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Cosmetics. 

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2018-03-11 17:27:43 +00:00
parent 4443e647ec
commit 1b1acc05d7
1 changed files with 11 additions and 10 deletions
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21
protocol/protocol.tex
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@ -312,7 +312,7 @@ electronic commerce and payment, financial privacy, proof of work, zero knowledg
\newcommand{\joinSplitDescription}{\term{JoinSplit description}}
\newcommand{\joinSplitDescriptions}{\term{JoinSplit descriptions}}
\newcommand{\JoinSplitDescriptions}{\titleterm{JoinSplit Descriptions}}
\newcommand{\sequenceOfJoinSplitDescriptions}{\changed{sequence of} \joinSplitDescription\changed{\term{s}}\xspace}
\newcommand{\sequenceOfJoinSplitDescriptions}{\changed{sequence of} \joinSplitDescription{}\kern -0.05em\changed{\term{s}}}
\newcommand{\joinSplitTransfer}{\term{JoinSplit transfer}}
\newcommand{\joinSplitTransfers}{\term{JoinSplit transfers}}
\newcommand{\JoinSplitTransfer}{\titleterm{JoinSplit Transfer}}
@ -639,7 +639,8 @@ electronic commerce and payment, financial privacy, proof of work, zero knowledg
\newcommand{\maximum}{\mathsf{max}}
\newcommand{\floor}[1]{\mathsf{floor}\!\left({#1}\right)}
\newcommand{\trunc}[1]{\mathsf{trunc}\!\left({#1}\right)}
\newcommand{\ceiling}[1]{\mathsf{ceiling}\left({#1}\right)}
\newcommand{\ceiling}[1]{\mathsf{ceiling}\!\left({#1}\right)}
\newcommand{\sceiling}[1]{\mathsf{ceiling}\left({#1}\right)}
\newcommand{\vsum}[2]{\smashoperator[r]{\sum_{#1}^{#2}}}
\newcommand{\vproduct}[2]{\smashoperator[r]{\prod_{#1}^{#2}}}
\newcommand{\vxor}[2]{\smashoperator[r]{\bigoplus_{#1}^{#2}}}
@ -2023,9 +2024,9 @@ A \joinSplitTransfer spends $\NOld$ \notes $\nOld{\allOld}$ and \transparent inp
$\vpubOld$, and creates $\NNew$ \notes $\nNew{\allNew}$ and \transparent output
$\vpubNew$.
It is associated with an instance of a \joinSplitStatement (\crossref{joinsplitstatement}),
for which it provides a \zkSNARKProof.
for which it provides a \zkSNARKProof{}.
Each \transaction has a \sequenceOfJoinSplitDescriptions.
Each \transaction has a \sequenceOfJoinSplitDescriptions{}.
The \changed{total $\vpubNew$ value adds to, and the total} $\vpubOld$
value subtracts from the \transparentValuePool of the containing \transaction.
@ -2071,12 +2072,12 @@ that describe \spendTransfers and \outputTransfers, respectively.
A \spendTransfer spends a \note $\nOld{}$. Its \spendDescription includes a
\xPedersenValueCommitment to the value of the \note.
It is associated with an instance of a \spendStatement (\crossref{spendstatement})
for which it provides a \zkSNARKProof.
for which it provides a \zkSNARKProof{}.
An \outputTransfer creates a \note $\nNew{}$. Similarly, its \outputDescription
includes a \xPedersenValueCommitment to the \note value.
It is associated with an instance of an \outputStatement (\crossref{outputstatement})
for which it provides a \zkSNARKProof.
for which it provides a \zkSNARKProof{}.
Each \transaction has a sequence of \spendDescriptions and a sequence of
\outputDescriptions.
@ -2826,7 +2827,7 @@ let $\AuthProveBase = \FindGroupJHashOf{\ascii{Zcash\_H\_}, \ascii{}}$.
Let $\reprJ$ be the representation function for the $\JubjubCurve$ \representedGroup,
instantiated in \crossref{jubjub}.
Let $\LEBStoOSP{} \typecolon (\ell \typecolon \Nat) \times \bitseq{\ell} \rightarrow \byteseq{\ceiling{\ell/8}}$
Let $\LEBStoOSP{} \typecolon (\ell \typecolon \Nat) \times \bitseq{\ell} \rightarrow \byteseq{\sceiling{\ell/8}}$
be defined as in \crossref{endian}.
\vspace{2ex}
@ -3702,7 +3703,7 @@ and integers:
\item $\LEOStoIP{} \typecolon (k \typecolon \Nat) \times \byteseq{k} \rightarrow \range{0}{256^k\!-\!1}$
such that $\LEOStoIP{k}(S)$ is the integer represented in little-endian order by the
byte sequence $S$ of length $k$.
\item $\LEBStoOSP{} \typecolon (\ell \typecolon \Nat) \times \bitseq{\ell} \rightarrow \byteseq{\ceiling{\ell/8}}$
\item $\LEBStoOSP{} \typecolon (\ell \typecolon \Nat) \times \bitseq{\ell} \rightarrow \byteseq{\sceiling{\ell/8}}$
defined as follows: pad the input on the right with $8 \mult \ceiling{\ell/8} - \ell$ zero bits
so that its length is a multiple of 8 bits. Then convert each group of 8 bits to a byte
value with the \emph{least} significant bit first, and concatenate the resulting bytes
@ -5920,7 +5921,7 @@ $4$ & $\lockTime$ & \type{uint32\_t} & A Unix epoch time (UTC) or block number,
in $\vJoinSplit$. \\ \hline
\Longunderstack{$1802 \mult$ \\ $\nJoinSplit\,\dagger$} & $\vJoinSplit$ & \type{JoinSplitDescription} \type{[$\nJoinSplit$]} &
A \sequenceOfJoinSplitDescriptions, each encoded as described in \crossref{joinsplitencoding}. \\ \hline
A \sequenceOfJoinSplitDescriptions{}, each encoded as described in \crossref{joinsplitencoding}. \\ \hline
$32$ $\ddagger$ & $\joinSplitPubKey$ & \type{char[32]} & An encoding of a $\JoinSplitSig$
public verification key. \\ \hline
@ -6456,7 +6457,7 @@ Define:
\begin{formulae}
\hfuzz=10pt
\item $\mean(S) := \left( \vsum{i=1}{\length(S)} S_i \right) \raisebox{-0.4ex}{\scalebox{1.4}{/\,}} \length(S)$.
\item $\median(S) := \sorted(S)_{\ceiling{\length(S) / 2}}$
\item $\median(S) := \sorted(S)_{\sceiling{\length(S) / 2}}$
\item $\bound{\Lower}{\Upper}(x) := \maximum(\Lower, \minimum(\Upper, x)))$
\item $\trunc{x} := \begin{cases}
\floor{x},&\caseif x \geq 0 \\