$.}
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Let $\ParamS{r} := 52435875175126190479447740508185965837690552500527637822603658699938581184513$.
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@ -7303,18 +7303,18 @@ Let $\GenS{1} \typecolon \SubgroupSstar{1} :=$
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\vspace{-1ex}
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\begin{tabular}{@{\tab}r@{}l@{}}
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$($\scalebox{0.81}[1]{$ 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507$} & $, $ \\
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\scalebox{0.81}[1]{$13395065449444764730204713799419212215849338759383496204265437364165114239563335064727246553533665349923917564415691$} & $)$.
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$($\scalebox{0.805}[1]{$ 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507$} & $, $ \\
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\scalebox{0.805}[1]{$13395065449444764730204713799419212215849338759383496204265437364165114239563335064727246553533665349923917564415691$} & $)$.
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\end{tabular}
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Let $\GenS{2} \typecolon \SubgroupSstar{2} :=$
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\vspace{-1ex}
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\begin{tabular}{@{\tab}r@{}l@{}}
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$($\scalebox{0.81}[1]{$ 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758$} & $\,\mult\, t\;+$ \\
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\scalebox{0.81}[1]{$ 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160$} & $, $ \\
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\scalebox{0.81}[1]{$ 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582$} & $\,\mult\, t\;+$ \\
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\scalebox{0.81}[1]{$ 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905$} & $). $
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$($\scalebox{0.805}[1]{$ 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758$} & $\,\mult\, t\;+$ \\
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\scalebox{0.805}[1]{$ 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160$} & $, $ \\
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\scalebox{0.805}[1]{$ 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582$} & $\,\mult\, t\;+$ \\
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\scalebox{0.805}[1]{$ 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905$} & $). $
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\end{tabular}
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$\GenS{1}$ and $\GenS{2}$ are generators of $\SubgroupS{1}$ and $\SubgroupS{2}$ respectively.
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@ -9069,9 +9069,9 @@ Define:
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\vspace{-0.5ex}
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\item \tab $\AveragingWindowTimespan\blossom{(\BlockHeight \typecolon \Nat)} + \trunc{\scalebox{0.98}{\hfrac{\ActualTimespan(\BlockHeight) - \AveragingWindowTimespan\blossom{(\BlockHeight)}}{\PoWDampingFactor}}}$
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\item $\ActualTimespanBounded(\BlockHeight \typecolon \Nat) := \bound{\MinActualTimespan\blossom{(\BlockHeight)}}{\MaxActualTimespan\blossom{(\BlockHeight)}}(\ActualTimespanDamped(\BlockHeight))$
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\item $\MeanTarget(\BlockHeight \typecolon \Nat) := \begin{cases}
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\item $\MeanTarget(\BlockHeight \typecolon \Nat) := \!\begin{cases}
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\PoWLimit, \hspace{16em}\text{if } \BlockHeight \leq \PoWAveragingWindow \\
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\mean(\listcomp{\!\ToTarget(\nBits(i)) \for i \from \BlockHeight\!-\!\PoWAveragingWindow \upto \BlockHeight\!-\!1\!}),\\
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\mean(\listcomp{\!\ToTarget(\nBits(i)\kern-0.1em) \for i \from \BlockHeight\!-\!\PoWAveragingWindow \upto \BlockHeight\!-\!1\!}),\\
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\hspace{20.7em}\text{otherwise.}
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\end{cases}$
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\end{formulae}
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@ -9080,7 +9080,7 @@ Define:
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The \targetThreshold for a given \blockHeight $\BlockHeight$ is then calculated as:
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\begin{formulae}
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\item $\Threshold(\BlockHeight \typecolon \Nat) \hspace{0.43em} := \begin{cases}
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\item $\Threshold(\BlockHeight \typecolon \Nat) \hspace{0.43em} := \hspace{0.3em} \begin{cases}
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\PoWLimit, \hspace{16em}\text{if } \BlockHeight = 0 \\
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\minimum(\PoWLimit, \floor{\hfrac{\MeanTarget(\BlockHeight)}{\AveragingWindowTimespan}}
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\mult \ActualTimespanBounded(\BlockHeight)),\\
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